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problemset9 - The University of Texas at Austin Department...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE362K: Introduction to Automatic Control—Fall 2009 Problem Set Nine C. Caramanis Due: Wednesday, November 25 2009. This problem set is emphasizes PID control and system type, as well as Nyquist plots, and stability. 1. Routh-Hurwitz: Consider a unity feedback loop connecting a controller D ( s ) and a plant G ( s ), where the plant is given by G ( s ) = 1 s 2 + 3 s - 4 , and the controller is given by D ( s ) = K 1 + 1 s K 2 + sK 3 . (a) Compute the closed loop transfer function from r to y . (b) Compute conditions on the constants K 1 , K 2 , and K 3 , so that the resulting closed loop system is stable. 2. System type and PID controllers. Consider the closed loop system shown in the figure below: G D W and let G ( s ) = β s ( τs + 1) . Consider a disturbance signal w ( t ) = t k 11( t ). If D ( s ) is a PI controller, what is the largest k for which the steady state response to the noise is zero?
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