1. Consider a negative unity-feedback control system whose plant transfer function is type- 1. Suppose you want to build a lead compensator so that -3 ± 5j are dominant poles. You observed that the angle deficiency at the desired dominant pole is 50°. Compute a 's+b' and b of the lead compensator (s+ 2) so that the error constant Ky is maximized. In other words, design the lead compensator in a way so that the steady-state error for ramp input is minimum

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QUESTION 1 A unity feedback system has open loop transfer function shown below. Find K1 so that the damping ratio = 0.4 and the peak time t,=2 seconds. Here the peak time tp = wa K1 s+ KzK2) HG(s) =

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An uncompensated system shown in Figure 3(a) has forward transfer function G(s) with a unity feedback. a. Design a phase lead compensator shown in Figure 3(b) cascaded with the uncompensated system shown in Figure 3(a) that will have a 40% or better improvement of the settling time, at least 3 times improvement in percent overshoot. Assume a compensator zero at (given value zc = -10).Show all the complete solution.

A unity feedback system has a forward path transfer function G(s)=16/(s2+8s). Find the value of delat time , rise time, percentage overshoot, peak time and settling time.

The block diagram representation of a tachometer feedback speed control system is shown in Figure 4. R(s) + 15.5 C(s) s+1 Tachometer Ko Figure 4 (i). Develop the closed loop transfer function. (ii). Evaluate the value of DC gain K and the time constant T with the assumption of tachometer feedback variable Ko. (ii). The system step response is represented by y = K(1 – e), sketch the step response curve for the system when the tachometer feedback variable Ko. (iv). Write a general MATLAB codes to reduce the block diagram into a single feedback control system, to calculate transfer function and to obtain unit step response and impulse response. (v). Comment on the step response curve which is obtained in (i) and (iv) with respect to K and time constant T. ko=2 k1=2.2 Note: Refer the Table for Ko and K, values.

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Q1: The total harmonic distortion of a closed loop system is 5%. Distortion without feedback is 10%. Calculate the sensitivity of the closed loop system.

Hybrid vehicle. FIGURE P1 shows the block diagram of a possible cascade control scheme for an HEV driven by a dc motor (Preitl, 2007). The block diagram of the speed control of an HEV taken from FIGURE P1, and rearranged as a unity feedback system is shown in FIGURE P2. Here the system output is C(s) = Kss V(s), the output voltage of the speed sensor/transducer. pC, Av,- Speed K, Gre(s) controller command Torque Amplifier controller output & power voltage amplifier Acro- Motive dynamie Armature Speed |drag torque Angular speed, Ref. circuit Armature torque Vehicle signal R,(s). error U(s) T(s)T,(s) current E,(s) speed, V(s) Gse(s) K, Grc(s) R. tot Friction Feedback speed signal Kss2(s) Feedback torque current signal Kes I(S) T,(s) E,(s) Back emf D=k ks Current sensor sensitivity Kcs Speed sensor sensitivity Kss FIGURE P1 Hybrid Vehicle R (s), E (s) Uc(s) |C(s) + Gsc(s) 0.11 (s + 0.6) SC s (s + 0.5173) + 5 (s + 0.6) (s + 0.01908) URE P2 Block diagram of the speed control of an HEV a....

QUESTION4 Consider the feedback system in the figure with G(s) Using the Ziegler-Nichols Oscillation Method. %3D (s+1)(s+3)(s+10) for an ideal PID controller C(s) - K, ++ Kps determine the gains K K, and K. Choose the closest set of gains. C(s) G(s) OK, - 18, K, = 12.81, K, = 6.32 O Kp = 4.80, K, = 2.65, Kp = 2.18 O Kp - 47.52, K, = 85.57, K, - 12.60 %3D O K, - 68.64, K, = 143.27, Kp = 8.22

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What is positive feedback system?