WSEAS TRANSACTIONS on SYSTEMS Issue 9, Volume 5, September 2006 ISSN

1109-2777

http://www.wseas.org

Motivational Behavior of Neurons and Fuzzy Logic of Brain Uziel Sandler, Lev Tsitolovsky

2025

Solving Fuzzy Regression Equations by Using Fuzzy Goal Programming Model Ruey-Chyn Tsaur Hsiao-Fan Wang

2033

Lateral Robust Control System Design of Hezarfen UAV via Hx Loop Shaping Approach and Sensitivity / Co-Sensitivity Analysis Kamuran Turkoglu, Elbrous M. Jafarov

2040

A Comparative Study of Invariant Range Image Multi-Pose Face Recognition Using K-Means, Fuzzy CMeans, Membership Matching Score and Center of Gravity Search Seri Pansang, Bang-on Makdee, Chom Kimpan

2048

Membership Matching score for Invariant Image Recognition Pisit Phokharatkul, Skul Kamnuanchai, Chom Kimpan

2056

Passivity and Energy based Control for Finding Optimal Compass Gaits Oumnia Licer, Noureddine El Alami, Mostafa Mrabti

2061

Tuning Three-Term Controllers for Power Station Processes K. G. Arvanitis, G. D. Pasgianos, A. K. Boglou

2069

An Algorithm for Capstan Motion Planning in Funicular Railways G. Moscariello, V. Niola, C. Rossi

2079

Uncertainty and Sensitivity Analysis Issues in Support Vector Machines Theodore B. Trafalis, Jin Park

2086

Applications of a Motion Planning Algorithm for Funicular Railways G. Moscariello, V. Niola, C. Rossi

2092

A Two-Stage Production Planning Model for Perishable Products Under Uncertainty Stephen C. H. Leung, W.L. Ng, K.K. Lai

2099

Three-Phase Brushless D.C. Motor: Logic Sequencer and Converter Gheorghe Baluta, Nikolaos Papachatzis

2105

Synthesis of a Asymptotically Stable Direct Model Reference Adaptive Controller for a Class of Processes not Satisfying a Positive Real Constraint Abdelaziz. M, Djahli.F

2113

Design of a PI-D Controller of a Scaled-Model Helicopter Hassan El Abiad, Mohamad Khaldi

2120

Design of Adaptive Three-Term Controllers for Unstable Bioreactors: A Lyapunov Based Approach K.G.Arvanitis, G.D.Pasgianos, G.Kalogeropoulos

2126

Logistic Regression Model for Determining Risks Factor for Hypertensive Disorders in Pregnancy Anna Gabriela Perez, Elizabeth Torres Rivas, Francklin Rivas Echeverria, Carlos Rivas Echeverria

2135

An Agent-based System Design for Complex Systems SeongKee Lee, SungChan Cho, HyengHo Lee, ChanGon Yoo, JungChan Park, JaeHyun Park, HoSang Yoon, CheolHo Kim

2140

Reassessment of the User-Perceived Web Quality Instrument in the Context of E-Government: A Confirmatory Factor Analysis Yi-Shun Wang

2147

Design of RFID Technology-Based Automated Gate System in a Container Terminal Hyung Rim Choi, Nam Kyu Park, Byung Joo Park, Dong Ho Yoo, Hae Kyoung Kwon, Joong Jo Shin

2155

Unmanned Aerial Vehicles: Challenges and Technologies for Improved Autonomy George Vachtsevanos, Ben Ludington

2164

A New Test Rig For Frictional Torque Measurement In Ball Bearings Ahmad Ghanbari, Sohrab Khanmohamadi

2172

A New Cryptography System to Combine Hyperelliptic Curves and Chaotic Systems Rodrigo Abarzua, Ivan Jiron, Miguel Alfaro,Ismael Soto

