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# HWCE_3 - negative root loci 4 Turn in a MATLAB generated...

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HW/CE# 3 Due Thursday, Oct 8, 2009 (Revised) 1. Problems from franklin’s text: 4.7 part a 4.16 part a 4.19 parts a,b,and c 4.23 part a; Use the simpler approximating realtionships on the first page of the reference sheets and do your design for two different values of ζ , 0.5 and 0.7 2. Consider a system where: ) 68 4 ( ) ( 2 s s s K s KL Make a hand sketch showing the complete positive and negative root loci. Find the angles of the asymptotes for roots approaching zeroes at infinity and identify (the intersection of the asymptotes). Find the range of values of K for stable performance. Find the value of positive K at which roots cross over into the right half plane and the values of the roots on the imaginary axis for this value of K. 3. Turn in a MATLAB generated plot for the root locus. (This should be consistent with your hand sketch. You may submit one plot for the positive and a second plot for the
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Unformatted text preview: negative root loci.) 4. Turn in a MATLAB generated Bode plot for ) 68 4 ( ) ( 2 s s s K s KL where K is set to the positive value determined in problem 2. at which roots cross over into the right half plane, i.e., roots on the imaginary axis. Estimate from your Bode plot the frequency at which the magnitude of the response is 1.0 (0 dB) and the angle of the response is -180 o . 5. A certain system has a controller: 8 1 ) ( s s D c a) Assume the sampling rate T is 10% of the controller time constant. Find approximate expressions for D c [z] for a digital realization of the controller using: Tustin’s method Euler’s method b) Find a difference equation relating controller output to controller input for the D c [z] you found using Tustin’s method....
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