二.問答題
 1.請概述目前疫情對臺灣與美國的情況,並依據模型說明疫情對臺灣產出以及股票大盤指數的影響效果,陳述你的論點。

2.下圖為美的經濟政策不確定性指標·依據下圖的情况,嘗試以總體模 型說明對美國以及臺灣的消費以及失業的影響。

(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. 

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