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1 VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year B.E. EC6405 CONTROL SYSTEM ENGINEERING UNIT I CONTROL SYSTEM MODELLING Basic Elements of Control System Open loop and Closed loop systems - Differential equation - Transfer function, Modeling of Electric systems, Translational and rotational mechanical systems - Block diagram reduction Techniques - Signal flow graph PART A Q.No Questions BT Level Domain 1. Compare the Open loop System with Closed loop System. BTL 4 2. Design the Electrical analogous network for the mechanical system shown in the fig. using Force-Voltage Analogy. BTL 6 3. Mention the transfer Function of the System. 4. List the advantages of Closed loop System? 5. What are the Properties of Signal flow graphs? 6. Give Mason s gain formula of Signal flow graph. BTL 2

2 7. Explain any two dynamic models to represent control system. BTL5 8. Discuss about the block diagram and its components of a control system. BTL 2 9. Demonstrate the basic elements used for modelling a mechanical rotational system. BTL Assess feedback and its types employed in Control system. BTL Negative feedback is preferred in control system. Justify BTL Write F-V Analogy for the elements of mechanical rotational system? 13. Illustrate any two rules to be followed in block diagram reduction techniques. BTL Define Control System 15. Analyze non-touching loops. BTL Interpret signal flow graph BTL Name the two types of electrical analogous for mechanical system. 18. Formulate force balance equation of ideal spring, ideal mass. BTL Calculate transfer function of the network BTL3 20. Describe mathematical model of a system. BTL 2 PART B 1. i. Determine the Transfer Function of the system Shown in the fig. BTL 5 ii. Determine the Transfer function of the electrical network shown in the fig.

3 BTL 5 2. (i) Modify the Block diagram to its Canonical form and obtain C(s)/R(s). (10M) BTL 6 BTL4 ii. Comparison between block diagram and Signal flow graph methods.(6m) 3. Solve C/R for the signal flow graph shown below. BTL 3 4. i. Consider the Mechanical system shown below and write the Differential equation. BTL1 ii. Draw the torque-voltage electrical analogous circuit for the mechanical

4 system shown below. 5. i. For the Signal flow graph shown below find C/R, using Mason s gain formula. BTL1 ii. Find the Transfer Function C(S)/R(S) of block diagram shown below. 6. i. Construct the Equivalent signal flow graph and obtain C/R using mason s gain formula for the block diagram show below. BTL6

5 ii. For the block diagram shown below, Calculate the output C/R 7. Using SFG, Analyze the overall Transfer function for the system shown in the fig. BTL3 BTL4 8. Give the differential equations governing the mechanical rotational system shown in Fig. and estimate the T-V and T-I electrical analogous circuits. 9. Write the differential Equations governing the mechanical system shown in the fig. and determine the transfer function. BTL1

6 10. Estimate the overall transfer function of the system shown in the fig. Fig(i) Fig(ii) UNIT II TIME RESPONSE ANALYSIS Time response analysis - First Order Systems - Impulse and Step Response analysis of second order systems - Steady state errors P, PI, PD and PID Compensation, Analysis using MATLAB PART A Q.No Questions BT Level Domain 1. Illustrate how a Control system is classified depending on the value of damping ratio? BTL 3

7 2. List the advantages of generalized error coefficients. 3. Why derivative controller is not used in Control systems? BTL 6 4. Give the steady state error values to standard inputs for type 2 systems. BTL 2 5. Determine the Damping ratio and natural frequency of oscillation for the closed loop transfer function of a second order system is given by 400. s 2 +2s+400 BTL 5 6. What is meant by peak overshoot? 7. Mention steady state error. 8. Define rise time. 9. The damping ratio and natural frequency of a second order system are 0.5 and 8 rad/sec respectively. Calculate resonant peak and resonant frequency. BTL With reference to time response, Examine peak time. BTL Describe the transient and steady state response of control system? BTL Give the units of kp, kv, ka. BTL Outline the response of the second order under damped system. BTL Point out the time domain specifications. BTL Summarize the generalized error and static error constants. BTL Compare position and velocity error constants. BTL Define damping ratio. 18. Demonstrate the test signals used in time response analysis. BTL Label a step signal. 20. Formulate ramp, parabolic and impulse signal. BTL 6 PART B 1. (i) For the system shown below, Analyze the effect of PD controller with Td= 1 / 10 on peak overshoot and settling time when it is excited by unit step input. BTL 4

