lab_4_f07 - EE 350 LINEAR SYSTEMS ANALYSIS Fall 2007...

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EE 350 LINEAR SYSTEMS ANALYSIS Fall 2007 Laboratory #4: Feedback Control The objectives of the fourth laboratory are as follows. Introduce MATLAB commands relevant to Laplace transform analysis. Show, by experiment, that a closed-loop system is more robust at rejecting disturbances than an open-loop system. MATLAB commands Relevant to Laplace Transform Analysis 1. The MATLAB command step calculates the step response of a LTI system. As an example, consider a second-order system with unity DC gain, ζ =0 . 2, ω n = 1 [rad/sec]: % Describe the system in terms of the transfer function Kdc = 1; z = 0.2; wn = 1; num = [Kdc*wn^2]; den = [1,2*z*wn,wn^2]; % Find the step response (MATLAB automatically plots the response) step(num,den) 2. When it is necessary to know the response of a system to a more general input, use the lsim command. Simulate the the response of the previous system to the input u ( t - 10) - u ( t - 40): % Construct the input f(t) t = linspace(0,100); f = [0*ones(1,10),ones(1,30),0*ones(1,60)]; lsim(num,den,f,t) %plot f on top of response hold plot(t,f,’r:’) 3. Another command of interest is pzmap , which constructs a pole-zero map for a given transfer function: % Describe the system in terms of the transfer function num = [1,3]; den = [1,2,2]; pzmap(num,den) 1

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4. The fourth command provides the partial fraction expansion of a transfer function:
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This note was uploaded on 07/23/2008 for the course EE 350 taught by Professor Schiano,jeffreyldas,arnab during the Fall '07 term at Pennsylvania State University, University Park.

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lab_4_f07 - EE 350 LINEAR SYSTEMS ANALYSIS Fall 2007...

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