ECE535_10S_hw7

# ECE535_10S_hw7 - ECE 535 DISCRETE TIME SYSTEMS HOMEWORK...

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ECE 535 DISCRETE TIME SYSTEMS SPRING 2010 HOMEWORK ASSIGNMENT #7 Due: 21 April 2010 1. In this problem you’ll design a state variable controller for a plant described by Y ( s ) = 1 s (10 s + 1) U ( s ) . (a) Write down state variable equations ˙ x ( t ) = F x ( t ) + G u ( t ) y ( t ) = H x ( t ) that describe the plant when x ( t ) = y ( t ) ˙ y ( t ) . (b) Let T = 1 and design a state feedback law u ( k ) = r ( k ) - K x ( k ) that places the controlled system’s poles at locations equivalent to s = - (1 / 2) ± j ( 3 / 2). Plot the response to a step input r ( k ) for the resulting design. (c) Design a deadbeat predictor estimator (that is, all poles of the estimator are at z = 0). (d) Use the estimated states for computing the control, while also introducing the ref- erence input so as to leave the state estimate undisturbed. Plot the step response from this reference input. Also plot the step response from a step disturbance acting at the plant input. (That is, u ( k

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ECE535_10S_hw7 - ECE 535 DISCRETE TIME SYSTEMS HOMEWORK...

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