课程名称︰自动控制 课程性质︰大三必修 课程教师︰王富正 开课学院：工 开课系所︰机械系 考试日期（年月日）︰2011/11/1 考试时限（分钟）：110 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.(10%) Suppose f(t)=[e^(-at)]*cos(wt),derive the Laplace Transform L[f(t)] (必须有推导过程) 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) ^ └───┘ └───┘ │ │ │ └─────────────────────┘ ※ 编辑: sidchu 来自: 140.112.252.238 (11/01 13:04)