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

科目：研究所、轉學考(插大)◆控制系統 | 年份：110年 | 選擇題數：0 | 申論題數：15

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所屬科目：研究所、轉學考(插大)◆控制系統

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申論題 (15)

(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 61c5404b8722c.jpg satisfying with (a). (Notes: To get points, you must get the correct controller, draw the correct Nyquist plot of 61c5405e12de1.jpg 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 61c540b7e828b.jpg . Give values of (61c540ca48652.jpg, a, b). 

(b) What is the maximum phase, 61c54127a5285.jpg , provided by the controller 61c5413d3591f.jpg?
(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. 
(a) Derive the state equation and the output equation of the plant. 
(b) For the system you derived in (a), design a state feedback control law to place the closed-loop pole at -2. 
(c) For the system you derived in (a), design an observer that has the observer pole located at -10.

(d) Combine the results in (b) and (c) and derive a dynamic compensator for the system. What is the control transfer function 61c541f3342ba.jpg
(e) Consider the control system in Fig.5 with the C(s) you derived in (d). Roughly sketch the root locus of the system as 0 ＜K＜ㆀ. Where does the root locus intersect with the imaginary axis and what is the corresponding K?