hmwk2_solns - C=4(1 2*s/s Integrator insures no steady...

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C=4*(1+2*s)/s Integrator insures no steady state error. Has rise time of 0.125 seconds, which is slightly less than 1/10 th the rise time of the plant in closed loop (1.5 seconds). Root Locus: -16 -14 -12 -10 -8 -6 -4 -2 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Root Locus Editor for Open Loop 1 (OL1) Real Axis Imag Axis
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Closed loop step response and closed loop control output: Step Response Time (sec) Amplitude Step Response Time (sec) Amplitude 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 System: Closed Loop r to y I/O: r to y Rise Time (sec): 0.125 System: Closed Loop r to y I/O: r to y Peak amplitude: 1.02 Overshoot (%): 2.09 At time (sec): 0.476 0 0.5 1 1.5 0 1 2 3 4 5 6 7 8 System: Closed Loop r to u I/O: r to u Time (sec): 0.332 Amplitude: 0.0941
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Open loop step response of plant to a step input of 1/20; rise time approx. 30 seconds: Closed loop step response of plant; rise time approx 1.5 seconds: Closed loop poles with controller ‘C’: -15.6, -0.513
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Bode Plot with gain and phase margins, and crossover frequency: c) Choose sampling frequency of 16.5*5 rad/sec = 82.5 rad/sec f=w/(2*pi) => Ts=2*pi/w = 2*pi/(82.5) seconds ZOH plant at this sampling time (use c2d command in matlab):
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