TEMPERATURE CONTROLLER USING AN AC HEATER
Report on the Graduation Project titled:
TEMPERATURE CONTROLLER USING AN AC HEATER: DESIGN AND ANALYSIS
KHALID TANTAWI , ZHACKERIA SAMMOUR, AWNI PITRO Mechatronics Engineering Dept.- University of Jordan
1
TEMPERATURE CONTROLLER USING AN AC HEATER
Table of contents Abstract
4
CHAPTER ONE: INTRODUCTION
5
1.1
Control Systems
5
1.2
Thermodynamics
9
1.3
Microcontrollers
11
CHAPTER TWO: TEMPERATURE MEASUREMENT 2.1
Temperature & Temperature Scale
13
2.2
Temperature Scale
14
2.3
Temperature Sensors
15
CHAPTER THREE: TEMPERATURE CONTROLLERS 3.1
Introduction
23
3.2
Kinds of Controllers
23
3.3
Selection Considerations
27
3.4
AC Voltage Controllers
31
CHAPTER FOUR: SOLID STATE RELAYS
23
33
4.1
Introduction
33
4.2
Types of SSR
33
4.3
Output Circuit Performance
35
4.4
Time Relationship & Synchronization
37
2
13
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER FIVE: SYSTEM MODLING
39
5.1
Introduction
39
5.2
General Thermal Model
39
5.3
Linear Continuous Model for a General Case PID Controller
5.4
System Control Block Diagram
40
43
CHAPTER SIX: CIRCUIT DESIGN
45
6.1
Introduction
45
6.2
PIC16F876
45
6.3
LM35
48
6.4
MOC3041
50
6.5
TRIAC
51
6.6
Wiring Diagram
52
CHATER SEVEN: PROGRAM
54
7.1
Introduction
54
7.2
Program Flow Chart
55
7.3
Detailed Program Procedures
56
Discussion & Recommendations
59
APPENDIX A: LM35 CHARATARISTICS
60
APPENDIX B: MOC3041 CHARACTARISTICS
62
APPENDIX C: PIC16F876 CHARACTERISTICS
65
References
68
3
TEMPERATURE CONTROLLER USING AN AC HEATER
Abstract This report analyses the Temperature Controller Using an AC Heater, which we built as our graduation project, the report includes a detailed discussion of the control, protection and power circuits that were used, and highlights some features of it like the use of microcontroller for delay timing and control, the use of a photocoupler and a shunt snubber for protection . At the beginning of the report is an introduction to control theory, thermal systems, microcontrollers and power electronics. Sources of error are also analyzed, however, the report includes no detailed discussion of errors and uncertainty, as it is not of our concern in this report, but we have included some great references that discuss uncertainity analysis for the interested reader . A 220 V, 50 Hz AC heater is being controlled to affect the temperature in a simple thermal system using the proportional type of control. An LM35 IC temperature sensor was used to feedback the temperature of the system to a PIC16F876 microcontroller which generates the error signal, acts as a proportional controller by modulating the pulse width and outputs a digital signal to an ON-OFF interfacing circuit with the heater using MOC3041 solid state relay. The proportional action decreases the average power being supplied to the heater as the temperature approaches set point by varying the ON and OFF ratios of the AC cycles over a small period of time. Chapters two through five include a brief review of temperature scale and sensors, selection considerations of the different types of the temperature controllers, solid state relays and , characteristics, time relationship and synchronization. Chapter six presents the parts used in this design and the wiring diagram for its circuits. In the last chapter, the program of the microcontroller is presented in a flowchart and in detailed steps. Three appendixes were added to show the characteristics of the parts used in this design.
4
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER ONE INTRODUCTION Temperature measurement generally involves using some instrument as a physical means of determining the temperature, which is the variable to be controlled. In this project we used an IC sensor for sensing temperature changes, This stage is represented as the variable detection stage, in this stage the change in temperature is converted into a change in electric potential. This change is sensed by the microcontroller through the built in analogto-digital converter. This stage represents the variable conversion stage because it converts the change in voltage to a digital signal. Although this voltage change is very small, the microcontroller can handle it easily, having a resolution of 1/ 1024, so it neeads no manipulation stage. The LM35 temperature sensor has the interesting characteristic that it can be connected directly to the microcontroller illuminating the need for a signal conditioning circuit. After the feedback signal is digitized, it is then ready to be processed by the control stage. Measured Medium (Temperature)
Primary Sensing Element (IC Sensor)
Variable Conversion Element ( ADC )
Data Transmission Element (wires)
Data (Pulse Width Modulated signal)
Controller
Variable Manipulation Element (amplifier)
Error Analysis: Before analyzing the main sources of error and accuracy of the control system, lets introduce some concepts that are used in this analysis. 1. Accuracy: it refers to the degree of closeness or conformity to the true value of the quantity under measurement. 2. Precision: refers to the degree of agreement within a group of measurements or instruments. 3. Significant figures: the number of significant figures is an indication of the precision of the measurement, the more significant figures, the greater the precision of measurement. We treated the above concepts carefully in our project since temperature measurement is largely effected by the sensitivity of the transducer used, and semiconductor devices are also effected by temperature change, interestingly hysterisis was also present (i. e slight deifferences are present when temperature is decreasing and when it is increasing). There 5
TEMPERATURE CONTROLLER USING AN AC HEATER
are many other factors that contribute to the limitations in accuracy and preceision of our measurements. Some of them are listed below: 1. accuracy is limited by the accuracy of resistors used in the sensor circuitry. Since the accuracy of the resistors used is ±5%, so the contribution of resistors to the accuracy of measurement must be at least ±5%. 2. the transistors used in the circuits in general are effected by temperature in the manner -1.2mV/ºC. so over a range of operation of 100 ºC, the maximum absolute change in voltage due to temperature is 120 mV, this also contributes to the accuracy of the controller, even though slightly. 3. loading effect: this means that some instruments change conditions to some extent when connected into a complete circuit. In other words, the measured quantity is altered by the method used. We can approximate the contribution of loading effect by a maximum of 1% of the measured temperature. If we let the contributions of other unknown factors to be 1% of measured temperature. Then the total accuracy of the temperature sensor would be approximately ±(7-10 %). Types of errors: The study of errors is important for two reasons: first because it is a first step in finding ways to reduce these errors, and second because it allows us to find the accuracy of the final result. We can classify errors under three main headings: 1. Gross errors: these are largely human errors, among them are incorrect adjustment and improper application of instruments, and computational mistakes. As long as human beings are involved, some gross errors must be present. Such errors cannot be treated mathematically, they can be avoided only by good practice and taking readings by several engineers 2. Systematic errors: short comings of the instruments, such as defective or worn parts, and effects of the environment on the equipment. As well as loading effect. This type of errors is devided into two categories: a) Instrumental errors: these are inherent in the instruments due to mechanical structure. b) Environmental errors: these are due to temperature, humidity, barometric pressure, magnetic or electrostatic fields. 3. Random errors: these are due to causes that cannot be directly established because of random variations in the parameter or the system of measurement. 1.1
Control Systems The configuration that will provide a desired system response is the core of
any physical system, and is called the controller of that system, it may be open loop or a closed- loop system. The basis for analysis of the temperature controller used is the foundation provided by linear system theory, which assumes a cause-effect relationship for the components of a system.
6
TEMPERATURE CONTROLLER USING AN AC HEATER
The figure below shows the block diagram for a closed loop negative feedback control system.
The prime difference between the open and the closed loop systems is the generation and utilization of the error signal E(S). The primary reason for using the closed loop control system is to reduce the sensitivity of the system to parameter variations. Considering a change in the transfer function G(S) such that G(S) +∆ G(S) to illustrate the effects of parameter variations. In the closed loop system : C (S ) G(S ) = R( S ) 1 + G (S ) × H ( S ) Automatic Controllers An automatic controller compares the actual value of the process output with the desired value, determines the deviation, and produces a control signal that will reduce the deviation to zero or a small value. The way in which the automatic controller produces the control signal is called the control action. The control actions normally found in industrial automatic controllers consist of the following: on-off, proportional, integral, derivative, and a combination of proportional, integral, or derivative. A good understanding of the basic properties of various control actions is necessary in order to select the one best suited for a particular application.
7
TEMPERATURE CONTROLLER USING AN AC HEATER
Digital Control In digital control a microcontroller uses data sampled at pre specified intervals, resulting in a time series of signals –sampled data-. The z-transform of a transfer function is used to analyze the stability and transient response of the system. The measurement data is converted from analog form to digital form by means of an analog to digital converter. After processing data, the microcontroller provides the output in a digital form, which requires another stage to convert it to analog form; this stage can be represented by a zero-order hold. The sampling time period, which is the fixed time period at which data enters or leaves the controller, in our case it is simply the reciprocal of the frequency, and since we used a 4 MHz crystal the sampling time would be
1 = 250ns . Each of this data is 4000000
discrete data not continuous as in classic control. The transfer function of the zero-order hold is:
(
1 e − sT 1 − e − sT = Go ( s ) = − s s s
)
The output of an ideal sampler r*(t), is a series of impulses with values r(kT).
