**Anna University**

**Department of ECE**

**4 Semester**

**EC2255 Control Systems**

#### Most Important Questions – 2014 Edition

**(Regulation 2008)**

**Unit-1**

1. Write the differential equations governing the Mechanical system shown in fig .and determine the transfer function. (16)

2. Determine the transfer function Y2(S)/F(S) of the system shown in fig. (16)

3. Write the differential equations governing the Mechanical rotational system shown in fig. Draw the Torque-voltage and Torque-current electrical analogous circuits. (16)

4. Determine the overall transfer function C(S)/R(S) for the system shown in fig. (16)

5. Obtain the closed loop transfer function C(S)/R(S) of the system whose block diagram is shown in fig. (16)

6. For the system represented by the block diagram shown in fig. Determine C1/R1and C2/R1. (16)

7. Obtain the closed loop transfer function C(S)/R(S) of the system whose block diagram is shown in fig. (16)

8. Find the overall gain of the system whose signal flow graph is shown in fig. (16)

9. Draw a signal flow graph and evaluate the closed loop transfer function of a system whose block is shown in fig. (16)

10. Derive the transfer function for Armature controlled DC servo motor. (16)

11. Derive the transfer function for Field controlled DC servo motor. (16)

**Unit-2**

1. (a) Derive the expressions and draw the response of first order system for unit step input. (8)

(b) Draw the response of second order system for critically damped case and when input is unit step. (8)

2. Derive the expressions for Rise time, Peak time, and Peak overshoot. (16)

3. A potential control system with velocity feedback is shown in fig. What is the

Response of the system for unit step input? (16)

4. Measurements conducted on a Servomechanism show the system response to be

c(t)=1+0.2 ê 60t-1.2 ê –10 t. when subjected to a unit step. Obtain an expression for closed loop transfer function. (16)

5. A positional control system with velocity feedback is shown in fig. What is the

response c(t) to the unit step input. Given that ς =0.5.and also calculate rise time, peak time, Maximum overshoot and settling time. (16)

6. A unity feedback control system has an open loop transfer function G(S) = 10/S(S+2). Find the rise time, percentage over shoot, peak time and settling time. ( 16)

7. A closed loop servo is represented by the differential equation, where c is the

displacement of the output shaft, r is the displacement of the input shaft and ( e= r-c) Determine undammed natural frequency, damping ratio and percentage maximum overshoot for unit step input. (16)

8. For a unity feedback control system the open loop transfer function

G(S) = 10(S+2)/ {S2 (S+1)}. Find (a) position, velocity and acceleration error constants.

(b) The steady state error when the input is R(S) where R(S) =3/S –2/S2 +1/3S3 (16)

9. The open loop transfer function of a servo system with unity feedback system is G(S) = 10/ S (0.1S+1).Evaluate the static error constants of the system. Obtain the steady state error of the system when subjected to an input given by the polynomial r(t) = a0 +a1t +a2 /2 t2 . (16)

**Unit-3**

1. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross over frequencies. G(S) = 10/ S(1+0.4S) (1+0.1S) (16)

2. The open loop transfer function of a unity feedback system is

G(S) = 1/ S(1+S)(1+2S) Sketch the Polar plot and determine the Gain margin and Phase margin. (16)

3. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin(S) = 0.75(1+0.2S)/ S (1+0.5S) (1+0.1S) (16)

4. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. G(S) = 10(S+3)/ S(S+2) (S2+4S+100) (16)

5. Sketch the polar plot for the following transfer function .and find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin.

G(S) = 10(S+2)(S+4)/ S (S2 -3S+10) (16)

6. Construct the polar plot for the function GH(S) =2(S+1)/ S2. Find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. (16)

7. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross over frequencies. G(S) =KS2 / (1+0.2S) (1+0.02S). Determine the value of K for a gain cross over frequency of 20 rad/sec. (16)

8. Sketch the polar plot for the following transfer function and find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin.

G(S) = 400/ S (S+2)(S+10) (16)

9. A unity feed back system has open loop transfer function G(S) = 20/ S(S+2)(S+5). Using Nichol’s chart, determine the closed loop frequency response and estimate all the frequency domain specifications. (16)

10. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. G(S) = 10(1+0.1S)/ S(1+0.01S) (1+S). (16)

11. Write the short notes on correlation between the time and frequency response? (16)

12. What is compensation? Why it is needed for control system? Explain the types of compensation? (16)

13. Realize the basic compensators using electrical network and obtain the transfer function. (16)

14. Design a suitable lead compensators for a system with unity feedback and having open loop transfer function G(S)= K/ {S(S+1) (S+4)} to meet the specifications. (i)Damping ratio=0.5

(ii) Undamped natural frequency. Wn =2 rad/sec. (16)

15. A unity feed back system has an open loop transfer function G(S)= K/ {S(S+1)(0.2S+1). Design a suitable phase lag compensators to achieve following specifications Kv= 8 and Phase margin 40 deg with usual notation. (16)

16. Explain the procedure for lead compensation and lag compensation? (16)

17. Explain the design procedure for lag- lead compensation. (16)

18. Consider a type 1 unity feed back system with an OLTF Gf(S) =K/{S (S+1) (S+4)}. The system is to be compensated to meet the following specifications Kv > 5sec and PM>43 deg. Design suitable lag compensators (16)

**Unit-4**

1. Using Routh criterion, determine the stability of the system whose Characteristics equation is S4+8S3+18S2+16S+5 =0. (16)

2. F(S)=S6 +S5-2S4-3S3-7S2-4S1-4 =0.Find the number of roots falling in the RHS plane and LHS plane. (16)

3. Draw 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 closed loop

System is stable. (16)

4. Construct Nyquist plot for a feedback control system whose open loop transfer function is given by G(S)H(S) =5/ S(1-S).comment on the stability of open loop and closed loop transfer function. (16)

5. Sketch the Nyquist plot for a system with the open loop transfer function G(S)H(S) =K({1+0.5S) (1+S)} /{ (1+10S) (S-1)). Determine the range of values of K for which the system is stable. (16)

**Unit-5**

1. Write notes on controllability and absorbability. (16)

2. Explain sampling theorem briefly and sample & hold operation. (16)

3. Explain stability analysis of sampled control system and Jury’s stability. (16)

4. Explain state space representation for descries time system. (8)

5. Explain state space representation for continues time system. (8)

6. Explain the solution for state equation for discrete time system. (8)

7. Explain the solution for state equation for continues time system (8)

8. Explain jury’s stability test. (16)

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