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ECE147B_2011_MOD6_sol

ECE147B_2011_MOD6_sol - Module 6 Solutions 1 The first...

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Module 6 Solutions 1. The first problem considers another design for the double integrator plant. (a) A lead controller suffices for this. Placing the zero relatively close to the origin helps the continuous design achieve a fast rise time with relatively slow overshoot. A relatively non- aggressive design is: g2159g2778g4666g2201g4667g3404 g2778g2777g4666g2201g2878g2777.g2779g2782g4667 g2201g2878g2785 (1) (b) Simulating this particular design shows that indeed the continuous response is acceptable, with a 1s rise time, 15% overshoot, and a 7s settling time. Figure (1) – Continuous design step response (c) Next, the controller is digitized using a prewarped Tustin, with the prewarping frequency chosen to be roughly half of the crossover frequency, since simply choosing crossover as the prewarping frequency results in unacceptably high overshoot. g2159g2778g4666g2208g4667g3404 g2784.g2779g2785g4666g2208g2879g2777.g2779g2777g2785g2778g4667 g2208g2878g2777.g2784g2780g2782g2780 (2)
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(d) & (e) The discrete response showcases a slightly faster risetime with increased oscillatory behavior. Figure (2) showcases the discrete response compared with the continuous
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