8
TEMPERATURE CONTROLLER USING AN AC HEATER ∞
r * (t ) = ∑ r (kT )δ (t − kT ) k =0
1.2
Thermodynamics
Thermodynamics is defined as the branch of science that deals with the relationship between heat and other forms of energy, such as work. The laws of thermodynamics are summarized below, they provide the frames and restrictions on how the different forms of energy are interconverted. The Three Laws of Thermodynamics:
•
Zeroth Law: If two objects are in thermal equilibrium with a third, then they
are in thermal equilibrium with each other. •
First law: Energy is conserved; it can be neither created nor destroyed.
•
Second law: In an isolated system, natural processes are spontaneous when
they lead to an increase in disorder, or entropy. As a result of the first law of thermodynamics, the property Total Energy existed. If the net work is the same for all adiabatic processes of a closed system between two specified states, the value of the net work must depend on the end states of the system only. This takes us to the conclusion that the net work must correspond to a change in a property. This property is the total energy. Back to our project, we observe that the electrical work done on an adiabatic system is equal to the increase in the energy of the system.
Win= P*t = 1000(wat)* t (sec) Figure 3.2: The electrical work done by the 1 KW heater on an adiabatic system is equal to the increase in the energy of the system.
∆E = 1000( w) * t
9
TEMPERATURE CONTROLLER USING AN AC HEATER
Again before we continue this discussion, recall that energy is a property as we showed before, and the value of a property does not change unless the state of the system changes. The change in the total energy of a system during a process is the sum of the changes in its internal, kinetic, and potential energies. So that: ∆E = ∆U + ∆KE + ∆PE
Where: ∆KE = 1 m(v1^ 2 − v 2^ 2) 2 ∆PE = mg (h 2 − h1)
However, our system in this project is stationary, that is it does not involve any changes in its velocity or elevation during a process, so that ∆KE = ∆PE=0, thus ∆E = ∆U. this leads to the consequence that there are only two mechanisms for energy transfer in our system, since the mass is fixed, which are heat transfer and work done. If the system is well-insulated and made adiabatic, then there is no way for energy transfer, but by electrical work. Energy Conversion Efficiency Efficiency indicates how well an energy conversion or transfer process is accomplished. The efficiency of a conventional electric water heater is about 90%. At this point it is worth saying that the efficiency of a water heater is defined as the ratio of the energy delivered to the house by the hot water to the energy supplied to the water heater, not the efficiency of the resistance heater, which is definitely 100% , as all electric energy is converted into heat.
Heater type
efficiency
Gas, conventional
55%
Gas, high efficiency
62%
Electric, conventional
90%
Electric, high efficiency
94%
Table 3.1: Typical efficiencies of conventional and high efficiency water heaters available in the market
“ Work is a mechanism for energy interaction between a system and its surroundings.” Y. C`engel.
10
TEMPERATURE CONTROLLER USING AN AC HEATER
1.3
Microcontrollers:
A microcontroller can be considered as a whole computational system that includes a microprocessor, a flash memory, a RAM, and a bus system. It is optimized to perform control functions for the lowest cost and at the smallest size-possible. Generally microcontrollers are used in the embedded system designs. There is a huge range of microcontroller applications. Some are drawn from volume markets - the motor car, domestic appliances, mobile phones and toys. These applications are sold in such high volume that dedicated controllers are frequently developed for them. Others, like medical or scientific instruments, are sold in smaller numbers, and are more likely to make use of the wide variety of general-purpose controllers that are available. At one extreme of complexity, simple (and very cheap) controllers are used to replace 'glue logic' in a digital system. At the other extreme, advanced 32-bit controllers perform sophisticated signal processing activities. Arising from their 'embedded control' environment, microcontrollers usually have the following features: •
Input/output intensive, i.e. they are capable of direct interface to a significant
number of sensors and actuators. •
A high level of integration, with many peripheral devices included 'on-chip’.
•
Physically small.
•
Comparatively simple program and data storage requirements.
•
Ability to operate in the real-time environment.
•
An instruction set optimized for the embedded environment, e.g. yielding
compact code, limited arithmetic and addressing capability, strong in bit manipulation. •
Low cost.
In many microcontroller applications either or both of the following features are also essential:
11
TEMPERATURE CONTROLLER USING AN AC HEATER
-An ability to operate in hostile environments, for example of high or low temperature, or high electromagnetic radiation. -A low power capability, and features which ease the use of battery power.
12
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER TWO TEMPERATURE SENSING AND MEASUREMENT 2.1 INTRODUCTION Several types of sensors have been used in industry for temperature measurement. Temperature is a useful measure of the thermodynamic state of an object or system. It is a macroscopic description of the aggregate amount of microscopic kinetic energy in a material. If two bodies are at the same temperature, they are in thermodynamic equilibrium with each other; if they were connected to each other, there is no net flow of heat from one to the other. Temperature is related to the laws of thermodynamics and fluid mechanics. The Zeroth law of thermodynamics gave the green light for the existence of the temperature scales. So many devices have been used for temperature sensing, we will classify them according to their principles of operation, which are of the following categories: 1. Mechanical expansion 2. Electrical conductance. 3. Thermoelectric potential. 4. Radiaton of energy All of the above methods for temperature measurement require a change in a physical characteristic to measure temperature. However, all processes that occur while "temperature sensing" must not violate the laws of thermodynamics. Although the first law of thermodynamics guarantees the conservation of energy, it does not indicate that all energy is converted from one form to another, since a slight amount of energy is stored in the material for deformation in the form of elastic energy. Table 2.1 lists the most common temperature sensing methods classified again according to their principle of operation. Table 2.1 Common temperature sensing methods Physical Electric Thermoelectric Energy expansion conductance potential radiatoin
Liquid in glass Resistance Tempratue Ideal gas relationship
Bimetallic Dependant strips (RTD)
Thermocouples
Optical Pyrometry Emittance Determination
Thermistors
13
Electric Potential
Semiconductors (I.C. sensors)
TEMPERATURE CONTROLLER USING AN AC HEATER
2.2
Temperature Scale
Interestingly, temperature is not a measure of the unit thermodynamic energy of a body; unit masses of differing materials can require differing amounts of energy to be added or removed to change their temperature by a given amount. Identical temperature of two bodies merely implies there would be no transfer of heat between the two, regardless of the actual energy stored as heat in each body. The International Temperature Scale of 1990 (ITS-90) is the current standard for temperature measurement, defining the Kelvin temperature scale. The standard is based on phase transition points of various pure substances; with the Kelvin degree defined as 1/273.16 the absolute temperature of the triple point of water. The reason for defining the temperature scale on the basis of freezing and triple points is that these events can be readily reproduced to a high degree of repeatability. This means that there need not be a standard kilogram of temperature locked in a vault somewhere. The Celsius and Fahrenheit scales, both measure the number of steps from freezing point to boiling point of water at one atmospheric pressure. For conversion between the two units the following formula is used: °F = 1.8 °C + 32 For the absolute scales, different units are given, we use the Kelvin for the absolute Celsius scale, and Rankine (°R) for the absolute Fahrenheit scale. These scales are given by equations: K = °C + 273.15 °R = °F + 459.67 Combining the previous equations, we get the relation between K and °R: °R = 1.8 K
14
TEMPERATURE CONTROLLER USING AN AC HEATER
2.3
Temperature Sensors 2.3.1
Introduction
As we have shown in the introduction of this chapter, temperature can be measured via a diverse array of sensors. All of them infer temperature by sensing some change in a physical characteristic. Most references consider Seven types with which the engineer is likely to come into contact, these are: thermocouples, RTDs and thermistors, infrared radiators, IC Sensors, bimetallic devices, liquid expansion devices, and change-of-state devices. It is well to begin with a brief review of each. Thermocouples consist essentially of two strips or wires made of different metals and joined at one end. As discussed later, changes in the temperature at that juncture induce a change in electromotive force (emf) between the other ends. As temperature goes up, this output emf of the thermocouple rises, though not necessarily linearly. Resistive temperature devices capitalize on the fact that the electrical resistance of a material changes as its temperature changes. Two key types are the metallic devices (commonly referred to as RTDs), and thermistors. As their name indicates, RTDs rely on resistance change in a metal, with the resistance rising more or less linearly with temperature. Thermistors are based on resistance change in a ceramic semiconductor; the resistance drops nonlinearly with temperature rise. Infrared sensors are noncontacting devices. As discussed later, they infer temperature by measuring the thermal radiation emitted by a material. IC sensors use the inherent temperature dependency in the voltage across a P-N transistor junction when biased with a constant current. This temperature dependency is so well known and understood that many IC designers go to great lengths to try to cancel it out because it can impact performance. For temperature sensing, we take advantage of it, amplifying it to provide a usable signal that is directly proportional to temperature.
