ECE 535 DISCRETE TIME SYSTEMS SPRING 2010 HOMEWORK ASSIGNMENT #3 Due: 3 March 2010 1. The basic transfer function of a satellite control is G ( s ) = 1 /s 2 . (a) Design a continuous lead network compensation so as to give closed-loop poles corresponding to ζ = 0 . 5 and a natural frequency ω n = 1 . 0. The ratio of pole to zero of the lead is to be no more than 10. Plot the step response of the design and note the rise time and the percent overshoot. What is the system type and corresponding error constant? (b) Select a sampling period to give 10 samples in a rise time and compute the discrete equivalent to the lead compensator using the bilinear transformation. Plot the step response of the discrete system and compare the rise time and overshoot to those of the continuous design. (c) Select a sampling period that will give 5 samples per rise time, compute the discrete equivalent using the bilinear transformation, and compare rise time and overshoot of this design with the continuous case. (d) Repeat the two discrete-time controller designs, but use the FOH-equivalent.
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