110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所系統控制組:控制系統(A)#100776

(1) (10%) Determine the characteristic equation of this system and the controller gains of K_p, K_i, K_v, such that the poles are located at -0.5±j0.5,-10.

(2) (10%) Determine the steady-state error with R=0 when the disturbance is (a) a unit step, (b) ramp function d(t)=3t, (c) parabolic function d(t)=t²/2.

(3) (10%) Neglect the real pole. Assume D=0 and R(t) is a unit step. Sketch the step response of this system.

(1) (10%) Draw the root-locus as K varies from 0 to infinity. Find asymptote, the value of K where the root loci cross the imaginary axis, the values of K at the break-away point, break-in point, and the closed-loop poles for these K values.

(2) (10%) When the system is stable, find the range of K for the system is underdamped, If the design specification requires the damping ratio for the dominant closed-loop poles is equal to 0.707, determine the value of K and the closed-loop poles for this K value.

(1) (5%) Sketch the Bode plots of L(s)=G(s)C(s).

(2) (5%) Sketch the Nyquist plot of L(s) = G(s)C(s).

(3) (5%) Calculate the gain margin of the system.

(4) (5%) Calculate the phase margin of the system. C(s) G(s)

(I) (5%) Suppose, sketch the root-loci of the closed-loop system as K :0 → ∞ . Mark the important values of K on the plot.

(2) (5%) Find the range of K that can maintain system stability by the Nyquist Criterion.

(3) (5%) Find the frequency ω1, where

(4) (5%) Design a first-order controller C(s) to assign all closed-loop poles at s=-2.

(5) (10%) Design a controllersuch that the system has a phase margin of greater than 45° and a bandwidth of less than s+p 20 rad/sec. s(s-9)'

110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所系統控制組:控制系統(A)#100776

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