15
TEMPERATURE CONTROLLER USING AN AC HEATER
Bimetallic devices take advantage of the difference in rate of thermal expansion between different metals. Strips of two metals are bonded together. When heated, one side will expand more than the other, and the resulting bending is translated into a temperature reading by mechanical linkage to a pointer. These devices are portable and they do not require a power supply, but they are usually not as accurate as thermocouples or RTDs and they do not readily lend themselves to temperature recording. Fluid-expansion devices, typified by the household thermometer, generally come in two main classifications: the mercury type and the organic-liquid type. Versions employing gas instead of liquid are also available. Mercury is considered an environmental hazard, so there are regulations governing the shipment of devices that contain it. Fluid-expansion sensors do not require electric power, do not pose explosion hazards, and are stable even after repeated cycling. On the other hand, they do not generate data that are easily recorded or transmitted, and they cannot make spot or point measurements. Change-of-state temperature sensors consist of labels, pellets, crayons, lacquers or liquid crystals whose appearance changes once a certain temperature is reached. They are used, for instance, with steam traps - when a trap exceeds a certain temperature, a white dot on a sensor label attached to the trap will turn black. Response time typically takes minutes, so these devices often do not respond to transient temperature changes. And accuracy is lower than with other types of sensors. Furthermore, the change in state is irreversible, except in the case of liquid-crystal displays. Even so, change-of-state sensors can be handy when one needs confirmation that the temperature of a piece of equipment or a material has not exceeded a certain level, for instance for technical or legal reasons during product shipment. Thermocouples: Consider first the thermocouple, probably the most-often-used and
least-understood. Essentially, a thermocouple consists of two alloys joined together at one end and open at the other. The emf at the output end (the open end) is a function of the temperature T1 at the closed end. As the temperature rises, the emf goes up. Often the thermocouple is located inside a metal or ceramic shield that protects it from a variety of environments. Metal-sheathed thermocouples are also available with many
16
TEMPERATURE CONTROLLER USING AN AC HEATER
types of outer coatings, such as polytetrafluoroethylene, for trouble-free use in corrosive solutions. The open-end emf is a function of not only the closed-end temperature (i.e., the temperature at the point of measurement) but also the temperature at the open end (T2). Only by holding T2 at a standard temperature can the measured emf be considered a direct function of the change in T1. The industrially accepted standard for T2 is 0°C; therefore, most tables and charts make the assumption that T2 is at that level. In industrial instrumentation, the difference between the actual temperature at T2 and 0°C is usually corrected for electronically, within the instrumentation. This emf adjustment is referred to as the cold-junction, or CJ, correction. Temperature changes in the wiring between the input and output ends do not affect the output voltage, provided that the wiring is of thermocouple alloy or a thermoelectric equivalent. The composition of the junction itself does not affect the thermocouple action in any way, so long as the temperature, T1, is kept constant throughout the junction and the junction material is electrically conductive. Similarly, the reading is not affected by insertion of non-thermocouple alloys in either or both leads, provided that the temperature at the ends of the "spurious" material is the same. This ability of the thermocouple to work with a spurious metal in the transmission path enables the use of a number of specialized devices, such as thermocouple switches. Whereas the transmission wiring itself is normally the thermoelectrical equivalent of the thermocouple alloy, properly operating thermocouple switches must be made of gold-plated or silver-plated copper alloy elements with appropriate steel springs to ensure good contact. So long as the temperature at the input and output junctions of the switch are equal, this change in composition makes no difference. RTDs: A typical RTD consists of a fine platinum wire wrapped around a mandrel and
covered with a protective coating. Usually, the mandrel and coating are glass or ceramic.
17
TEMPERATURE CONTROLLER USING AN AC HEATER
The mean slope of the resistance vs. temperature plot for the RTD is often referred to as the alpha value, alpha standing for the temperature coefficient. The slope of the curve for a given sensor depends somewhat on purity of the platinum in it. The most commonly used standard slope, pertaining to platinum of a particular purity and composition, has a value of 0.00385 (assuming that the resistance is measured in ohms and the temperature in degrees Celsius). A resistance vs. temperature curve drawn with this slope is a so-called European curve, because RTDs of this composition were first used extensively on that continent. Complicating the picture, there is also another standard slope, pertaining to a slightly different platinum composition. Having a slightly higher alpha value of 0.00392, it follows what is known as the American curve. Thermistors: The resistance-temperature relationship of a thermistor is negative and
highly nonlinear. This poses a serious problem for engineers who must design their own circuitry. However, the difficulty can be eased by using thermistors in matched pairs, in such a way that the nonlinearities offset each other. Furthermore, vendors offer panel meters and controllers that compensate internally for thermistors' lack of linearity. Thermistors are usually designated in accordance with their resistance at 25°C. The most common of these ratings is 2252 ohms; among the others are 5,000 and 10,000 ohms. If not specified to the contrary, most instruments will accept the 2252 type of thermistor. Infrared sensors: These measure the amount of radiation emitted by a surface.
Electromagnetic energy radiates from all matter regardless of its temperature. In many process situations, the energy is in the infrared region. As the temperature goes up, the amount of infrared radiation and its average frequency go up. Different materials radiate at different levels of efficiency. This efficiency is quantified as emissivity, a decimal number or percentage ranging between 0 and 1 or 0% and 100%. Most organic materials, including skin, are very efficient, frequently exhibiting emissivities of 0.95. Most polished metals, on the other hand, tend to be inefficient radiators at room temperature, with emissivity or efficiency often 20% or less.
18
TEMPERATURE CONTROLLER USING AN AC HEATER
To function properly, an infrared measurement device must take into account the emissivity of the surface being measured. This can often be looked up in a reference table. However, bear in mind that tables cannot account for localized conditions such as oxidation and surface roughness. A sometimes practical way to measure temperature with infrared when the emissivity level is not known is to “force” the emissivity to a known level, by covering the surface with masking tape (emissivity of 95%) or a highly emissive paint. Some of the sensor input may well consist of energy that is not emitted by the equipment or material whose surface is being targeted, but instead is being reflected by that surface from other equipment or material. Emissivity pertains to energy radiating from a surface whereas reflection pertains to energy reflected from another source. Emissivity of an opaque material is an inverse indicator of its reflectivity Ð substances that are good emitters do not reflect much incident energy, and thus do not pose much of a problem to the sensor in determining surface temperatures. Conversely, when one measures a target surface with only, say, 20% emissivity, much of the energy reaching the sensor might be due to reflection from, e.g., a nearby furnace at some other temperature. In short, be wary of hot, spurious reflected targets. An infrared device is like a camera, and thus covers a certain field of view. It might, for instance, be able to “see” a 1-deg visual cone or a 100-deg cone. When measuring a surface, be sure that the surface completely fills the field of view. If the target surface does not at first fill the field of view, move closer, or use an instrument with a narrower field of view. Or, simply take the background temperature into account (i.e., to adjust for it) when reading the instrument. IC Sensors: Semiconductor devices can also be used to measure temperature.
Because the P-N junction is the basic building block of diodes, transistors, and ICs, temperature sensing can be incorporated in many devices at low cost. This technique is used in the onboard temperature sensors of microprocessors and for the thermal-shutdown circuits of power-supply chips. The voltage across a transistor base-emitter junction is given as:
19
TEMPERATURE CONTROLLER USING AN AC HEATER
Where: k = Boltzmann's constant, 1.38 × 10-23 J/K T = absolute temperature in degrees K q = the charge of an electron, 1.6 × 10-19 C Is = reverse saturation current, 1 × 10-15 A Ic = forward junction current The nominal voltage across the junction is ~600 mV at room temperature, and the change with temperature is ~2 mV/ºC. So while the change is accurate and repeatable with respect to temperature, it is very small relative to the nominal voltage. Note that each sensor needs calibration because of device-to-device variations. Of the several techniques developed to extract the 2 mV/ºC change and eliminate individual calibration, the most popular involves switching two different currents and measuring the difference in voltage, VBE. Using known fixed currents or, more importantly, using a fixed ratio (N) of currents eliminates the Is term and the previous equation becomes
Therefore T = K ( VBE), where K = known constant While inexpensive and sometimes even free, P-N junction thermometers have several disadvantages. For instance, the room-temperature output voltage is about 600 mV, and even then the voltage varies both from unit to unit and with bias current. And with these devices, sensitivity also varies. 2.2.3
Selection Guides
RTDs are more stable than thermocouples. On the other hand, as a class, their temperature range is not as broad: RTDs operate from about -250 to 850°C whereas 20
TEMPERATURE CONTROLLER USING AN AC HEATER
thermocouples range from about -270 to 2,300°C. Thermistors have a more restrictive span, being commonly used between -40 and 150°C, but offer high accuracy in that range. Thermocouples are cheap, easy to use and have a wide temperature ranges. But they need signal conditioning for linearity and require a cold junction. Thermistors and RTDs share a very important limitation. They are resistive devices, and accordingly they function by passing a current through a sensor. Even though only a very small current is generally employed, it creates a certain amount of heat and thus can throw off the temperature reading. This self-heating in resistive sensors can be significant when dealing with a still fluid (i.e. neither flowing nor agitated), because there is less carry-off of the heat generated. This problem does not arise with thermocouples, essentially zero-current devices. Although the RTDs are more linear than the Thermistors and Thermocouples but they are relatively expensive, and not as linear as IC sensors. Also, RTDs and Thermistors require additional circuits or bridges in order to measure the temperature. Infrared sensors, though relatively expensive, are appropriate when the temperatures are extremely high. They are available for up to 3,000°C (5,400°F), far exceeding the range of thermocouples or other contact devices. The infrared approach is also attractive when one does not wish to make contact with the surface whose temperature is to be measured. Thus, fragile or wet surfaces, such as painted surfaces coming out of a drying oven, can be monitored in this way. Substances that are chemically reactive or electrically noisy are ideal candidates for infrared measurement. The approach is likewise advantageous in measuring temperature of very large surfaces, such as walls that would require a large array of thermocouples or RTDs for measurement. Silicon IC temperature sensors are a flexible and low-cost single-component solution for many existing and emerging applications. They are linear and do not require additional circuits for signal conditioning. Both analog and digital formats are well catered for allowing easy interfacing to standard microcontrollers. Complete subsystems can even be integrated on a single chip. The benefits of integration include low component count, low cost, and inherent high reliability. Adding control functionality completes the picture by providing
21
TEMPERATURE CONTROLLER USING AN AC HEATER
flexible closed-loop control where needed. But IC sensors have low temperature ranges (from -55 to 150ºC) with an accuracy of about 1ºC.
