課程名稱︰自動控制 課程性質︰大三必修 課程教師︰王富正 開課學院：工 開課系所︰機械系 考試日期（年月日）︰2011/11/1 考試時限（分鐘）：110 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(10%) Suppose f(t)=[e^(-at)]*cos(wt),derive the Laplace Transform L[f(t)] (必須有推導過程) 2.(35%) Consider the passive optical table of figure 2, where the inputs are the table force Fs and the ground disturbance Zr, and the output is the table weighs Ms, with linear spring k and linear damper c. (1)(5%) Derive the dynamic equation of the system. (2)(5%) Find the transfer funtions from Fs to Zs,and from Zr to Zs. (3)(5%) Find the steady state Zs(∞) to a step input Fs(t)=1,suppose Zr(t)=0 with zero initial conditions. (4)(5%) Find the steady state Zs(∞) to an impulse disturbance Zr(t)=δ(t), suppose Fs(t)=0 with zero initial conditions. (5)(5%) Set state as x=[Zs Zs']^T ,inputs u=[Fs Zr]^T,and output Zs, write the state space model of the system.Double check your result by calculating the transfer function matrix from this state space realization. ┌────┐ │ Ms │ └────┘ ──┐ ║ │ Zs ║ ┌┐ k║ └┘c ║ │ ────── ──┐ Zr 3.(10%) Given the following system , fnd the Jordan form realization of the system and draw the corresponding block diagram. 4.(20%) Consider the folloeing system: x'(t)= ┌ ┐ ┌ ┐ │ -1 0 0│x(t)+ │ 1│u(t) │ 0 -1 1│ │ 1│ │ 0 0 -1│ │ 1│ └ ┘ └ ┘ y(t) = [1 -2 -1]x(t) (1)(10%) Find the transfer function of the system. (2)(10%) Using the state transtion matrix (e^(At)),find the response x(t) to an initial x(0)=[1 1 1]^T ,suppose u(t)=0. 5.(25%) Considering Figure 5, where G(s)= α and K =β/s ------------- T (s+1)(s+10) (1) Find sensitivities of Sα ,where T(s)=T R(s)->Y(s) (2) Find the steady state error to a step disturbance Td(t)=1. (3) Suppose 1<=β<=100 , find the minimum absolute steady state error due to a ramp disturbance Td(s)=1/s^2. What is the correspinding value of β? (4) Using the β from (3) and suppose 1<=α<=10, find the minimum absoulte steady state error to a ramp input R(t)=t. What is the corresponding value of α? (5) Using the β from (3) and α from (4) ,derive the output Y(s) to a step input R(s)=1/s. What is the steady state y(∞)? ┌───┐ ︳Td(s) ┌───┐ │ │ v + │ │ R(s) ───>o───>│ K │-->o────>│ G(s) │───>Y(s) ^ └───┘ └───┘ │ │ │ └─────────────────────┘ ※ 編輯: sidchu 來自: 140.112.252.238 (11/01 13:04)