8 (ii) Discuss the effect of PID controller in the forward path of a system. 2. The Unity feedback system is characterized by the open loop transfer function G (S) = k s(s+10). Estimate the gain K, so that the system will have the damping ratio of 0.5. For this value of K, Determine the settling times, peak overshoot, and time to peak overshoot for a unit step input. 3. Evaluate the Expression for Rise time, fall time, settling time, peak overshoot. 4. The open loop transfer function of a unity feedback control system is given by G(S) = k s(st+1) where K and T are positive constants. Illustrate by what factor the amplifier gain should be reduced so that the peak overshoot of unit step response of the system is reduced from 75% to 25%. BTL 5 BTL3 5. Consider a Second order model Y(S) response y (t) to a unit step input. R(S) = ω2 n s 2 +2εω n s+ω2 ; 0 < ε < 1. Find the n 6. (i) A unit ramp input is applied to a unity feedback system whose output response is C(s)= 100/(s 2 +5s+100). Analyze the time response and steady state error. (ii) For a unity feedback control system the open loop transfer function G(s) = 10(s+2)/s 2 (s+1). Calculate K p, K V, K a and the steady state error when the input is R(s) where R(s) s s 3s. 7. (i) Derive an Expression to find steady state error of closed loop system. (ii) A unity feedback system has the forward transfer function G(S) = KS/ (1+S) 2 for the input r(t)=1+5t, formulate the minimum value of K so that the steady state error is < 0.1. (Use final value theorem). 8 (i) Determine the unit step response of the control system shown in the fig. BTL 4 BTL3 BTL 6 BTL1

9 (ii) The open loop transfer function of a unity feedback system is given by G(s) = 20/ S(S+2). The input function is r(t)=2+ 3t + t 2. Determine generalized error coefficient and steady state error. 9 i. A unity feedback system with unit step input for which open loop transfer function G(s) =16/s(s+8).Find the transfer function, the natural Frequency, the damping ratio and the damped frequency of oscillation. ii. Write the response of undamped second order system for unit step input. 10 The unity feedback system is characterized by an open loop transfer function G(s) = K(2s+1)/ s(5s+1)(1+s) 2 with r(t) = (1+6t). Estimate the minimum value of K if the steady error is to be less than 0.1. BTL1 UNIT III FREQUENCY RESPONSE ANALYSIS Frequency Response - Bode Plot, Polar Plot, Nyquist Plot - Frequency Domain specifications from the plots - Constant M and N Circles - Nichol s Chart - Use of Nichol s Chart in Control System Analysis. Series, Parallel, series-parallel Compensators - Lead, Lag, and Lead Lag Compensators, Analysis using MATLAB. PART A Q.No Questions BT Level Domain 1. Derive the transfer function of a lead compensator network. BTL 6 2. Define Phase margin & gain margin. 3. Illustrate the need for compensation. BTL3 4. What is Nyquist plot? 5. Describe Lag-Lead compensation. 6. Sketch shape of polar plot for the open loop transfer function G(s)H(s) = 1 s(1+ts)

10 7. Analyze the effects of addition of open loop poles. BTL 4 8. Summarize the advantages of Frequency Response Analysis. 9. Mention gain crossover Frequency. 10. Express M and N circles in detail 11. Demonstrate the MATLAB Command for drawing Bode Plot for BTL3 Y(S)/U(S)= 4S+6/S 3 +3S 2 +8S Explain compensators and list types of compensators. BTL Formulate the transfer function of a lead compensator network. BTL List the advantages of Nichol s chart 15. Estimate the corner frequency in frequency response analysis? 16. Draw the circuit of lead compensator and draw its pole zero diagram. 17. Frame the specifications required for frequency domain analysis? BTL3 18. Compare series compensator and feedback compensator BTL Determine the Phase angle of the given transfer function G(S) = 10 / S (1+0.4S) (1+0.1S) 20. Evaluate the frequency domain specification of a second order system when closed loop transfer function is given by C(S)/R(S)= 164 s 2 +10s+64 PART B 1. Given G(s) = ke 0.2s /s(s + 2)(s + 8) Draw the Bode plot and find K for the following two cases: (i) Gain margin equal to 6db (ii) Phase margin equal to An UFB system has G(s) = 10. Design a Lead Compensator for the s(s+1) following specification e ss = 20sec, Phase Margin = 50 deg. and Gain Margin 10dB 3. The open loop transfer function of a unity feedback control system is G(s) = k s(s+1)(s+2).illustrate a suitable lag-lead compensator so as to meet the following specifications static energy velocity error constant K v =10 sec -1, phase margin =50 and gain margin 10db. BTL 5 BTL 5 BTL6 BTL3 4. Consider a unity feedback system having an open loop transfer function K GS ( ) S(1 0.5 S)(1 4 S)