2178

Improving Image Retrieval By Fuzzy C-Means Initialized by Fixed Threshold Clustering : Case Studies Relating to a Color Temperature Histogram And a Color Histogram Doungporn Niyomua, Siriporn Supratid, Chom Kimpan

2182

Cost Reduction and Transmission Security Augment in Unit Commitment Using UPFC Ahad Kazemi, Mohsen Najafi, M. Mousaei Nierang, Mehdi Kashanian

2189

Fault Tolerance for Robust Anti-Windup Compensation Implementation Addison Rios-Bolivar, Richard Marquez

2197

A New Technique For Decoupling of Non-Minimum Phase Multivariable Systems M. A. Sadrnia, M. M. Zalloi, A. A. Gharaveisi

2204

Robust Fault Diagnosis Observer Design Using H-infinity Optimization Mohammad Ali Sadrnia

2210

A Technique for Enamel Diagnostics Using Results of the Infrared Optical Non-Destructive Control Examination Bustillo Diaz M.M., Mehrdad Roham, Anait Gabrielyan, Melekhin V. F.

2218

Scheduling in Flexible Job Shops under Machine Breakdowns with Initial Setup Times – A Practical Application Shahid Ikramullah Butt, Sun Hou Fang, Zhang F Ping, Amir Manzur Wain

2224

Non-Defective Welding Process Design Using Collaborative Tools Tomas Kaminskas, Genadijus Kulvietis, Leonas Keblas

2230

Visual Servoing of Moving ObjectUsing an Event-Based Path Generation and Dynamic Windowing method Iraj Hassanzadeh, Hamed Jabbari

2236

Open Architecture Systems for the Compliance Robots Control Luige Vladareanu

2243

Control and Parameter Estimation of a Mini-Helicopter Robot Using Rapid Prototyping Tools Carlos M. Velez S., Andres Agudelo

2250

Electrical Appliances Testing Platform E. Antonidakis, J. Chatzakis, M. Vogiatzaki, H. Rigakis, M. Manitis, D. Kolokotsa

2257

Stochastic Linear Programming to Optimize Some Stochastic Systems G. Perez-Lechuga, M. M. Alvarez-Suarez, J. Garnica-Gonzalez, H. Niccolas-Morales, F. Venegas-Martinez

2263

Control and parameter estimation of a mini-helicopter robot using rapid prototyping tools CARLOS M. VÉLEZ S., ANDRÉS AGUDELO Departamento de Ciencias Básicas Universidad EAFIT Cra. 49 No. 7 sur 50, Medellín, Antioquia COLOMBIA [email protected], [email protected], http://www.control-systems.net

Abstract: - This paper shows the control and parameter estimation of a mini-helicopter robot using a rapid prototyping environment based on Matlab/Simulink. The parameter estimation task is facilitated by the availability of a block-based visual simulation model and its integration in a general Matlab environment, with the feasibility of use of many other tools. The environment is integrated by modules which use common Matlab tools (ground control station, linearization, parameter estimation, heuristic identification) and own modules developed specifically for simulation, state estimation and multirate control. An example is presented in a software-in-the-loop context, showing all possibilities of the software environment including supervisory, estimation, linearization, and control tasks. Key-Words: - Aerospace simulation, parameter estimation, helicopter control, software-in-the-loop, rapid prototyping

1 Introduction This paper describes the application of a Rapid Software Prototyping Environment (RSPE) called Colibri (hummingbird in Spanish) [1] to automatic control and parameter estimation of a mini-helicopter. The control and parameter estimation tasks are facilitated by the availability of a block-based visual simulation model and its integration in a general Matlab environment, with the feasibility of use of many other tools. The control and identification tasks are described in a software-in-the-loop simulation example, but the whole RSPE is being tested over a real system. Rapid software prototyping is the process of automatic early development of a working version (prototype) of a system used to test out certain key features of a design, demonstrate concepts or methods, and gather early user feedback [2], [3]. Flight control of Unmanned Aerial Vehicles (UAV) is an area of intense development in the world [4], but it is necessary to focus on the problem of autonomy to take advantage of their capabilities, and here rapid software prototyping can play a powerful role. An adequate RSPE must integrate different tools and must be easily reconfigurable for different tests, including software-in-the-loop (SIL), hardware-inthe-loop (HIL) and man-in-the-loop (MIL) simulation. For example, Matlab/Simulink [5] is a RSPE which provides a proper user interface allowing the development of simulation models and prototypes, either on machine time or in real time. Automatic code generation and integration with the

