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

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EE 429 FINAL EXAM 6 May 1998 Name: ID#: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total 100 This test consists of four problems. Answer each problem on the exam itself; if you use additional paper, repeat the identifying information above, and staple it to the rest of your exam when you hand it in. The quality of your analysis and evaluation is as important as your answers. Your reasoning must be precise and clear; your complete English sentences should convey what you are doing. For your convenience, a z-Transform table and ruler are provided on pages 16 and 17, respec- tively. 1
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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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FE_s98 - EE 429 FINAL EXAM 6 May 1998 Name: ID#: DO NOT...

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