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me352_hw5

# me352_hw5 - (b Which system would have the smallest...

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1 ME 352 System Dynamics and Control Homework #5 Due: Fri 15.04.2011 [1]. Determine the type of the following unity-feedback systems for which the forward-path transfer functions are given. (a) ) 8 1 )( 4 1 )( 1 ( ) ( s s s K s G + + + = (b) ) 3 )( 2 ( ) 1 ( 10 ) ( + + + = s s s s s G (c) ) 5 5 ( ) 1 ( 10 ) ( 2 3 + + + = s s s s s G (d) ) 20 1 )( 10 1 )( 1 ( 10 ) ( 2 . 0 s s s e s G s + + + = - [2]. For the unity-feedback control systems described in Problem 1, determine the steady-state error for a unit-step input, a unit-ramp input and a parabolic input ) ( 1 ) 2 ( 2 t t . [3]. Consider a system with the plant transfer function [ ] ) 1 ( 1 ) ( + = s s s G . You wish to add a dynamic controller so that ω n =2 rad/s and ζ≥ 0.5. The following dynamic controllers have been proposed: (i) 8 3 5 ) ( + + = s s s D (ii) ) 01 . 0 )( 8 ( ) 1 . 0 )( 3 ( 5 ) ( + + + + = s s s s s D (a) Using MATLAB, compare the resulting transient and steady-state responses to reference step inputs for each controller choice. Which controller is best for the smallest rise time and smallest overshoot?
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Unformatted text preview: (b) Which system would have the smallest steady-state error to a ramp reference input? (c) Compare each system for peak control effort; that is, measure the peak magnitude of the plant input u(t) for a unit reference step input. (d) Based on your results from parts (a) to (c), recommend a dynamic controller for the system from the candidate designs. [4]. A compensated motor position control system is shown in below. Assume that the sensor dynamics are s s H + = 1 ) ( . (a) Can the system track a step reference input r with zero steady-state error? If yes, give the value of the velocity constant. (b) Can the system reject a step disturbance w with zero steady-state error? If yes, give the value of the velocity constant....
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