target computer, where the control software runs, can be achieved in Simulink by means of the Real-time Workshop Toolbox (RTW). RTW generates and executes stand-alone C code for developing and testing algorithms modeled in Simulink.

Fig.1. X-Cell 0.60 Gas Graphite helicopter Colibri has some differences with other similar environments, where Matlab is used mainly for simulation and design purposes, without some interesting possibilities. For example, the software in [6] is focused in real-time and scheduling issues, using Matlab only for control task. MoSART [7] is an interactive Matlab-based environment which is used for analyzing, designing, visualizing, and evaluating the performance of aircraft control systems. MultiUAV2 [8] is an environment based on Matlab

for cooperative flight, but mostly using script functions programmed in C++ and limited to simulation. In [9], a prototype simulation and 3D visualization tool for cooperating UAVs, working semi-autonomously or manually, is described. Commercial aerospace applications based on Matlab [10], [11] show the validity of this kind of prototyping environment. The paper is organized as follows. Section 2 introduces the key ideas of mini-helicopter modeling and simulation, explained with details in [12] and [24]. Section 3 describes the parameter estimation problem based on advantages of having a visual simulation model in Simulink blocks. Section 4 describes other modules of the proposed Colibri RSPE. An example, with application of modules, is presented across the paper. Concluding remarks and ideas for future work are provided in Section 5.

The mini-helicopter used in this work is an X-Cell Gas Graphite hobby helicopter (Fig. 1). Inputs and states of the mini-helicopter system are given in (1) and (2). δ lon δ lat

δr

δt ]

(1)

T

x = [u , v, w, p, q, r , ϕ, θ, ψ, x, y, z , a1 , b1 , Ω ]

T

v = ( pw − ru ) + g cos θ sin ϕ + Y / M a w = ( qu − pv ) + g cos θ cos ϕ + Z / M a

(2)

(δcol, δlon, δlat, δr, δt): control inputs (main rotor collective, longitudinal cyclic, lateral cyclic, tail rotor collective and throttle) (u, v, w): vehicle velocities in body axes (p, q, r): vehicle angular rates in body axes (φ, θ, ψ): Euler angles (roll, pitch, yaw) (x, y, z): vehicle position in navigation axes (a1, b1): longitudinal and lateral main rotor flapping angles Ω: main rotor angular speed The mini-helicopter is an eight-degree-of-freedom system: three lineal displacements (u, v, w), three angular movements (p, q, r) and two main rotor flapping angles (a1, b1). The rigid-body dynamics of such vehicles are described by the Newton-Euler equations of motion. There are two reference frames: body-fixed and earth-fixed. The differential equations describing the minihelicopter translational and rotational motion in the body-fixed reference are given in (3), where [X Y Z]T is the vector of external forces acting on the vehicle center of gravity (c.g.), [L M N]T is the vector of external moments, Ma is the helicopter mass and I is the inertial tensor.

