FE_s98

FE_s98 - EE 429 FINAL EXAM 6 May 1998 Name ID DO NOT TURN...

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Problem 1: (25 points) Happy Valley Technologies, Inc. has been contracted to replace an existing analog PI control system with a digital controller as shown in Figure 1, where α and β are the proportional and integral control gains respectively. + - Σ R(z) α+β 1 z -1 Y(z) E(z) z - 0.5 Plant Controller U(z) 1 Figure 1: Sampled-data control system. 1. (5 points) Find the closed-loop transfer function Y ( z ) /R ( z ) in terms of the control gains α and β . 2. (10 points) Suppose that the sample period T = 1 s and β =3 / 2. Determine the steady-state error e ss due to a ramp input r ( k )= kTu o ( k ). Does the steady-state error depend on α ? 3. (10 points) With β set to 3/2, use the Jury stability test to determine the range of α for which the closed-loop system is BIBO stable.
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This note was uploaded on 07/23/2008 for the course EE 482 taught by Professor Schiano during the Spring '08 term at Penn State.

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FE_s98 - EE 429 FINAL EXAM 6 May 1998 Name ID DO NOT TURN...

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