22
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER THREE: TEMPERATURE CONTROLLERS 3.1
Introduction
To accurately control process temperature without extensive operator involvement, a temperature control system relies upon a controller, which accepts a temperature sensor as input. It compares the actual temperature to the desired control temperature, or set point, and provides an output to a control element. The controller is one part of the entire control system, and the whole system should be analyzed in selecting the proper controller. The following items should be considered when selecting a controller: •
Type of input sensor (thermocouple, RTD, IC sensor) and temperature range.
•
Type of output required (electromechanical relay, SSR, analog output).
•
Control algorithms needed (on/off, proportional, PID).
•
Number and type of outputs (heat, cool, alarm, limit).
3.2
Kinds of Controllers
There are three basic types of controllers depending upon the system to be controlled: on-off, proportional and PID. 3.2.1
On/Off
An on-off controller is the simplest form of temperature control device. The output from the device is either on or off, with no middle state. An on-off controller will switch the output only when the temperature crosses the set point. For heating control, the output is on when the temperature is below the set point, and off above set point. Since the temperature crosses the set point to change the output state, the process temperature will be cycling continually, going from below set point to above, and back below. On-off differential prevents the output from “chattering” (that is, engaging in fast,
23
TEMPERATURE CONTROLLER USING AN AC HEATER
continual switching if the temperature’s cycling above and below the set point occurs very rapidly). On-off control is usually used where a precise control is not necessary, in systems which cannot handle the energy’s being turned on and off frequently, where the mass of the system is so great that temperatures change extremely slowly, or for a temperature alarm. 3.2.2
Proportional
Proportional controls are designed to eliminate the cycling associated with on-off control. A proportional controller decreases the average power being supplied to the heater as the temperature approaches set point. This has the effect of slowing down the heater, so that it will not overshoot the set point but will approach the set point and maintain a stable temperature. This proportioning action can be accomplished by turning the output on and off for short intervals. This “time Proportioning “varies the ratio of ‘on’ time to ‘off‘time to control the temperature. The proportioning action occurs within a “proportional band” around the set point temperature. Outside this band, the controller functions as an on-off unit, with the output either fully on (below the band) or fully off (above the band). However, within the band, the output is turned on and off in the ratio of the measurement difference from the set point. At the set point (the midpoint of the proportional band), the output on: off ratio is 1:1; that is, the on-time and off-time are equal. If the temperature is further from the set point, the on- and off-times vary in proportion to the temperature difference. If the temperature is below set point, the output will be on longer; if the temperature is too high, the output will be off longer.
24
TEMPERATURE CONTROLLER USING AN AC HEATER
The proportional band is usually expressed as a percent of full scale, or degrees. It may also be referred to as gain, which is the reciprocal of the band. Note, that in time proportioning control, full power is applied to the heater, but is cycled on and off, so the average time is varied. The cycle time and/or proportional band are adjustable, so that the controller may better match a particular process. Systems that are subject to wide temperature cycling will also need proportional controllers. Depending upon the process and the precision required, either a simple proportional control or one with PID may be required. Processes with long time lags and large maximum rate of rise (e.g., a heat exchanger); require wide proportional bands to eliminate oscillation. The wide band can result in large offsets with changes in the load. To eliminate these offsets, automatic reset (integral) can be used. Derivative (rate) action can be used on processes with long time delays, to speed recovery after a process disturbance. There are also other features to consider when selecting a controller. These include auto- or self tuning. 3.2.3 PID
The third controller type provides proportional with integral and derivative control, or PID. This controller combines proportional control with two additional adjustments, which helps the unit automatically compensate for changes in the system. These adjustments,
25
TEMPERATURE CONTROLLER USING AN AC HEATER
integral and derivative, are expressed in time-based units; they are also referred to by their reciprocals, RESET and RATE, respectively. The proportional, integral and derivative terms must be individually adjusted or “tuned” to a particular system, using a “trial and error” method. PID controllers provide the most accurate and stable control of the three controller types & are best used in systems which have a relatively small mass, those which react quickly to changes in energy added to the process. It is recommended in systems where the load changes often, and the controller is expected to compensate automatically due to frequent changes in set point, the amount of energy available, or the mass to be controlled. What Do Rate and Reset Do, and How Do They Work?
Rate and reset are methods used by controllers to compensate for offsets and shifts in temperature. When using a proportional controller, it is very rare that the heat input to maintain the set point temperature will be 50%; the temperature will either increase or decrease from the set point, until a stable temperature is obtained. The difference between this stable temperature and the set point is called offset. This offset can be compensated for manually or automatically. Using manual reset, the user will shift the proportional band so that the process will stabilize at the set point temperature. Automatic reset, also known as integral, will integrate the deviation signal with respect to time, and the integral is summed with the deviation signal to shift the proportional band. The output power is thus automatically increased or decreased to bring the process temperature back to set point.
26
TEMPERATURE CONTROLLER USING AN AC HEATER
3.3
Selection Considerations
When you choose a controller, the main considerations include: The precision of control that is necessary, and how difficult the process is to control. For easiest tuning and lowest initial cost, the simplest controller which will produce the desired results should be selected. Simple processes with a well matched heater and without rapid cycling can possibly use on-off controllers. For those systems subject to cycling, or with an unmatched heater, a proportional controller is needed. Also selecting the controller depends on: •
Type of Input
The type of input sensor will depend on the temperature range required, the resolution and accuracy of the measurement required, and how and where the sensor is to be mounted. •
Placement of the Sensor
The correct placement of the sensing element with respect to the work and heat source is of the utmost importance for good control. If all three can be located in close proximity, a high degree of accuracy, up to the limit of the controller, is relatively easy to achieve. However, if the heat source is located some distance from the work, widely different accuracies can be obtained just by locating the sensing element at various places between the heater and the work. Before selecting the location for the sensing element, determine whether the heat demand will be predominantly steady or variable. If the heat demand is relatively steady, placement of the sensing element near the heat source will hold the temperature change at the work to a minimum. On the other hand, placing the sensing element near the work, when heat demand is variable, will enable it to more quickly sense a change in heat requirements. However, because of the increase in thermal lag between the heater and the sensing elements, more 27
TEMPERATURE CONTROLLER USING AN AC HEATER
overshoot and undershoot can occur, causing a greater spread between maximum and minimum temperature. This spread can be reduced by selecting a PID controller. •
Control Algorithm (Mode)
This refers to the method in which the controller attempts to restore system temperature to the desired level (i.e. using an ON\OFF controller, Proportional controller or PID controller. •
Type of Control Output Hardware
The output hardware in a temperature controller may take one of several forms. Deciding on the type of control hardware to be used depends on the heater used and power available, the control algorithm chosen, and the hardware external to the controller available to handle the heater load. The most commonly used controller output hardware is as follows: o Time Proportional or On/Off
Mechanical Relay
Triac (ac solid state relay)
Dc Solid State Relay Driver (pulse)
o Analog Proportional
4-20 mA dc
0-5 Vdc or 0-10 Vdc
A time proportional output applies power to the load for a percentage of a fixed cycle time. For example, with a 10 second cycle time, if the controller output were set for 60%, the relay would be energized (closed, power applied) for 6 seconds, and de-energized (open, no power applied) for 4 seconds. The electromechanical relay is generally the most economical output type, and is usually chosen on systems with cycle times greater than 10 seconds and relatively small loads.
28
TEMPERATURE CONTROLLER USING AN AC HEATER
Choose an ac solid state relay or dc voltage pulse to drive an external SSR with reliability, since they contain no moving parts. They are also recommended for processes requiring short cycle times. External solid state relays may require an ac or dc control signal. An amplitude proportional output is usually an analog voltage (0 to 5 Vdc) or current (4 to 20 mA). The output level from this output type is also set by the controller. If the output were set at 60%, the output level would be 60% of 5 V, or 3 V. With a 4 to 20 mA output (a 16 mA span), 60% is equal to (0.6 x 16) + 4, or 13.6 mA. These controllers are usually used with SCR power controllers or proportioning valves. The power used by an electrical resistance heater will usually be given in Watts. The capacity of a relay is given in amps. A common formula to determine the safe relay rating requirements is: W = V × A × 1.5 or A = W/ [V × 1.5] Where : A = relay rating in amps W = heater capacity in watts V = voltage used 1.5 = safety factor
The types of hardware available, external to the controller, to allow it to handle the Load, are as follows: o Mechanical Contactor o Ac controlled solid state relay o Dc controlled solid state relay o Zero crossover SCR power controllers o Phase angle fired SCR power controller
Mechanical contactors are external relays, which can be used when higher amperage than can be handled by the relay in the controller is required, or for some three-phase systems. They are not recommended for cycle times shorter than 15 seconds.
