L(S) E(s) elt) R(S) r(1) K(S) U(S) u(1) GS) Y($) y(t) Fig. 1 The loop transfer function (LTF) L(s) of a typical feedback

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L S E S Elt R S R 1 K S U S U 1 Gs Y Y T Fig 1 The Loop Transfer Function Ltf L S Of A Typical Feedback 1 (230.05 KiB) Viewed 46 times

L S E S Elt R S R 1 K S U S U 1 Gs Y Y T Fig 1 The Loop Transfer Function Ltf L S Of A Typical Feedback 2 (31.77 KiB) Viewed 46 times

L(S) E(s) elt) R(S) r(1) K(S) U(S) u(1) GS) Y($) y(t) Fig. 1 The loop transfer function (LTF) L(s) of a typical feedback control system. r(t) u(t) y(t) K G(S) K b G(5)= s + a Fig. 2 A dual-loop motor speed tracking control system. (a) Consider the dual-loop motor speed tracking control system shown in Fig. 2. The plant G(s) is a DC motor with transfer function b G(s) = sta where the output y(t) and the control input ult) represent the motor speed and the electric voltage, respectively. The controller is composed of one integrators and two constant parameters K, and K. The integrator is included to guarantee zero steady-state error due to step tracking input, and K, and K, are to be determined based on the desired transient performance and robust stability subject to controlinput constraints. First of all, show that the loop transfer function is bK2 L(s) s(s+a-bki) (b) Let b = 145.5 and a = 43.14. Find the characteristic equation of the closed-loop system, and determine the values K, and K, so that the damping ra and the natural frequency of the closed-loop system are s = 0.9 and 0 = 50 rad/s, respectively. c) With the K, and K, designed in (b), we are ready to evaluate the performance of the closedloop system. Assume the control input u(t) is required to be less than 15V to avoid actuator saturation, and the reference input is expected to be below 40 rad/s. Let the
reference input be r(t) = 40 u, (t) rad/s. Plot the closed-loop responses y(t) and u(t). Inspect the performance of y(t) in terms of steady-state error, rise time, maximum overshoot, and settling time. Also check if the control-input constraint is satisfied for uſt).