110年 - 110 國立臺灣大學_碩士班招生考試_生物機電工程學研究所甲、丙組:自動控制#102177

(3) Let a = 4 and b = 3. (i) find the transfer function Y(s)/U(s) [ 計 分-3分) and (il) determine the state-transition matrix Φ(t) of the system.【計分:10分】

(1) Find the transfer functions,respectively.【計分:6分】

(2) Let Ki, be a very high gain amplifier. Show that when H_i(S)/H_e(S) =- (Ra. + La^s), the motor velocity ωm(t) is totally independent of the load-disturbance loryweT_L【計分.3分】

(3) Find the transfer function betweenΩ_m(s) and Ωr(S) (TL = 0) when Hi(S) and He(s) are selected as in part(2).【計分:6分]

(a) What is the relation between the motor speed ω_m and the link speed ω_L, and determine the equivalent moment of inertia referred to the motor shaft. (5%)

(b) Using τw as the control input and the rotation angle (say, θ) of the link as output, obtain the transfer function describing the dynamic relation between the torque im and the output angle  θ. (5%)

(c) If Im-0.01Kg•m² ,I _L=lKg•m² , n=10, b_m=0.001 Kg•m²/s, determine the system type and find the impulse response and step response of the single-link robot respectively (15%)

(1) rising time ≦ 0.1sec, overshoot ≦ 10%, steady state error ≦  5% for the unit step reference commandr