(3)

p = qr ( I y − I z ) / I x + L / I x q = pr ( I z − I x ) / I y + M / I y r = pq ( I x − I y ) / I z + N / I z

Higher-order effects are taken into account to improve the rigid-body model accuracy. These extensions are rotor dynamics, engine-drive train and actuators dynamics. The coupled rotor and stabilizer bar equations are lumped into one first-order equation of motion. This procedure is done for both lateral and longitudinal tip-path-plane flapping. The equations are given in (4) and detailed explained in [12] and [24]. a1 = −

2 Mini-helicopter simulation model

u = [δ col

u = ( vr − wq ) − g sin θ + X / M a

Aδ a1 − q + lon δlon τe τe

⎡ ⎤ ⎛ 4δcol ⎞ u − uw ⎢ 2 kµ ⎜ 3 − λ o ⎟ Ω R ⎥ ⎝ ⎠ mr mr 1 ⎢ ⎥ (4) + τe ⎢ w − ww ⎥ 16µ 2mr sign µ mr ⎢ + kµ ⎥ Ω mr Rmr ⎥⎦ 8 µ mr + amr σ mr ⎢⎣ b 1 ⎛ 4δ ⎞ v − vw + b1 = − 1 − p + 2kµ ⎜ col − λ o ⎟ τe τe 3 ⎝ ⎠ Ω mr Rmr +

Bδlat τe

δlat

The simulation model was coded in Simulink using blocks, without functions or S-functions, and integrated in a single Simulink file. So, the real-time code generation is straightforward and may be used in SIL, HIL or MIL simulations. This characteristic was used for validation of logical model structure by an expert pilot, using a joystick and a 3D visual interface. The parameters of the mini-helicopter model are defined in [12] and [24]. In [24], details of mini-helicopter simulation model are given. Figures 8, 9 and 10 show the front-end (mask) of model. An interesting application is the software-in-theloop simulation (SIL), as it needs to run in real-time and requires almost all Colibri modules (see section 2). Fig.2 shows a typical SIL configuration with three computers. PC2 and PC3 are actual systems. The mini-helicopter is represented by its simulation model running in real-time. In a pilot-in-the-loop simulation, PC2 is changed for a joystick interface. Fig.3 shows Simulink configuration for Real-Time Workshop (RTW) compiling; SM_control (PID controllers in Fig. 9) and SS_Helicopter subsystems are compiled, while SC_Console (setpoint and plot

blocks together with virtual reality blocks) is the Ground Control Station (GCS). Parametric and heuristic identification, and state feedback, PID, fuzzy and multirate control (using linearization) may be applied.

Fig.2. Software-in-the-loop simulation architecture

experimental one, or directly with the simulation model, using heuristic methods (like evolutionary computation and optimization) and closed-loop data (e.g., with a PID control) with persistent excited reference signals, using the Matlab “Parameter Estimation Toolbox”. So, the non-linear identified model and the simulation model are the same. This is a really interesting approach, because any indirect computation such as linearization [14] is unnecessary. Moreover, it is important to take in account that closed-loop identification with parametric methods (least squares, prediction error, etc) is inexact due to negative effects of feedback, which generates a bias in the estimation. The parameter estimation method was applied in closed loop using PID controllers (Fig. 9). Persistent excited reference signals were applied to obtain better results [21], [28]. Three parameters were obtained (Fig. 4) using Matlab “Parameter Estimation Toolbox”, which allows the selection of several estimation methods: amr (main rotor blade lift curve slope), cmr (main rotor chord) and ctr (Tail rotor chord). Tests show, in concordance with [27], that the best results are obtained exciting each reference input separately.

Fig.3. Software-in-the-loop simulation blocks in Matlab/Simulink

3 Parameter estimation It is important in the flight control development process to use experimental data, additional to pilot simulation tests, to refine the simulation model and, at the same time, obtain a more accurate and reliable linear mathematical model for control design. There exist methods like MOSCA and CIFER that point in that direction [14], [18], [19]. The interaction between both models (theoretical and estimated) helps to identify some system parameters, without using wind tunnels [20], [21]. In these approaches, it is necessary to obtain a linear model for each operational point [27]. Mini-helicopter simulation model in blocks allows the application of different parametric and heuristic identification methods, in open and closed loop. It is possible to estimate some parameters indirectly, comparing a good theoretical linear model with an

