110年 - 110 國立臺北科技大學_碩士班招生考試_機械工程系機電整合碩士班(甲組)：自動控制#108258

科目：研究所、轉學考(插大)◆自動控制系統 | 年份：110年 | 選擇題數：0 | 申論題數：17

試卷資訊

所屬科目：研究所、轉學考(插大)◆自動控制系統

選擇題 (0)

申論題 (17)

(a). Assume Gc(s) = 1 in the beginning, if the reference input r(t) = 1, find the transient response and the steady-state response of system output c(t). (8%)

(b). According to the results in (a), find the steady-state error if it exists. (2%)

(c). The steady-state error in (b) can be removed by designing the controller Gc(s) = K /s, please prove it. (8%)

(d). According to (c), determine the range of K, so that the unity feedback control system is stable. (2%) R(s) C(s) Gc(s) G(s)

(a). Find the closed-loop transfer function C(s)/R(s). (4%)

(b). Try to find the damping ratioy of this system. (5%)

(c). Try to find the undamped natural frequency ω_n of this system. (5%)

(d). Try to decide K and T. (6%)

(a). Determine the range of K, so that the unit-feedback control system is stable. (4%)

(b). Determine the range of K, so that there is only one unstable pole in the system. (4%)

(c). Determine all the root locus crossing points on the imaginary axis. (4%)

(d). Determine the departure angle of its root locus at the complex poles. (4%)

(e). If G_c(s) = K/(s + a), and a pair of the system poles are located at -1 ±1.5j, please determine K and a. (4%)

(a). For Figure (a), what's the relation of T₁ and T₂? Also, determine the stability of this negative feedback control system by applying Nyquist stability criterion. (10%)

(b). For Figure (b), what's the relation of T₁ and T₂? Also, determine the stability of this negative feedback control system by applying Nyquist stability criterion. (10%)

(a). Determine the gain crossover frequency ω_c.(10%)

(b). Determine the value of K, so that the phase margin is 50°. (10%)