(a) Figure Q.2(a) illustrates a unity feedback system with a forward transfer function of a plant having a unit step input. R(s) C(s) Ge(s) G(s) Figure Q.2(a) The open-loop transfer function G(s) is given as G(s) = 1 (s+2)(s+5)(s +20) A controller, Ge(s) is required to improve the performance of the uncompensated system G(s). The system is operated at 20% of overshoot with the dominant poles given as Sa=-2.67 ±j5.22. (i) (ii) Determine the gain, K, the settling time, T,, and the peak time, Tp, of the closed loop system at the given dominant poles. From Q.2(a)(i), determine the new dominant poles, San if the compensated system settles three time faster than the uncompensated system. (iii) Using the new dominant poles, Sans design the PD controller and determine the values of proportional gain, KP, and derivative gain, KD, of the controller.

)) The Nyquist Plot of a system G(s) = in a unity feedback loop (Figure 3) is shown in Figure (s+1)² 4 for K = 1: a). Is the closed-loop system stable for K = 1? Justify your conclusion with Nyquist Stability Criterion ? b). Discuss the impact of the value of K, increasing or decreasing, on the closed-loop system stability and find the critical value of K in Nyquist Plot. Applying Routh-Hurwitz Criterion to validate your conclusions. R(s) + Y(s) G(s) Figure 3: Nyquist Diagram 15- 05 Real Asis

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Q2) Consider the following feedback system outlined in Figure Q2 Plant R(s) 10 C(s) S+1 Figure Q2 a) Derive the closed loop transfer function GRe(s). b) Calculate the value of Ky that will result in the closed loop system to have a maximum overshoot of 35% and a peak time of approximately 1 second. c) For the following systems assume zero initial conditions. Determine i) The peak overshoots. ii) Corresponding peak times iii) Decay rate characteristics. Produce a sketch of the unit step response using the above values calculated. vate ett

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(A): Convert the Block Diagram showing in figure (2) to a Signal-Flow Graph (SFG). (B): Reduce the block diagram shown in figure (2) to a single transfer function Y(s)/R(s). (C): For the close loop system, find the values of damping ratio (), natural frequency (wn), percent overshoot (%OS), Peak time (Tp), Rise time (Tr), and settling time (Ts) Y(s) 2500 %3D R(s) s2 + 50 s + 2500 R(s) Y(s) 1 1 K s+0.4 2+1.7s+0.25 G1(s) G2(s) G3(s) Figure (1) 0.1 s+0.1 H(s) R(s) V1(s) V2(s) G1(s) V4(s) V5(s) Y(s) G3(s) G4(s) V3(s) Figure (2) G2(s) V6(s) H(s)

A plant of transfer function G(s) is to be operated in closed-loop, with unity negative feedback, and a controller in the forward path as shown in Figure Q4 R E controller G(s) Figure Q4 (a) Discuss the main steps of generating the root-locus plot for the closed-loop system of Figure Q4 (b) If the controller is a simple gain factor K, produce an estimated root-locus plot for the system with G(s) = S+8 (s+4)(s+6)(S-1)

For the feedback control system given in the figure on the right, R(s) + (a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain Kusing Routh-Hurwitz criterion. (c) What is the type of the system? (Hint: you need to convert the system to a simple unity feedback.) K 1 s(s+2)(s+5) C(s) (d) Sketch the root-locus in Matlab (hint: you need to use the open-loop transfer function with K = 1) and validate the stability region you found in (b). (e) Plot the step responses up to 10 seconds for the input of 1.5u(t) when the gain K = 22 and has the value that makes the system marginally stable on the same plane. (f) Calculate the steady-state error for the input step of 1.5u(t) for K = 22. Confirm the result with the related plot you obtained in (e). (g) Calculate the steady-state error now for an input ramp of 1.5tu(t) for K = 22 and plot this response together with the input function up to 10 seconds in order to indicate the steady-state error…

a) Consider the feedback system in Figure Q4 with controller G (s)=- and plant s+a 100 G,(s)=- s+25 Specify K and a of G,(s) such that the overall closed-loop response to a unity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1 x100% ] 0.6 b) To make the steady-state error to a unit step reference input zero, add an integrator to K. the controller of Q4a, i.e. G,(s)=- Assuming that a has the value derived in s(s+a) Q4a do the following: (0 Draw the root-locus of the closed-loop system, as K takes all positive real values, by computing the locus on the real axis, the angles of asymptotes, the point of intersection of the asymptotes with the real axis and the break points. Show clearly with arrows the direction of the loci. (ii) Find the value of K so the closed-loop system becomes marginally stable. In that case compute the points of intersection of the loci with the imaginary axis.…

As far as signals  & sytems(s&s) is concerned, discuss using s&s concepts in summary, how a feedback system can be utilized in controlling a gas cooker in a restaurant.Also make a simple block diagram sketch of the feedback system.