3. Modify the Routh criteria so that it can apply to the case in which all the poles are to be to the left of a when a ＞ 0 to the polynomial: s³ + (6 + K)s² + (5 + 6K) + 5K = 0, with the assume value of c-1.(15%)

(a) Draw the block diagram for the plant with the condition that one integrator for each state variable. (4%)

(b)Find the transfer function. (4%)

(c)Find the closed-loop characteristic equation if the "state feedback" is u = -[K1  K2]x;(6%)

(d)Find the closed-loop characteristic equation if the "output feedback" is u = -K•y . (6%)

(a) Write the state equation for the circuit. The input u(t) is current, and the output y is voltage. Let X1 =iL and x2 = vc . (5%)

(b) What condition on R, L, and C will guarantee that the system is "controllable"? (5%)

(c What condition on R, L, and C will guarantee that the system is "observerable"? (5%)

6. Assume the closed-loop system of Fig. 4 has a feedforward transfer function given by Design a lag compensator D(s) so that the dominant poles of the closed-loop system are located at s = -1 ± j and the steady-state error to a unit ramp input is less than 0.2. (15%)

1. (10 Points) A 6-m long by 50-mm diameter rod of aluminum alloy (E = 70 GPa, a = 22.5 x /℃, and v = 0.346) is attached at the ends to supports that yield to permit a change of 1.0 mm in the rod when stressed. When the temperature is 35℃, there is no stress in the rod. After the temperature of the rod drops to - 20 ℃, determine (a) the maximum normal stress in the rod and (b) the change in diameter of the rod.

2. (10 Points) The brass pipe AD is fitted with a jacket used to apply a hydrostatic pressure of 3.5 MPa to portion BC of the pipe. Knowing that the pressure inside the pipe is 0.7 MPa, determine the maximumn normal stress in the pipe.

110年 - 110 國立臺灣大學_碩士班招生考試_電機工程研究所甲組:控制系統(C)(含電路系統分析)#101161

109年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所甲組:控制系統(C)(含電路系統分析)#105839