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Unformatted text preview: 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: gG¡¢£ ¤ G¥¡¢¦¥.§¨£ ¢¦© (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. gG¡ª£ ¤ «.§©¡ª¬¥.§¥©G£ ª¦¥.«¨ (2) (d) & (e) The discrete response showcases a slightly faster risetime with increased oscillatory behavior. Figure (2) showcases the discrete response compared with the continuous behavior....
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This note was uploaded on 12/28/2011 for the course ECE 146b taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08