29
TEMPERATURE CONTROLLER USING AN AC HEATER
Solid state relays have the advantage over mechanical contactors, in that they have no moving parts, and thus can be used with short cycle times. The shorter the cycle time, the less dead lag and the better the control. The “switching” takes place at the zero voltage crossover point of the alternating current cycle; thus, no appreciable electrical noise is generated. An ac controlled solid state relay is used with either a mechanical relay or triac output from the controller, and is available for currents up to 90 amps at voltages of up to 480 Vac. DC solid state relays are used with dc solid state driver (pulse) outputs. The “turn on” signal can be from 3 to 32 Vdc and models are available to control up to 90 amps at up to 480 Vac. Zero crossover SCR power controllers are used to control single or three-phase power for even larger loads. They can be used for currents up to 200 amps at 480 volts. A 4-20 mA dc control signal is usually required from the controller. The zero crossover SCR power controllers convert the analog output signal to a time proportional signal with a cycle time of about two seconds or less, and also provide switching at the zero crossover point to avoid generating electrical noise. Phase angle SCR power controllers also are operated by a 4-20 mA dc controller output. Power to the load is controlled by governing the point of turn on (firing) of each half cycle of a full ac sine wave. This has the effect of varying the voltage within a single 0.0167 second period. By comparison, time proportional controllers vary the average power over the cycle time, usually more than 1 second, and often more than 15 seconds. Phase angle SCR’s are only recommended for low mass heating elements such as infrared lamps or hot wire heaters. 3.4
AC Voltage Controllers
AC voltage controllers are most commonly used in industrial heating, on-load transformer connection changing, light controls, speed control of polyphase induction motors, and AC magnet controls. There are two types of controllers: 1.
On-off control
2.
Phase angle control
30
TEMPERATURE CONTROLLER USING AN AC HEATER
In on-off control, thyristor switches connect the load to the AC source for a few cycles of input voltage and then disconnect it for another few cycles. Principles of ON-OFF Control
The principle of on-off control can be explained with a single-phase full-wave controller. The thyristor switch connects the ac supply to load for a time Tn. The thyristors (TRIAC) are turned on at the zero-voltage crossing point of AC input voltage. Advantages of on-off control over phase-angle control: •
Due to zero-voltage and zero-current switching, the harmonics generated by switching actions are reduced.
•
On-off control is used in applications that have highly inductive loads, like industrial heating (high thermal time constant) and speed control of motors (high mechanical inertia). The rms output voltage is found from the equation:
Where : n = number of cycles the input voltage is connected to load m = number of cycles the input voltage is disconnected from load k = n / (m + n), and k is called the duty cycle. 2π ⎡ ⎤ n Vo = ⎢ 2Vs 2 sin 2ωtd (ωt )⎥ ∫ ⎣ 2π (n + m ) 0 ⎦
∴Vo = Vs
PF =
Po = VA
n = Vs k m+n n = k m+n
Note that the power factor is always lagging.
31
TEMPERATURE CONTROLLER USING AN AC HEATER
The average and rms values of the current passing through the thyristor connected to load are found to be: π
Iavg =
n k Im Im n = Im sin ωtd (ωt ) = ∫ 2π (m + n) 0 π ( m + n) π
π ⎡ ⎤ n Irms = ⎢ Im 2 sin 2 ωtd (ωt )⎥ ∫ ⎣ 2π (m + n) 0 ⎦
1/ 2
=
Im 2
n Im k = m+n 2
Notes: •
The PF and output voltage vary with the square root of the duty cycle. The PF is
poor at the low value of the duty cycle k, that’s why we should avoid low values of duty cycle, for example the Pf at a duty cycle of 0.4 will result in a power factor of 0.632 of course lagging. •
If T is the period of input voltage, (m+n)T is the period of on-off control. (m+n)T
must be less than the thermal time constant.
32
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER FOUR: SOLID STATE RELAYS 4.1
Introduction
A solid-state relay (SSR) is an ON-OFF control device in which the load current is conducted by one or more semiconductors- e.g., a power transistor, an SCR, or a TRIAC. (The SCR and TRIAC are often called “thyristors,” a term derived by combining thyratron and transistor, since thyristors are triggered semiconductor switches.) Like all relays, the SSR requires relatively low control circuit energy to switch the output state from OFF to ON, or vice versa. Since this control energy is very much lower than the output power controllable by the relay at full load, "power gain" in an SSR is substantial--frequently much higher than in an electromagnetic relay (EMR) of comparable output rating. To put it another way, the sensitivity of an SSR is often significantly higher than that of an EMR of comparable output rating. 4.2
Types of SSR
It is convenient to classify SSR's by the nature of the input circuit, with particular reference to the means by which input-output isolation is achieved. Three major categories are recognized: •
Reed-Relay-Coupled SSR's; in which the control signal is applied (directly,
or through a preamplifier) to the coil of a reed relay. The closure of the reed switch then activates appropriate circuitry that triggers the thyristor switch. Clearly, the input-output isolation achieved is that of the reed relay, which is usually excellent.
33
TEMPERATURE CONTROLLER USING AN AC HEATER
•
Transformer-Coupled SSR's; in which the control signal is applied (through
a DC-AC converter, if it is DC, or directly, if It is AC) to the primary of a small, low-power transformer, and the secondary voltage that results from the primary excitation is used (with or without rectification, amplification, or other modification) to trigger the thyristor switch. In this type, the degree of input-output isolation depends on the design of the transformer.
•
Photo-coupled SSR's; in which the control signal is applied to a light or
infrared source (usually, a light-emitting diode, or LED), and the radiation from that source is detected in a photosensitive semi-conductor (i.e., a photosensitive diode, a photo-sensitive transistor, or a photo-sensitive thyristor). The output of the photo-sensitive device is then used to trigger (gate) the TRIAC or the SCR's that switch the load current. Clearly, the only significant “coupling path” between input and output is the beam of light or infrared radiation, and electrical isolation is excellent. These SSR's are also referred to as “optically coupled” or “photo-isolated”.
In addition to the major types of SSR's described above, there are some specialpurpose designs that should be mentioned: Direct-control AC types, Direct-control DC types, SCR types designed for DC, and Designs using special isolating means.
34
TEMPERATURE CONTROLLER USING AN AC HEATER
4.3
Output Circuit Performance
Clearly, the most significant output-circuit parameters are the maximum load-circuit voltage that may be impressed across the relay output circuit in the OFF condition without causing it to break down into conduction or failure, and the maximum current that can flow through the output circuit and load in ON condition. Note that these parameters are (at least at first glance) analogous to the usual voltage and current ratings of the contacts on an electro-magnetic relay. There are, however, differences between EMR output ratings and SSR output ratings; differences that will be examined in detail as this exposition proceeds. In the most general approach, one may say that the “contact ratings” of an SSR are determined almost entirely by the characteristics of the loadcurrent switching device. Perhaps this fact is most apparent from an examination of the simplest type of ac SSR, a direct-control (non-isolated) design, such as that drawn next, with its equivalent circuit for both the ON and OFF states. In the ON state (b), the TRIAC exhibits a nearly constant voltage drop (i.e., almost independent of load current) approximately equal to that of two silicon diodes; less than 2 volts. The passage of load current through this voltage drop causes power dissipation (Pd = Vd x Iload), and this power will cause a temperature rise in the TRIAC junction. If proper “heatsinking” is provided (i.e., thermal conduction from the TRIAC case to the outside air or to a heat-conductive metal structure that can in turn dissipate the power to the surrounding air without significant temperature rise) then the TRIAC temperature will not rise above the rated maximum
35
TEMPERATURE CONTROLLER USING AN AC HEATER
value for reliable operation (typically, 100°C). With generous heat sinking, the current rating of the SSR may be determined, not by power dissipation, but by the current rating of the TRIAC. The equivalent circuit of this very simple SSR in the OFF state (c). Note that even when the TRIAC is turned off, a very small amount of leakage current can flow. This current path, represented by a resistance in the equivalent circuit, is actually a non-linear function of the load-circuit voltage. The normal practice, in rating TRIAC’s, is to specify a worst case maximum value for this “OFF-state leakage” and a typical value is 0.001 A max (for a 5-ampere load-current rating). The load circuit voltage rating is simply that determined by the blocking voltage rating of the thyristor. The output-circuit ratings of the more common isolated SSR’s, most of which are designed to control ac load circuits, are very similar to those described above, except that OFF-state leakage is usually higher (on the order of 5 mA at 140 V for a 5ampere device) still only about one-thousandth of the load current rating. The voltage and current waveforms in the load circuit are drawn for both OFF and ON states.
Note that the ON-state voltage-drop curves are drawn to a much expanded scale compared with the OFF state and load voltage curves.
