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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 COMPUTER AIDED DESIGN OF CONTROL SYS. Instrumentation And Control Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Define and explain types of controllability for a discrete-time system.

[10+6]

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(b) What are the tests for the controllability of a discrete-time system? 2. Explain the selection criteria for the design of inverse nyquist diagram.

[16]

3. Explain the multi variable circle criterion.

[16]

4. (a) When a system with polynomial matrix representation is said to be strictly proper.

or

(b) Differentiate ‘linear time invariant systems’ and ‘linear time variant systems’. Give examples for both types. [8+8]

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5. Write a MATLAB programme that reads an input temperature in degrees Fahrenheit (o F),converts in to an absolute temperature in kelvins T(o K) = 5/9[t(o F)-32.0]+273. [16] 6. Sketch an inverse Nyquist plot for a system with g(s) = semicircle for a phase lag compensator. 7. Sketch the Nyquist plot for the system (S+2) G(S) = S(S+1) (S+4)

1 (s+1)4

with a superimposed [16] [16]

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8. Consider the system defined and Y=CX  by X=AX+BU   0 1 0 0   0 1  B =  0  C= 1 0 0 where A =  0 −5 −6 0 1 design a state feed back gain matrix such that the closed loop poles are located at S=-10,S=-10,S=-15. [16] ?????

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 COMPUTER AIDED DESIGN OF CONTROL SYS. Instrumentation And Control Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Briefly explain following system specifications to be specified for a control system

(b) Sensitivity (c) Offset (d) Linearity.

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(a) Conditional stability

[16]

2. (a) Explain the mode of a system.

or

(b) Write the standard Mc Millan form.

3. Discuss the procedural steps to determine greshgorin bands.

[8+8]

[16]

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4. What are the control statements in MATLAB and explain each with one simple example? [16] 5. Draw a typical diagram for design of phase lag compensator using inverse Nyquist 1 diagram for a system g(s) = (s+1) 6 . How it is useful for the design of the compensator. [16] 6. Explain the foolowing MATLAB commands with examples (a) rlocus

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(b) impulse (c) isim

(d) step.

[16]

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7. Explain the effect of adding phase lag compensator to the system e−2s

[16]

8. Derive the sufficient and necessary condition for observability of the following system X ((K + 1)T ) = GX(KT ) and Y(KT) = CX(KT ) [16] ?????

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 COMPUTER AIDED DESIGN OF CONTROL SYS. Instrumentation And Control Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Explain the decoupling of the multivariable control systems? And explain how decoupling in useful. [16]

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2. (a) State the stability theorem using inverse Nyquist diagram for a closed loop polynomial SISOsystem.

(b) Briefly explain the advantages of inverse Nyquist diagram for stability studies. [8+8]

(a) AB (b) A−1 B (c) AT B

or

3. Write a MATLAB programme for the following with a suitable examples

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(d) AB−1 Where A and B are 3×3 matrices.

[16]

4. Write short notes on:

(a) Decoupling zeros

(b) Pole zero cancellation

(c) Mathematical model for a plant.

[6+5+5] n

n

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+b1 z +−−−−−−−+bn ) y(z) = (b(z0 zn +a 5. Consider the discrete - time system defined by u(z) n−1 +−−−−−+a ) . Show n 1z that a state space representation of this system may be given     by   x1 (k + 1) 0 1 0 −− −− 0 x1 (k) 0  x2 (k + 1)   0   x2 (k)   0 0 1 −− −− 0        − − −−   −− −−   −−   −− −− −− −− −−        − − −−  =  −− −−   −−  +  −− −− −− −− −−        xn−1 (k + 1)   0 0 0 −− −− 1   xn−1 (k)   0 xn −an −an−1 −an−2 −− −− −a1 xn (k) 1   x1 (k)  x2 (k)     + b0 u(k) −− y(k) = [bn − an b0 : bn−1 − an−1 b0 : − − −− : b1 − a1 b0 ] x     −−  xn (k) [16]

6. Explain the following MATLAB commands with examples 3

     u(k)   

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(a) ssdata (b) zpkdata (c) isim (d) tf.

[16]

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7. Briefly explain design of compensator for a closed loop SISO system using inverse Nyquist diagram. [16]

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or

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4

[16]

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8. Compare the inverse nyquist diagram technique and root locus technique.

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1. Write a MATLAB programme for the following (a) To add two 3×3 matrices 

ld .

 0 1 0 0 1 . (b) Polynomial equation for the matrix A =  0 −5 −6 0 (c) Explain commands conv and deconv.

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 COMPUTER AIDED DESIGN OF CONTROL SYS. Instrumentation And Control Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

[5+5+6]

(a) State space model (b) Transfer function and (c) Polynomial representations.

or

2. Briefly explain the differences of the following with suitable examples

[16]

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3. Explain the procedure for the compensation using root loci.

[16]

4. Explain, with an example why a continuous - time system is not observable, if it has got an o.d.zero. [16] 5. Sketch a typical inverse Nyquist plot with a superimposed semicircle for phase 1 lead compensator. If phase cross over frequency on the semicircle is ωpc is 0.4 and compensator gain factor is 10, Calculate the time constant to obtain maximum phase advance compensation. [16]

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6. Explain the following:

(a) Diagonal dominance

(b) Sensitivity.

[8+8]

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7. Explain the foolowing MATLAB commands with examples (a) isdt

(b) isct

(c) isim

(d) isproper.

[16]

8. State and prove the stability theorem using Nyquist diagram for a polynomial closed loop SISO system. [16] ????? 5