Fig.4. Trajectories of estimated parameters using a heuristic identification method

4 Modules of the Colibri environment Colibri RSPE includes various modules (Fig. 5). Some modules were developed using Simulink: XCell non-linear simulation model, filters, navigation filter with an Extended Kalman Filter, multirate control [25], [24], [16], fuzzy control [15], and other control structures. The Ground Control Station (GCS) was built with Virtual Reality Toolbox and Gauges Blockset. Other tools were adapted and may be adapted directly from Matlab: linearization, parameter identification, heuristic identification,

fuzzy control, etc. A trajectory generator and a Finite State Machine for managing discrete events are being developed. The core of the software environment is the mini-helicopter simulation model, which interacts easily with other Matlab tools.

Fig.5. Interaction of Colibri environment modules All developed functions are written entirely in Simulink (which can be considered a visual programming language), without using functions and with the possibility of automatic code generation for the QNX real-time operating system [23]. Both a commercial [17] and a custom [26] target solution were used to generate and transfer code to the target machine with QNX. A normal session with Colibri RSPE includes the following stages: 1) development or tuning of a simulation model for analysis, design and simulation; 2) separation of controller, estimation, filter, transformations, and logical blocks from the plant model; 3) attachment of driver blocks; 4) automatic C code generation and conversion to real-time executable code; 5) load onto target hardware; 6) connection to target; 7) monitoring and tuning of signals parameters using Simulink as a graphical user interface; 8) load of data for analysis. Providing input to the model in execution time is done with different user interface objects including special gauges (e.g. sliders), text boxes, or a joystick control (custom input) for pilot-in-the-loop tests. The target computer in the environment is a PCbased system which can be a normal desktop computer or an embedded flight computer (PC-104 form factor). Standard communication technologies as Ethernet, wireless 802.11b and UDP/IP and TCP/IP protocols, are used for both file transferring and monitoring in a laboratory setting. The mini-

helicopter is equipped with a wireless bridge, and an ah-hoc wireless LAN network formed with the helicopter flight computer and one or more laptop computers, which can play the role of ground or monitoring stations. Telemetry during flights requires special attention as flight tests demand an updated view of the helicopter state. A special blockset was developed to satisfy this need. The module, available through Simulink design interface, takes model parameters and sends them through network using UDP, which is a fast and efficient protocol for timesensitive purposes. Colibri RSPE has some advantages: 1) it encourages and requires active participation in the design process through a block diagram modeling environment; 2) it accelerates the learning curve and simplifies the information exchange between different technological domains; 3) the prototype is equivalent to a specification document; 4) errors can be detected earlier, reducing costs and development time; 4) it increases creativity; 5) it speeds up the development cycle due to the refinement of design by rapid iteration between algorithm design and prototyping.

4.1 Inertial navigation module It is not realistic to assume that all output vehicle variables can be measured. Even if it were possible, there are measurement errors and noise that could be minimized using data from different sensors (navigation aids), such as GPS, barometer, sonar, magnetometer, accelerometers and gyros [22] (the last two are integrated into an Inertial Measurement Unit - IMU).

Fig.6. Extended Kalman Filter algorithm An Extended Kalman Filter (EKF) is an optimal predictor-corrector estimator for Gaussian disturbances, which uses the knowledge of kinematical models, measurement errors, sensor models, and initial condition information to estimate position, velocity and attitude of a vehicle (its state). The estimated state is a combination of a predicted state and a correction using measurement data. Fig. 6

shows the respective equations and algorithm. The EKF was implemented in the environment using only Simulink blocks (Fig. 7 and 8), which makes possible the automatic code generation.

