(1) (10%) The control objective is 2% settling time of the dominant poles needs to be 4 sec. Find the value of K to meet this requirement.

(1) (10%) If r(t) = 2cos (t + θ) and y(t) = Acos (t + 45°), obtain values of Oand A.

(2) (20%) Given a unit step input, it is known that. Determine y(t) using the inverse Laplace transform approach without solving differential equations.

(2) (10%) The control objective is damping ratio of the dominate poles is equal to 0.707. Dosign the value of K in order to reach this goal.

3.(26%) With r(t) as the input and y() as the output, this problem considers a linear system that can be represented by  where R(s) and Y(s) are the Laplace transforms of r(V) and y(t), respectively. With r(t) = cos21, it is known that the steady-state response of this system can be represented as Acos(at - π). Based on such information, please determine A, d, and T.

4.(24%) This problem considers six transfer functions G1 = 1/(s+1), G2 = 2/(s+2), G3 = 1/(s2+s+1),G4 = 3(s2+s+3), G5 =2/(s2+3s+2), and G6 = (s+10)((s2+s+10). Their step responses (AI, A2 , A6) are amplitude spectra (B1, B2 , B6) are given in the figures shown in the following pages. Please pair each of the transfer functions to one of the step responses and one of the amplitude spectra.(That is, if you think A1 is the step response of G1 and B1 is the amplitude spectrum of GI, write your answer for G1 as G1-A1-B1. Please present your answers in this way for all the six transfer functions considered in this problem.

(d)若工程師B希望設計控制器為C(s)=K(s-z)(S-p時,且希望閉路的 poles均為2時則C(S)該如何設計?(10分) 

(c)若工程師A希望降低穩態誤差,將控制器設計為C(s)=K/s時,卻發現系統有可能會不穩定,請問使得整個閉迴路系統(closed1oop system)穩定的K的範圍為何?(5分)

(b)如(a)中選擇C(s)=K時,Y(S所對應的反應y(t)的overshoot 有多少 percent(%)?(5分)

(a)當C(s)=K時,其中K為一固定正數,請此系統的穩態誤差(steady state error)為何?(5分)

3.(25分)下圖A描述一個簡單的避震系統,包含質量M、彈簧K、與阻尼v的動態系統::質量M在垂直黏滯摩擦v的滑軌內只能上下滑動,M被頂在直彈簧上,弹簧係數為K。圖B描述了M 之受力的自由體圖:固定重力g向下、彈簧力K*(y(t)-yw(t)向下、黏滯摩擦力v*d(yt) yw(t)/dt 向下、外加施力F(0)向上,而yw為彈簧與阻尼器的被設定的繫點的相對於地面固定位 置的向上垂直座標、y為M在彈頂端的位置向上垂直座標、0彈力時彈簧長度為L0。*請列出描述M的力的平衡動態方程式,是位置時間函數的時間微分方程式,請寫出其對應的拉氏域的代數方程式,別忘了包括y(t)與(d/dt)y(t)的初始值(10分) 這樣一個二階系統的動態特徵分母多項式 般寫成為 阻尼因數。 .*請問與系統元件的特性參 數M、K・v之函數關係為何?(7分)*已知 階梯響應的突波ovesoo比例.*若希望完 全沒有突破,Mp該如何選,而為了避震系 統不至於產生暈眩,只需要突波不太大,可 以選擇Mp≦0.0948,如此請問應該如何 選?M、K、v應該如何?(8分)

110年 - 110 國立中央大學_碩士班招生考試_機械工程學系/共同(一般生):自動控制#111071

110年 - 110 國立中山大學碩士暨碩士專班招生考試_機電系碩士班/丙組:自動控制#105564