(a) Derive the state equation and the output equation of the plant. 

(a) Under the conditions of min(Ib ㅡal) and lal ＞ Ibl, please give your controller( K,, a, b ) to satisfy above specifications. 

(b) Use Nyquist Criterion, Z=N+P, to figure out the stability of the closed-loop system with the controller satisfying with (a). (Notes: To get points, you must get the correct controller, draw the correct Nyquist plot of and give the correct values of Z, N, and P.) 

(c) What is the steady-state error of (r()-y(t) responding to unit ramp input on R(s)?

(d) What is the Gain Margin (G.M.) for (b)? 

(a) Design a controller G(s) for the plant Gp(s) shown above to results in no change in gain crossover frequency. The controller is in the form of . Give values of (, a, b). 

(b) What is the maximum phase, , provided by the controller ?

(c)What is the phase margin PM for the system shown in Figure 3? (Notes: (b) will counted only when (a) is correct! (c) will counted only when (b) is correct!)

(a) Derive the state equation for the system in Fig. 4(a). In this figure, C represents a linear damper which generates a reaction force proportional to its velocity (with C being the proportional constant), M is a mass, and F is the applied force input. You should use the velocity of mass, v, as the state variable.(3pts) (b) Derive the state equation for the system in Fig. 4 (b). In this figure, in addition to the damper (C) and the force input F, K represents a linear spring (with K being the spring constant). You should use the deformation of the spring, x, as the state variable. 

(c) Derive the state equations and the output equation for the system in Fig. 4 (c) using x and v as the state variables and the endpoint velocity No as the output. 

(d) Find the condition relating M, K, C1, and C2 that renders the system in Fig. 4 (c) uncontrollable. Also find the condition that results in an unobservable system. 

110年 - 110 國立清華大學碩士班考試入學試題_動力機械工程學系/乙組(電機控制組):控制系統#105247

110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:控制系統#104974

110年 - 110 國立臺灣大學_碩士班招生考試_工程科學及海洋工程學研究所丙組:控制系統(B)#100939

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