11 Outline the polar plot and determine the value of K so that (i) Gain margin is 20db (ii) phase margin is A unity feedback control system has G(s) = plot. Find K when GCOF = 5rad/sec. ks 2 (1+0.2s)(1+0.02s)_ Draw the Bode 6. Sketch the polar plot and find the gain and phase margin of a control system 1 has G(s) = with unity feedback. s 2 (s+1)(1+2s) 7. Discuss a suitable lead compensator for a system with G(S) = the specifications. (i) Kv = 20 sec -1 (ii) Phase Margin = +50 (iii) Gain margin +10db k s(s+2) to meet 8. A Unity feedback system has an open loop transfer function, G(s) = k s(1+2s). Select a suitable lag compensator so that phase margin is 40 and the steady state error for ramp input is less than or equal to Recommend a Lead Compensator for a Unity feedback System with Open loop transfer function G(S) = K/S(S+1)(S+3) to Satisfy the following Specifications. i) Velocity error Constant, Kv 50 ii) Phase Margin is 20 degrees. 10. Explain in detail the procedure for Nichol s chart with M and N circles. BTL4 BTL 5 BTL4 UNIT-4 STABILITY ANALYSIS Stability, Routh-Hurwitz Criterion, Root Locus Technique, Construction of Root Locus, Stability, Dominant Poles, Application of Root Locus Diagram - Nyquist Stability Criterion - Relative Stability, Analysis using MATLAB PART A Q.No Questions BT Level Domain 1. Illustrate any two limitations of Routh-stability criterion. BTL 3 2. Report the advantages of Nyquist stability criterion over that of Routh s BTL 3 criterion. 3. Explain stability of a system. BTL 4

12 4. State Nyquist stability criterion. 5. Assess Routh Hurwitz stability criterion. BTL 5 6. What is the advantage of using root locus for design? 7. Express the rules to obtain the breakaway point in root locus. BTL 2 8. Describe BIBO stability Criterion. BTL 2 9. What is Centroid? BTL1 10. Quote Root locus 11. Associate the necessary and sufficient condition for stability. 12. Name the effects of addition of open loop poles? 13. Elaborate the Parameters which constitute frequency domain Specifications BTL Define characteristic equation. BTL1 15. In routh array what conclusion you can make when there is a row of all BTL 5 zeros 16. Relate roots of characteristic equation to stability. BTL Infer on dominant pole. BTL Compare the regions of root locations for stable, unstable and limitedly BTL 4 stable systems. 19. Mention asymptotes. How will you find the angle of asymptotes? BTL1 20. Using Routh Criterion, design the stability of the system represented by the characteristic equation s 4 +8s 3 +18s 2 +16s+5=0. BTL 6 PART B 1. Using Routh criterion, (i) Investigate the stability of a unity feedback control system whose open-loop transfer function is given by BTL 6 G(s) = e st s(s+2) (ii) Investigate the stability Closed loop control system has the characteristics equation S S S+1.5 = (i) Discuss the stability of a system with characteristics equation S 4 +S 3 +20S 2 +9S+100 = 0 using Routh Hurwitz criterion. BTL 2 (ii)explain the rules to construct a root locus.

