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Midterm1 - The current dynamics are described by the...

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ME 451 Control Systems Summer 2008 Midterm Exam 1 Wednesday, June 25, 2008 Answer all questions. Show all your work for full credit. Books and Notes are NOT allowed. One side of a page (handwritten) may be used for reference. You may use any of the handouts. Duration: 50 minutes Department of Mechanical Engineering Michigan State University Problem 1: (20 points) For the block diagram shown below, obtain C(s)/R(s) Problem 2: (30 points) a) For the system given below, the input r( t )=5cos 4 t, is applied at t= 0. Find the steady state system response and the range of t for which the system is in steady state. R(s) C(s) b) The simple electrical circuit shown below consists of a linear inductor with inductance L = 10 henry, a constant source V o = 80 volts, and a non-linear resistor element, across which the voltage drop is V r (i) = 60i + 20i 2 . (The current i is measured in amperes). The current dynamics are described by the first-order ordinary differential equation
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Unformatted text preview: The current dynamics are described by the first-order ordinary differential equation ) ( i f dt di L where f(i)=V o-V r (i). Linearize f(i) about the steady state value of current i o .( i o =1 amp). Write the linearized differential equation. 5 4 s Page 2 Department of Mechanical Engineering Michigan State University Problem 3: (25 points) For the mechanical translational system shown below: a) Write the governing differential equations b) Determine the transfer function X(s)/F(s) Problem 4: (25 points) The unity feedback system is characterized by an open loop transfer function G(s) = K/s(s+10). a) Find the closed loop transfer function for the system b) Determine the gain K, so that the system will have a damping ratio of 0.5. c) Determine settling time, percentage peak overshoot and time to peak overshoot for a unit step response. Unity feedback system...
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