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題組內容

PROBLEM 1(40%) Given a system described by the following differential equation
where u is the control input and y is the output.

(a) (10%) Find the transfer function of the system.

其他申論題

PROBLEM 2(15%) Consider a system with the following unit step response y. Determine the poles and zeros of the system.

PROBLEM 3 (15%) Assume the operational amplifier in Fig. 3 is ideal. Show that the transfer function for the circuit can be written in the form Determine the values of KP, KI, KD.

a. (15%) Determine for the range of real number & the feedback system is stable

b. (15%) Assuming k=0, estimate the amplitude of the steady-state error when the reference input is r(t) = cos(2t).

(b) (10%) Find the zero-input response y(t).

(c) (10%) Choose, among the following types of control, ones that are likely to stabilize the system (One or more answers may be correct. Answers without supporting explanation are not acceptable) : (i) P control (ii) I control (iii) D control (iv) PID control (v) PD control (vi) PI control

(d) (10%) Choose, among the following types of control, ones that are likely to regulate the system output to a constant level 0.5 with zero steady state error (One or more answers may be correct. Answers without supporting explanation are not acceptable): (1) P control (ii) I control (iii) D control (iv) PID control (v) PD control (vi) PI control

(a) (10%) Derive a state-space representation of this LCR circuit.

(b) (10%) Suppose L =C=R=1 and x1(0)=x2(0)=1. What is the output y in steady state if u =sin(t)?

(c) (10%) Following 2(b), let the control be u(t)=-k1x1(t)-k2x2(t). Choose the gains k1 and k2 such that the closed loop poles are -2 and -3.

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