複選題

9. Consider the state-space model given by
     
where x is the system state, u is the input, and y is the output. Which of the following statements are true?
(A) This state-space model is a minimal realization.
(B) The poles of this model are at -2 and 4. (s+3)
(C) The transfer function of this model from u to y is
(D) This model has a transmission zero at -3.
(E) The state feedback law u = -Kx yields the closed-loop poles at –10 and –20 when k = [32 80].

1. Consider the operational-amplifer circuit as shown in Figure 1. Which of the following parameter assign- , ments implement a lead-lag compensator ?(A) R1 = 2MΩ, R2 = 500kΩ, R3 = 8MΩ, R4 = 300kΩ,R5 = iMn, and R6 = 1MΩ. (B) R1= 2MΩ, R2 = 200kΩ, R3 =  8MΩ, R4 = 300kΩ, R5 = 1MΩ, and R6 = 1MΩ. (C) R1 = 2MΩ, R2 = 200kΩ, R3 = 8MΩ,R4 = 300kΩ,R5 = 3MΩ, and RΩ = 1MΩ. (D) C1 = 0.1μF and C2 = 0.5μF. (E) C1 = 0.5μF and C2= 0.1μF.

2. Consider a non-linear dynamic model  Which of the following statements are true? (A) The linearized model at the equilibrium point x1 =x2 = 0 has poles at -0.5 ± j3.12 (B) The linearized model at the equilibrium point x1 =x2 = 0 has poles at 0.5± j3.12 (C) The linearized model at the equilibrium point x1 = π, x2 = 0 has poles at -3.7 and 2.7 (D) The lin arized m odel at the equilibrium point  x1 = π, x2 = 0 has poles at 3.7 and -2.7 (E) The linearized model at the equilibrium point  x1 = π, x2 = 0 has poles at 0.5 ± j3.12

複選題3. Which of the following staternents regarding non-minimum phase (NMP) zeros are true? (A) The effects of NMP zeros can be cancelled by feedback control techniques. (B) The effects of NMP zeros can be cancelled by feedforward control techniques. (C) The transfer function of the system that contains NMP zeros cannot be iuniquely determined from the magnitude plot of the Bode diagram. (D) NMP zeros add leading phase to a system. (E) There is always a undershoot in the step response if the corresponding system has NMP zeros.

複選題4. Consider the system P(s) and input u(t) given byWhich of the following terms are expected to appear in the steady state output of P(s)? (A) 1 (B)(C) (D) sin(4t) (E)cos(5t) 

複選題5. Consider a second-order LTI plant P(s) Which of the following statements are true? (A) The D.C. gain of P(s) is 0.5. (B) The natural frequency of P(s) is 16 rad/s. (C) The rise time of the step response of P(s) is larger than 1 s. (D) The settling time of the step response of P(s) is less than 1 s. (E) The maximum overshoot of the step response of P(8) is less than 5%.

複選題6. Which of the following statements are true?  (A) Given the characteristic equation 3s2+ 5s+k = 0 of a linear control system, increasing the value of k will decrease the frequency of oscillation of the system.(B) can be approximated bysince the pole at -20 is much larger than the dominant poles at O and -1. (C) For a stable open-loop system with a perfect model P(s), it is always possible to have a stable and causal feedforward controller F(s) such that P(s)F(s) = 1. (D) The maximum overshoot of is possibly exceed 100 percent when and T are all positive. (E) If a unity-feedback control system type is 2, then it is certain that the steady-state error of the system to a step or a ramp input will be zero. 

複選題7. Consider the closed-loop feedback control architecture shown in Fig. 2, where P(s) is the open-loop plant, C1(s) and C2(s) are the feedback controllers, and H(s) is the transfer function from the reference r(t) to the output y(t), respectively. Assume thatand H(s) is asymptotically stable, which of the following reference signal r(t) can be tracked by Hr(s without steady-state error? (A) r(t) =sin(10t). (B) r(t) = sin(20πt). (C) r(t) = sin(0.1t). (D)r(t)=sin(0.2πt). (E) A 100 Hz triangular wave reference r(t).

複選題8. Which of the following statements regarding system robustness are true? (A) A closed-loop system must beco ome unstable when the transmission lag is large enough. (B) A closed-loop system must be stable when both gain margin and phase margin are positive. (C) The gain margin is always ininite for second-order systers. (D) It is possible to have infinite phase margin. (E) Reduction of gain increases the gain margin without sacrifcing the steady-state error.

複選題10. Read the following paragraph that introduces the concept of model predictive control(MPC): Model predic- tive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refneries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynanic models of the process, most often linear empirical models ob- tained by system identifcation. The main aduantage of MPC is the fact that it allous the current timeslot to be optimized, while keeping future timeslots in account. This is achieued by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from Linear- Quadratic Regulator (LQR). Aiso MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digitaI control, although there is research into achieving jaster response times with specially designed analog circuitry. (test acquired from Wilipedia) According to the above paragraph, which of the following statements are true? (A) MPC applies an optimization solver to acquire the optimal control action with the consideration of the predicted responses and system constraints. (B) PID controllers do not have the predictive ability because they can be tuned without knowing the dy- namic model. (C) The performance of MPC may be deteriorated if the dynamic model is inaccurate. (D) LQR control cannot optimize the control action over a finite time-horizon. (E) Although it is possible to implement MPC on analog circuitry, MPC is usually implemented on computers or microprocessors.

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