(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.

3. (20 Points) Determine the stress state and the corresponding von Mises cquivalent stress of the point A subjected to the plane-strain condition, knowing that the following strains have been obtained by the use of the rosette shown: ε1 = -50 x. Assume that Young's modulus and Poisson's ratio of the material are 200 GPa and 0.3, respectively.

4. (20 Points) The structural tube shown has a uniform wall thickness of 8 mm. Knowing that the 60-kN load is applied 4 mm above the base of the tube, determine the stress state at point a.

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