36
TEMPERATURE CONTROLLER USING AN AC HEATER
4.4
Time Relationship & Synchronization
Even at this early stage in the examination of SSR performance, it is necessary to consider the time relationships between the control signal and the ac load-circuit voltage and current. With respect to timing, there are two classes of switching SSR’s. In one, no particular effort is made to achieve synchronism between the alternations of the load circuit-power line and the turning on of the thyristor switch. In this “non-synchronous” class, then, the response delay between the application of control voltage and the beginning of load-circuit conduction is very short; typically from 20 to 200 microseconds in optically coupled and transformer types, and less than one millisecond in hybrids (longer due to the reed relay operation time). The current waveform on turn-on in non-synchronous designs is clearly a function of when in the ac cycle the control signal is applied. In synchronous (zero-voltage turn-on) designs, the effect of the application of a control signal is delayed (if necessary) until the power-line voltage is passing through zero. (This is done by internal gating circuitry that senses the magnitude of the line voltage, and prevents triggering the thyristor until the next zero crossing occurs). Thus, if the control signal happens to be applied immediately after a zero crossing, the SSR would not actually begin conducting until almost a full half-cycle later. On the other hand, if the control signal happens to be applied just before a zero-crossing is about to occur, the SSR would begin to conduct almost immediately, with only the very small turnon delays described above for non-synchronous designs. Clearly, then, the turn-on delay of a synchronous SSR can have any value from less than a millisecond to a full half-cycle of the power line (about 8.3 milliseconds for a 60-Hz power line). Usually, for 60 Hz service, the rating is given as 8.3 milliseconds maximum for all-solid-state designs, and 1.5 milliseconds maximum for hybrid designs. The final major characteristic of the AC-switching SSR is its turn-off behavior. Because a thyristor, once triggered, will not stop conducting until the load current flowing through it falls to zero, there is a maximum possible turn-off delay (between the removal of
37
TEMPERATURE CONTROLLER USING AN AC HEATER
the control signal and the cessation of load current) of one half cycle. As in the case of turnon, the minimum turnoff delay is close to zero. Thus, a typical 60-Hz rating for turn-off time is 9 milliseconds maximum. The following graph describes the AC-switching SSR behavior for its turn-on and turn-off characteristics, and shows the difference between synchronous and non-synchronous SSR’s.
38
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER FIVE: SYSTEM MODELING 5.1
Introduction
This chapter describes the system modeling for the design of the temperature controller. The first part defines the terms of controlling a basic thermal system in its general case. The second part shows the calculation to find the mathematical model and the transfer functions for the temperature controller controlling a basic thermal system. And the last part shows the block diagram for the design of the temperature controller used in this project. 5.2
General Thermal Model
The general case of the system considered in this project comprises an electrical heater of heat capacity Ch connected via a thermal resistance Rho to the chamber, heat capacity Co. The chamber loses heat to the environment, at temperature Te, through the thermal resistance Ro of its insulation. The temperature controller adjusts the power dissipated in the heating elements, W, by comparing the chamber temperature, To, with the set-point temperature Ts.
The diagram shows the thermal components, and the electrical devices.
5.3
Linear Continuous Model for the Temperature Controller
39
TEMPERATURE CONTROLLER USING AN AC HEATER
The following Figure shows the block diagram of a continuous data, linear PID control system acting on an error signal E(S).
We can approximate the controller as a proportional-Integral controller (lag controller), the reason is because a large duty cycle is required to run the temperature controller normally, this is mainly due to the fact that the heater has a very large thermal time constant compared to other electronic parts. In other words, we do not expect to detect the results of a variation of the duty cycle at any time, only after a long time lag, to compensate for this the error signal must be slowed down by means of a lag compensator. The Gp1(S) block represents the transfer function of the chamber while the Gp2(S) block represents the transfer function of the temperature sensor. The next figure shows the diagram of a typical temperature chamber with the simplified equivalent circuit where: Tc = Chamber Temperature Ta = Ambient Temperature qi(t) = Input Heat Flow Rate qo(t) = Heat Loss Flow Rate qc(t) = Heat Flow Rate Rt = Thermal Resistance of Chamber to Ambient Ct = Thermal Capacitance of Chamber
40
TEMPERATURE CONTROLLER USING AN AC HEATER
Applying the thermal equations on the system: Ct =
Q Tc
or
qc(t) =
Ct ⋅ dTc dt
(Tc - Ta) qo(t)
or
qo(t) =
(Tc - Ta) Rt
qi(t) =
Ct ⋅ dTc (Tc - Ta) + dt Rt
also Rt =
differential equation for the chamber is : qi(t) = qc(t) + qo(t)
or
and its Laplace transform is : [Tc(S) - Ta(S)] Qi(S) = Ct(S) ⋅ Tc(S) ⋅ S + Rt(S) or Qi(S) =
[Ct ⋅ Tc ⋅ Rt ⋅ S + Tc - Ta] Rt
or Qi(S) ⋅ Rt = Tc ⋅ (Ct ⋅ Rt ⋅ S + 1) - Ta therefore, [Qi(S) ⋅ Rt + Ta] [Ct ⋅ Rt ⋅ S + 1] where Qi(S) = (Kp + Ki/S + KdS)Kh
Tc =
the Laplace transfer function of chamber is : G(S) = Tc =
[Kp ⋅ Kh ⋅ Rt ⋅ S + Ki ⋅ Kh ⋅ Rt + Kd ⋅ Kh ⋅ Rt ⋅ S 2 + Ta ⋅ S] [S(Ct ⋅ Rt ⋅ S + 1)]
41
TEMPERATURE CONTROLLER USING AN AC HEATER
The next figure shows the equivalent circuit for the temperature sensor where: Tc = Actual Chamber Temperature Tp = Indicated Chamber Temperature Rp = Thermal Resistance of the Sensor Cp = Thermal Capacitance of the Sensor Note : before we continue, we must mention that the model presented assumes a linear, continuous, time invariant control system.
42
TEMPERATURE CONTROLLER USING AN AC HEATER
Tp =
1 ⋅ [q(t) ⋅ dt] Cp
and q(t) =
[Tc - Tp] Rp
and its Laplace transform is : Tp(s) =
[Tc - Tp] [Cp ⋅ Rp ⋅ S]
where Cp ⋅ Rp = Tp
or
Tp =
Tc [Rp ⋅ Cp ⋅ S + 1]
the Laplace transfer function of sensor is : H(S) =
1 Tp = Tc [Tp ⋅ S + 1]
Now by constructing the closed loop error equation. The error signal for a closed loop system is : R(S) [1 + G(S) ⋅ H(S)] where R(S) = 1/S for step input
E(S) =
Tc = CtRt After substituti on and arranging the terms : E(S) =
S 2 + S( 1/Tp + 1/Tc ) + 1/Tc ⋅ Tp S + S ( 1/Tc + 1/Tp + Kd ⋅ Kh ⋅ Rt/Tc ⋅ Tp ) + S( (1 + Kp ⋅ Kh ⋅ Rt + Ta)/Tc ⋅ Tp ) + Ki ⋅ Kh ⋅ Rt/Tc ⋅ Tp 3
5.4
2
System Control Block Diagram
The model used in this design is different from the models shown above by that this model is only a Proportional controller, the Integral and Derivative parts should be omitted when calculating its model. The second difference is that the previous designs assume continuous control while this design uses discrete digital control in order to be able to use a microcontroller.
43
TEMPERATURE CONTROLLER USING AN AC HEATER
The block diagram shows the steps of this temperature controller: I. Set point value is determined through a potentiometer and outputs a voltage signal between 0 and 5 V. II. The input voltage is being sampled to get a discrete signal to be used in digital control. III. The sampled signal enters a summing junction with a negative feedback from the output. IV. The discrete error signal is being controlled proportionally (P controller). V. A zero-order hold is applied for the logic voltage output sampled signal. VI. The logic voltage controls the 220 V, 50Hz AC voltage signal through an ON/OFF interfacing circuit. VII. The AC voltage signal is converted through the electrical heater to generate heat. VIII. The heat generated affects the thermal system and changes its temperature according to the desired set value. IX. The thermal system temperature is being captured through a temperature sensor which converts the temperature into a voltage signal between 0 and 1 V. X. The output voltage from the sensor is being sampled to get a discrete signal to be used in digital control. XI. The sampled signal is conditioned to be more comparable with the type of the input voltage signal from the potentiometer (set point value) when it enters the summing junction. Note: Steps II, III, IV, X and XI are being performed through the microcontroller.
44
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER SIX: CIRCUIT DESIGN 6.1
Introduction
This chapter includes in more details the system hardware. In its first sections a detailed description about the basic components is introduced and in the last section a wiring diagram and the connections between the parts are shown. The main components in this design are PIC16F876, LM35, MOC3041 and TRIAC. PIC16F876 is a controllable Microchip microcontroller. LM35 is a National Semiconductor IC temperature sensor. Motorola’s MOC3041 and TRIAC are parts used in the interfacing circuit between the microcontroller and the heater.
6.2
PIC16F876
Microchip Inc. and the PICTM microcontroller.
