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# hw4 - ECE 147A FEEDBACK CONTROL SYSTEMS THEORY AND DESIGN...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 4 Due Friday, October 23, 2009 Explain all answers! Problem 1 Fact (which you will see explained later in the course): A third order polynomial equation s 3 + as 2 + bs + c = 0 has roots with negative real part if and only if the coefficients a , b and c are all positive and ab > c . For the third order plant P ( s ) = 50 ( s + 1)( s + 5)( s + 12) consider using a PI controller with a zero at s = - 1. 1. Find the range of nonnegative values for the gain of the controller so that the closed-loop system in unity negative feedback is stable. 2. Use the ‘bode’ command in matlab to plot the loop gain when the gain of the PI controller is so that the closed-loop is on the border of stability. Comment on the slope of the magnitude plot at the crossover frequency, and also the phase angle at the crossover frequency. 3. Using the same Bode plot as in the previous plot, determine the crossover frequency when

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hw4 - ECE 147A FEEDBACK CONTROL SYSTEMS THEORY AND DESIGN...

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