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Question:-1(i)
(ii):_
A compensated motor position control system is shown in Fig. 3.1. Assume the sensor dynamics are H(s) = 1. a) What is the type of the system with respect to reference tracking? b) Can the system track a step reference input r with zero steady-state error? If yes, give the value of the velocity constant. c) For what input the system would give bounded error? What is the value of error and the value of error constant? d) What is the type of system with respect to disturbance rejection? e) Can the system reject a step disturbance w with zero steady-state error? If yes, give the value of the velocity constant. f) Compute the sensitivity of the closed-loop transfer function to changes in the plant pole at -3. А ОТ (Hint: Compute TA' where A was inserted for the pole at the nominal value of SI 3.) g) In some instances there are dynamics in the sensor. Repeat parts (a) to (f) for H(s) = 25/(s + 25) and compare the corresponding velocity constants. (Hint: Do not spend time on computing everything from scratch. First analyze H(s) at s = 0 and draw conclusions to answer the questions.) W Ro– Σ Compensator s+5 200 s + 20 Σ Plant 1 s(s+3) OY Sensor H(s) Figure 3.1
Consider the liquid level control system with the plant transfer function: 14 G(s) = s2 + 9 + 14 a) Design a proportional controller so that the damping ratio is = 0.6. b) Design a PI controller so that the rise time is less than 1 sec. c) Design a PD controller so that the rise time is less than 0.7 sec. d) Design a PID controller so that the settling time is less than 1.8 sec.