It was the General Instruments Corporation, back in the late 1970s, which first produced the PIC microcontroller. In its early years it did not make a wide impact. The design was later taken over by Microchip Inc., and PICs are now one of the fastest moving families in the 8-bit arena, in more senses than one. First, they run very fast; second, the family is growing at a tremendous rate; and third, at the time of writing Microchip only operates with 8-bit controllers, and therefore has a special interest in making this controller size as attractive as possible. PICs cover a very wide range of 8-bit operation. At the lower end, they are simpler, cheaper and smaller, than most devices that the competition can offer, and are thus used in situations where controllers would not be thought of as the right solution, even down to simple glue logic applications. At the high end, however, they are quite ready to take on the best of the 8-bit competition, with sophisticated devices equipped 45
TEMPERATURE CONTROLLER USING AN AC HEATER
with excellent peripherals. PICs have made themselves particularly attractive to the student and low-budget developer. Development tools (both hardware and software) are cheap .and readily available, and Microchip is very supportive of the novice designer. Microchip offers five closely related families of microcontroller, starting from 12CXXX, 16C5X, 16C/FXXX, 17CXXX to 18CXXX family which are different by the program memory, number of instructions and instruction execution time. All PIC controllers use a RISC-like structure, with Harvard architecture and pipelined instruction execution. This leads to one of the strengths of the PIC family: a very high instruction throughput. PIC16F876 is a 28 pin controller, 8-Bit CMOS FLASH Microcontrollers with the
following features: PIC16F876 Core Features:
•
High performance RISC CPU
•
Only 35 single word instructions to learn
•
All single cycle instructions except for program branches which are two cycle
•
Operating speed: DC - 20 MHz clock input DC - 200 ns instruction cycle
•
Up to 8K x 14 words of FLASH Program Memory,
•
Up to 368 x 8 bytes of Data Memory (RAM)
•
Up to 256 x 8 bytes of EEPROM Data Memory
•
Pinout compatible to the PIC16C73B/74B/76/77
•
Interrupt capability (up to 14 sources)
•
Eight level deep hardware stack
•
Direct, indirect and relative addressing modes
•
Power-on Reset (POR)
•
Power-up Timer (PWRT) and Oscillator Start-up Timer (OST)
•
Watchdog Timer (WDT) with its own on-chip RC oscillator for reliable operation
•
Programmable code protection 46
TEMPERATURE CONTROLLER USING AN AC HEATER
•
Power saving SLEEP mode
•
Selectable oscillator options
•
Low power, high speed CMOS FLASH/EEPROM technology
•
Fully static design
•
In-Circuit Serial Programming⎢ (ICSP) via two pins
•
Single 5V In-Circuit Serial Programming capability
•
In-Circuit Debugging via two pins
•
Processor read/write access to program memory
•
Wide operating voltage range: 2.0V to 5.5V
•
High Sink/Source Current: 25 mA
•
Commercial, Industrial and Extended temperature ranges
•
Low-power consumption: -
< 0.6 mA typical @ 3V, 4 MHz
-
20 µA typical @ 3V, 32 kHz
-
< 1 µA typical standby current
Peripheral Features:
•
Timer0: 8-bit timer/counter with 8-bit prescaler
•
Timer1: 16-bit timer/counter with prescaler, can be incremented during SLEEP via external crystal/clock
•
Timer2: 8-bit timer/counter with 8-bit period register, prescaler and postscaler
•
Two Capture, Compare, PWM modules
•
Capture is 16-bit, max. resolution is 12.5 ns
•
Compare is 16-bit, max. resolution is 200 ns
•
PWM max. resolution is 10-bit
•
10-bit multi-channel Analog-to-Digital converter
•
Synchronous Serial Port (SSP) with SPI⎢ (Master mode) and I2C⎢ (Master/Slave)
•
Universal Synchronous Asynchronous Receiver Transmitter (USART/SCI) with 9-bit address detection
47
TEMPERATURE CONTROLLER USING AN AC HEATER
•
Parallel Slave Port (PSP) 8-bits wide, with external RD, WR and CS controls (40/44-pin only)
•
Brown-out detection circuitry for Brown-out Reset (BOR) Pin Diagram:
6.3
LM35
The LM35 series are precision integrated-circuit temperature sensors, whose output voltage is linearly proportional to the Celsius (Centigrade) temperature. The LM35 thus has an advantage over linear temperature sensors calibrated in ° Kelvin, as the user is not required to subtract a large constant voltage from its output to obtain convenient Centigrade scaling. The LM35 does not require any external calibration or trimming to provide typical accuracies of ±1⁄4°C at room temperature and ±3⁄4°C over a full −55 to +150°C temperature range. Low cost is assured by trimming and calibration at the wafer level. The LM35’s low output impedance, linear output, and precise inherent calibration make interfacing to readout or control circuitry especially easy. It can be used with single power supplies, or with plus and minus supplies. As it draws only 60 µA from its supply, it has very low self-heating, less than 0.1°C in still air. The LM35 is rated to operate over a −55° to +150°C temperature range, while the LM35C is rated for a −40° to +110°C range (−10° with improved accuracy). The LM35 series is available packaged in hermetic TO-46 transistor packages, while the LM35C, LM35CA, and LM35D are also available in the plastic TO-92 transistor package. The LM35D is also available in an 8-lead surface mount small outline package and a plastic TO-220 package. 48
TEMPERATURE CONTROLLER USING AN AC HEATER
Features
6.4
•
Calibrated directly in ° Celsius (Centigrade)
•
Linear + 10.0 mV/°C scale factor
•
0.5°C accuracy guarantee able (at +25°C)
•
Rated for full −55° to +150°C range
•
Suitable for remote applications
•
Low cost due to wafer-level trimming
•
Operates from 4 to 30 volts
•
Less than 60 µA current drain
•
Low self-heating, 0.08°C in still air
•
Nonlinearity only ±1⁄4°C typical
•
Low impedance output, 0.1 Ω or 1 mA load
MOC3041
The MOC3041 is a 6-pin dip zero cross opto isolator triac driver output (400 Volts Peak). It is a device consists of gallium arsenide infrared emitting diodes optically coupled to
49
TEMPERATURE CONTROLLER USING AN AC HEATER
a monolithic silicon detector performing the function of a Zero Voltage Crossing bilateral triac driver. They are designed for use with a triac in the interface of logic systems to equipment powered from 115 Vac lines, such as solid–state relays, industrial controls, motors, solenoids and consumer appliances, etc. Main Features:
•
Simplifies Logic Control of 115 Vac Power
•
Zero Voltage Crossing
•
dv/dt of 2000 V/µs Typical, 1000 V/µs Guaranteed
Recommended for 115/240 Vac(rms) Applications:
6.5
•
Solenoid/Valve Controls
•
Temperature Controls
•
Lighting Controls
•
E.M. Contactors
•
Static Power Switches
•
AC Motor Starters
•
AC Motor Drives
TRIAC
50
TEMPERATURE CONTROLLER USING AN AC HEATER
The triode AC switch (TRIAC) is a power-switching device as is the SCR. The TRIAC conducts currents in both directions while the SCR allows current in only one direction. A common application is for lighting controllers. In response to a trigger, the triac conducts until the AC voltage applied reaches zero, then blocks flow until the next trigger occurs. Since a trigger can cause it to trigger current in either direction, it is an efficient power controller from essentially zero to full power. The symbol of the triac appears below:
The triac is a five-layer device having a P-N-P-N path in either direction between its two terminals and can hence conduct in either direction as the symbol clearly indicates. The triac can be switched into the on-state by either positive or negative gate current.
6.6
Wiring Diagram
51
TEMPERATURE CONTROLLER USING AN AC HEATER
The first circuit describes the interfacing between the PIC16F876 and the load (heater). The “hot” side of the line is switched and the load connected to the cold or neutral side. The load may be connected to either the neutral or hot line. Rin (360Ω) is calculated so that IF is equal to the rated IFT of the MOC3041 (15 mA). The 39 ohm resistor and 0.01 mF capacitor are for snubbing of the triac and may or may not be necessary depending upon the particular triac and load used.
Pin 2 is connected to RB0 (pin 21) in the PIC16F876, it receives logic 1 or logic 0 to deactivate or activate the circuit. The second circuit shows the PIC16F876 connections: • The potentiometer is connected to RA0/AN0 (pin 2) to get the desired set value. • The sensor (LM35) is connected to RA1/AN1 (pin 3) to get the current temperature; a 10 Kohm resistor is being added to stabilize the reading of the sensor at different set values. • The MOC3041 pin 2 is connected to RB0 (pin 21) of the microcontroller, which sends a logic voltage signal in order to control the circuit. • MCLR (pin1) is connected to +5V. • A 4 MHz clock is connected to CLCKIN (pin 9) & CLCKOUT (pin10).
52
TEMPERATURE CONTROLLER USING AN AC HEATER
• Voltage supply and ground are connected to their corresponding pins.
53
TEMPERATURE CONTROLLER USING AN AC HEATER
CHAPTER SEVEN: PROGRAM 7.1
Introduction
This chapter describes in brief the assembly code which used to program the PIC16F876 microcontroller in this temperature controller. The importance of the program is that the microcontroller act as the summing junction in this feedback system. It also acts as the proportional controller in this control system. The potentiometer and the sensor signals are the input and the feedback signals respectively, which enter the summing junction and then the error is being proportionally controlled, to output an ON/OFF signal to the interfacing circuit with the heater. The proportional technique used is by controlling the duration of the ON signal over a 10 seconds period according to the error generated. This technique will control the number of cycles of the AC signal over the 10 seconds. With a 50 Hz source, 500 cycles will be generated in 10 seconds, by controlling the number of cycles where the heater will be ON or OFF, this will act as a proportional controller with 0.2 % accuracy.