13 3. Determine the range of K for stability of unity feedback system whose OLTF is k G(s) = Using RH criterion. s(s+1)(s+2) BTL 4 BTL 5 4. (i) Draw the root locus of the G(s) = k s 2 2 s 2s 3 whose H(s) = 1. Determine open loop gain k at = 0.7.(ii) Determine the range of K for which system is stable using RH Criterion S S S 2 +S +k = (i)Sketch the root locus of the system whose open loop transfer function is K/S(S+2)(S+4). Find the value of K so that the damping ratio of the Closed loop system is 0.5. (ii) Determine the range of values of K for which the unity feedback system, whose G(S) = K/S(S2+S +1) (S+4). Is stable and determine the frequency of sustained oscillations. 6. (i) Estimate Routh array and determine the stability of the system whose characteristic equation is S 6 +2S 5 +8S 4 +12S 3 +20S 2 +16S+16=0. Also determine the number of roots lying on right half of S-plane, left half of S- plane and on imaginary axis. BTL1 (ii) Explain the procedure for Nyquist Stability Criterion BTL4 7. (i) Interpret Routh array and determine the stability of the system whose characteristic equation is S 5 +S 4 +2S 3 +2S 2 +3S+5=0. Comment on the location of the roots of Characteristic equation. (ii) Summarize the rules used for construction of the Root Locus of a feedback system. 8. Label the Root Locus of the System whose open loop transfer function is G(S) = K / S (S+1) (S+3). Determine the Value of K for Damping Ratio equal to Demonstrate the Nyquist plot for a system, whose open loop transfer function is given by G(S) H(S) = K(1+S) 2 / S 3. Find the range of K for stability. 10. Demonstrate the Nyquist plot for the System whose open loop transfer function is G(s) H(s) = K / S (S+2) (S+10). Determine the range of K for which the closed loop System is Stable. BTL3 BTL3

14 UNIT V STATE VARIABLE ANALYSIS State space representation of Continuous Time systems State equations Transfer function from State Variable Representation Solutions of the state equations - Concepts of Controllability and Observability State space representation for Discrete time systems. Sampled Data control systems Sampling Theorem Sampler & Hold Open loop & Closed loop sampled data systems. PART A Q.No Questions BT Level Competence 1. Name the methods of state space representation for phase variables. 2. What is meant by quantization? 3. Write the properties of State transition matrix? 4. Determine the controllability of the system described by the state equation. BTL 5 5. Evaluate modal matrix. BTL5 6. What are the advantages of Sate Space representations? 7. Describe State and State Variable. 8. Define State equation. 9. Explain the concept of Controllability. BTL Summarize Sampled data Control System. BTL Discuss the advantages of State Space approach? BTL Explain Alias in sampling process? BTL4 13. State sampling theorem. 14. Propose the need for State variables. BTL Illustrate Observability of the System. BTL Design the Nyquist contour for the Pole which lie at origin BTL Illustrate closed loop sampled data systems. BTL3 18. Analyze the term Compensation. BTL Examine Open loop sampled data systems. BTL3 20. Distinguish type and order of the system. BTL 2 PART-B

15 1. Determine the state Controllability and Observability of the system described by x=[ 1 0 1]x +[ 0 0] u y= [ ]x i) Mention in detail a state space representation of a continuous time systems and discrete time systems. 3. Consider the system with state equation x ( x 2) =( 0 0 1) ( x 2 ) + ( 0) u(t) x x 3 1 x 1 BTL 5 BTL 3 Illustrate the controllability of the system. 4. For a given state variable representation of a second order system given below,write the state response for a unit step input and [ x 1 ]=[ 0 1 x ] [x 1 x ] + [ ] [u] [x 1 (0) x 2 (0) ] =[0 ] by using discrete time 1 approximation 5. A system is represented by State equation X = AX+BU; Y=CX Where A=[ ], B=[ 0 ] and C= [1 0 0].Explain the Transfer function of the System. 10 BTL 4 6. Y(S) A System is characterized by the Transfer function = U(S) 3. (s 3 +5s 2 Express whether or not the system is completely +11 s+6) controllable and observable and Identify the first state as output. BTL 2 7. i) The State model matrices of a system are given below A=[ ] B=[ 0] and C= [3 4 1] Generalize the Observability of the System using Gilberts test. ii) Find the Controllability of the System described by the following equations BTL 6 X =[ ] [X 1 ] + [ 0 X 2 1 ]u(t)

16 8. i) Analyze the Transfer function of the matrix from the data given below A= [ ] B= [1 1 ] C=[ 1 1] D= 0 ii) The Transfer function of a Control System is given by Y(S) (s+2) = U(S) (s 3 +9s s+24) and plan the controllability of the system. BTL3 BTL 4 BTL6 9. Mention the Transfer Function of the system. The State Space representation of a System is given below x x 1 0 ( x 2) =( ) ( x 2 ) + ( 0) u x x 3 1 BTL1 x 1 Y= (0 0 1) ( x 2 ) x i) Estimate the Controllability of the following state space system. x 1 = x 2 + u 2 x 2 = x 3 x 3 = 2x 2 3x 3 + u 1 + u 2 ii) Obtain the transfer function model for the following state space system. A = [ ] B = [1 ] C = [1 0] D 0 s

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