Consider the transfer function G(s) from 01.1 in the closed-loop system shown in Fig. 3. T,(s) G(s) R(s) + E(s) Kr(s+2)

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Consider The Transfer Function G S From 01 1 In The Closed Loop System Shown In Fig 3 T S G S R S E S Kr S 2 1 (46.58 KiB) Viewed 26 times

Consider the transfer function G(s) from 01.1 in the closed-loop system shown in Fig. 3. T,(s) G(s) R(s) + E(s) Kr(s+2) S Uc(s)+U(s) Process G(s) K s² + 2as + ² H(s) Kos Y(s) Fig. 3. Closed-loop system for Q2. Q2.1. [5] Find the closed-loop transfer function from the reference signal R(s) to Y(s) parametrically in terms of G, G, and H, i.e., Y(s)/R(s) when Ta(s) = 0. (Do NOT use the numerical values of G from your solution in Q1.1). Then replace the transfer functions with their paramaters as shown in Fig. 3. Assume the known paramaters are K, a, and and the unknown paramaters are Kp. z. and Kp Q2.2. [2] Determine a condition on K, based on K, a, and such that G(s)/(1+G(s)H(s)) is a 2nd-order critically damped system. Q2.3. [15] Using the condition from Q2.2, find a condition on K, and z based on K and such that the closed- loop system undergoes a pole-zero cancellation and also behaves like a 2nd-order critically damped system. Determine the closed-loop settling time. (Hint: Using coefficient matching, equate the desired characteristic equation to the closed-loop characteristic equation while applying the given conditions of pole-zero cancellation and critically damped behaviour). Q2.4. [8] Show that the final value of the output due to a unit step disturbance will approach zero, that is if R(s) = 0 and Ta(s) = 1/s then y0 as too. (You do not need to have solved Q2.2 and Q2.3 to solve this question.)