Fig.7. Implementation of EKF in Simulink

4.3 Control module Some control methods (Fig. 9 and 10) have been tested with the mini-helicopter simulation model. The first one is a heuristic PID control (parameters are tuned by trial and error), which is used to obtain control input values in different operational points (e.g., hover or cruise) and as an initial control which helps to compare other model-based methods. Fig.9 shows the simulation of PID controllers with a decoupled configuration, sensor models (from experimental data) and state estimation using an EKF. The PID controllers use position and velocity errors separately, which improve closed-loop behavior. Wind gust and inaccuracies in parameters and initial conditions are introduced. So, simulation is achieved into a common environment considering several aspects of control design. Other implemented controllers: fuzzy [15], state feedback and multirate [24]. In Fig.10, a multirate control is applied to mini-helicopter supposing different input and output sampling rates, using the Multirate Control Toolbox [16]. A single-rate state feedback control u = -Kx is obtained for a linearized model around a hover operating point (obtaining with the PID controller) and then is translated into a multirate control using the multirate modeling method exposed in [24]. The linearization is performed using model linearization module. Hereafter, novel control methods can be applied.

Fig.8. Application of EKF to state estimation

4.2 Model linearization module Linear control design from a complex non-linear mini-helicopter model is not a trivial problem. Usually, approximated or theoretical models are used and tuned around a selected operational point. In the environment, linearization is accomplished easily using Matlab tools (Table 1) and the mini-helicopter simulation model, excluding subsystem models such as actuator, quaternion and fuel dynamics. The linearized model was also obtained theoretically from mathematical equations and compared with models from other references [14], [13]; this process helped in the validation process of simulation model and to estimate different model parameters from experimental data.

Fig.9. PID control with state estimation

Table 1. Matlab linearization code % x_op = [u v w p q r roll pitch yaw x y z a1 b1 Omega] x_op = [0 0 0 0 0 0 0.0795 0 0 0 0 -60 0 0.00769 167]; % u_op = [d_col d_lon d_lat d_ped throttle] u_op = [0.6123 0 0.0191 0.4273 0.5283]; [A,B,C,D] = linmod('colibri_linearization_model', x_op, u_op);

Fig.10. Multirate control

4.4 Ground Control Station module The Ground Control Station (GCS) was developed completely in Matlab/Simulink and may be configured according to a specific test; for example, the GCS is different for identification, experimental tests or supervision tasks. It is not a single program, but the integration of several elements: gauges, virtual reality model, time plots, maps, etc (Fig. 11). In this sense, laptop is the station and can be composed taking advantage of several Matlab tools. This is an interesting concept, because designers usually think about a ground station as a single program.

necessary to validate and exploit all possibilities of whole software environment. The environment is being tested over a real system, where it is intended to reduce developing time and cost, giving to developer more time to focus on mathematical and algorithmic methods. The future work will be focused on control design interfaces, discrete event modeling, real applications, and multirate control possibilities and benefits. Parameter estimation using mini-helicopter Simulink model has a great potential if it is used together with tools as genetic algorithms or evolutionary computation, due to advantages that implies an accurate and intuitive mathematical model for simulation and control design. Acknowledgment: This work was supported by Colciencias (Colombian Institute for Development of Science and Technology) under code 1216-14-14884. The authors would like to express thanks to students of Mathematical Engineering of Eafit University by their constant support to the project.

Fig.11. Ground control station for supervision of an autonomous mini-helicopter robot

5 Conclusions The Colibri RSPE allows the analysis, design and rapid prototyping development of real-time control for an X-Cell mini-helicopter, in an intuitive and efficient way, with reduction of programming, debugging and learning time of the system and problem. The environment integrates general tools based on Matlab toolboxes, with the possibility of adding new functions according to new requirements. With the environment, it is possible to test new methods (control, monitoring, signal processing, estimation, identification, etc) in an easy and flexible manner. Specially, non-linear model identification and parameter estimation tasks are facilitated by the availability of a block-based visual simulation model and the possibility of applying different parametric and heuristic (like evolutionary computation and optimization) identification methods, in open or closed loop. Up to date, successful tests have been done with avionics and software in flight, but other tests are

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