First, a brief flow chart for the basic steps in the program is being introduced, and then a procedure for each step is presented in details. Two main features of the PIC16F876 were used; the ADC module & the timer0 including the
timer0 interrupt. Additional information about these features is available in the appendix.
54
TEMPERATURE CONTROLLER USING AN AC HEATER
7.2
Program Flow Chart
55
TEMPERATURE CONTROLLER USING AN AC HEATER
7.3
Detailed Program Procedures I. Getting the desired temperature:
The desired temperature (set point) is taken from potentiometer as an analog signal and is being converted using the Analog to Digital Conversion (ADC) feature of the microcontroller, and it is being saved into an 8 bits digital form. The potentiometer reading is something between 0 ~ 5 V, and it is expressing the temperature between 0 ~ 128 °C.
0 V = 0000 0000 = 0 °C 5 V = 1111 1111 = 128 °C The least significant bit (LSB) = 0.0196 V II. Getting the sensor reading:
The sensor reading is converted using ADC and saved into an 8 bits digital form. This signal is being fixed in order to be more comparable with the potentiometer (set point) reading. The sensor reading is something between 0 ~ 1 V, and it is expressing the temperature between 0 ~ 100 °C. Each bit expresses a 0.05 V or 0.5 °C, so using an 8 bit binary system: 1111 1111 = 1.28 V = 128 °C. But the sensor can only measure up to 100°C, so binary values more than 1100 1101 are not used. 0 V = 0000 0000 = 0° C 1 V = 1100 1101 = 100 °C The least significant bit (LSB) = 0.05 V III. Comparing the two readings:
The two readings are compared and the difference is saved into a register for further usage.
56
TEMPERATURE CONTROLLER USING AN AC HEATER
IV. Determining the control region:
There are 3 control regions in this system:
a) ON region. OFF region.
b) c)
Proportional region. The control region is determined according to the difference between the sensor and the set point readings. This difference also determines the ON and OFF times in the proportional region; when the sensor reading is above the set point the ON time is inversely proportional to the difference, and when the sensor reading is below the set point the ON time is directly proportional to the difference. The ON time region is when the sensor reads 21 °C below the set point, and the OFF time region is when the sensor reads 21 °C above the set point. Between the two regions is the Proportional region symmetrically distributed around the set point and is divided into 7 equal regions, each region performs 6 °C. The lowest region has an 87.5% ON time and 12.5% OFF time. This percentage of the total cycle time is then increased in the upper regions according to the next table. In this controller a 10 seconds total cycle time is being used. According to the difference from the set point, one of the control regions or one of the proportional regions is being selected. V. Setting the ON and OFF times:
According to the region being selected and according to the previous table, a number act as a multiplier is being inserted, this number performs the duration of the ON time. This number is then multiplied by a fixed delay of 0.05 seconds created by the microcontroller to generate the ON time, or its compliment to 10 seconds to generate the OFF time.
57
TEMPERATURE CONTROLLER USING AN AC HEATER
Difference from set point
Percentage ON time
Percentage OFF time
+ 21 °C & more +15 ~ +21 °C +9 ~ +15 °C +3 ~ +9 °C 0 ~ +3 °C -3 ~ 0 °C -9 ~ -3 °C -15 ~ -9 °C -21 ~ -15 °C -21 °C & less
0% 12.5 % 25 % 37.5 % 50 % 50 % 62.5 % 75 % 87.5 % 100 %
100 % 87.5 % 75 % 62.5% 50 % 50 % 37.5 % 25 % 12.5 % 0%
ON time
OFF time
(second) 0 1.25 2.5 3.75 5 5 6.25 7.5 8.75 10
(seconds) 10 8.75 7.5 6.25 5 5 3.75 2.5 1.25 0
Total cycle time 10 sec. 10 sec. 10 sec. 10 sec. 10 sec. 10 sec. 10 sec. 10 sec. 10 sec. 10 sec.
VI. Starting the cycle time:
The timer0 feature is used to create the 0.05 seconds delay, and using the timer0 interrupt the multiplier is being decreased until it ends to zero.
Starting with the ON time; the output pin of the microcontroller is set to logic 0 (0V output), and every 0.05 seconds the multiplier is decreased by 1 until it approaches zero where the OFF time begins; the output pin is then set to logic 1 (5 V output) and the compliment of the multiplier to 10 seconds is decreased every 0.05 seconds until it approaches zero where the total cycle time ends and the program is being restarted from the beginning. During the 0.05 seconds delay, the program performs no operation, so the programmer is free to add any function during this delay like using a subroutine to display the current temperature on an LCD display.
58
TEMPERATURE CONTROLLER USING AN AC HEATER
DISCUSSION AND RECOMMENDATIONS This project showed the design of an AC temperature controller using power electronics to perform the ON/OFF interfacing circuit and it used PIC16F876 to vary the duty cycle based on sensed temperature. The advantages of this design are basically that it is easy to construct and low cost compared with other designs. Using microcontroller made it less complicated than other electronic circuits. It also achieves a high accuracy in measuring and controlling temperature. Furthermore, this design is very much adjustable since it only requires modifications on programming. By using MOC3041 a big advantage is gained; the controlling circuit and the high voltage AC heater are in complete isolation from each other since there is no physical contact between the two circuits, by optocoupling, which protect the controlling circuit from damaging due to high voltages. Another advantage of this part is that it has a built in zero crossing circuit for synchronization. Using IC temperature sensor gave very accurate readings for temperature and more linear and less cost than other measuring instruments, which helped in increasing the efficiency of the controller. Furthermore, IC sensors are easy to interface with electronic circuits, which simplify the design. Easy modification on this design could be implemented to control heaters with up to 400 Volts and about 4 KWatts. This design can control heaters up to 100°C but it can be easily modified to control temperatures up to 200°C but with higher cost. An LCD display could be added to show the current and the desired temperatures. By modifying the microcontroller program and modifying the proportional region better temperature control could be achieved. All of that shows the flexibility of this design.
59
TEMPERATURE CONTROLLER USING AN AC HEATER
There are no major disadvantages in implementing this design, only that it needs a transformer or another voltage source to give a 5 V DC voltage for the electronic parts and it is more difficult to troubleshoot than other circuits. A major problem that faced us in this project is finding a linear accurate low cost temperature sensor, it is worth saying here that we first picked a positive temperature coefficient thyristor as the temperature sensor, but it had several disadvantages of most important are its highly nonlinear behavior, and its need for a very accurate conditioning circuit. An RTD was then our next choice, but it had the disadvantage of a low thermal time constant, an RTD costs more than ten times an I.C sensor, we finally made our descision to use the LM35 I.C sensor as our temperature sensing device. We learned much more about our study thanks to this project, we learned more about the concept of control, we learned more about temperature sensors, we learned about electronics, we learned about programming microcontrollers and the most of all we have improved our teamwork abilities and it gave us more potential in designing more complicated projects which will enhance our chances in getting success in our future.
60
TEMPERATURE CONTROLLER USING AN AC HEATER
APPENDIX A: LM35 CHARACTERISTICS
61
TEMPERATURE CONTROLLER USING AN AC HEATER
62
TEMPERATURE CONTROLLER USING AN AC HEATER
APPENDIX B: MOC3041 CHARACTARISTICS
63
TEMPERATURE CONTROLLER USING AN AC HEATER
64
TEMPERATURE CONTROLLER USING AN AC HEATER
65
TEMPERATURE CONTROLLER USING AN AC HEATER
APPENDIX C: PIC16F876 CHARACTERISTICS
66
TEMPERATURE CONTROLLER USING AN AC HEATER
67
TEMPERATURE CONTROLLER USING AN AC HEATER
REFERNCES 1.
M. Rashid, Power Electronics Circuits, devices, and Applications, 3rd edition-
2004 by Prentice Hall. 2.
F. Mitchell, Introduction to Electronics Design, 1988 by Prentice Hall.
3.
Dorf, Bishop, Modern Control Systems, 9th edition 2001, Prentice Hall
4.
Y. Cengel, Fundamentals of Thermal Fluid Sciences, chapters 5 and 6, 2001
McGraw Hill. 5.
Wobschall, Circuit Design for electronic instrumentation. Prentice Hall
6.
K. Ogata, System Dynamics, 4th edition, 2004, Prentice Hall.
7.
Franklin and others, Feedback Control of Dynamics Systems, Addison-Wesley
publishing company, inc., 1986 8.
Phillips, Harbor, Feedback Control Systems, Prentice Hall, 1988
9.
Wilmshurt, an Introduction to the Design of Small-scale Embedded Systems,
Palgrave, 2001 10.
C.T. Chen, Analog and Digital Control Systems Design, Oxford Univ. Press,
11.
Close, Fredrick, Modeling and Analysis of Dynamic Systems, 2nd edition,
1997 Houghton Mifflin, Boston, 1993 12.
Microchip inc. PIC16F876 datasheet www.microchip.com
13.
National Semiconductor, http://www.national.com/support/ (November 29, 2004 8:40 PM)
14.
Omega Engineering, INC. http://www.omega.com/temperature/tsc.html (November 27, 2004 6:15 PM)
15.
Omega Engineering, INC. ,’Electric Heaters’, http://www.omega.com/promo/PromoRedir.html?id=52 (November 27, 2004 10:15 PM)
68
