14 - PoleZeroEffects14 filled

14 - PoleZeroEffects14 filled - ME575 Handouts Effect of...

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ME575 Handouts 1 ME575 Session 14 – Pole/Zero Effects School of Mechanical Engineering Purdue University Slide 1 Zero Complementary Sensitivity at all Zero Complementary Sensitivity at all Uncancelled Plant and Controller Zeros and Controller Zeros The zeros of the complementary sensitivity function include all uncancelled plant and controller zeros Sensitivity Value of 1 at all Sensitivity Value of 1 at all Uncancelled Uncancelled Plant Zeros Plant Zeros No command following or output disturbance rejection available a No command following or output disturbance rejection available a t t frequencies corresponding to pure imaginary plant zeros Zero Sensitivity at all Zero Sensitivity at all Uncancelled Plant/Controller Poles The zeros of the sensitivity function include all The zeros of the sensitivity function include all uncancelled uncancelled plant plant and controller poles and controller poles Complementary Sensitivity Value of 1 at all Complementary Sensitivity Value of 1 at all Uncancelled Uncancelled Plant and Controller Poles Plant and Controller Poles Perfect command following and disturbance rejection at frequenci Perfect command following and disturbance rejection at frequenci es es corresponding to pure imaginary poles of plant and controller . Effect of Plant Poles and Zeros Effect of Plant Poles and Zeros ME575 Session 14 – Pole/Zero Effects School of Mechanical Engineering Purdue University Slide 2 Lemma 8.1 (System Types for Reference Command) Lemma 8.1 (System Types for Reference Command) For stable CL system with one-DOF controller configuration, assume that open-loop TF has i free integrators or i poles at the origin, i.e., GC 0 1 i D (s)D (s) s D (s)D (s), i 1 D (0)D (0) c 0 N (0)N (0) c 0 = =≠ Then, for a step output step disturbance or step reference command, the error e(t) satisfies t 0 lim e(t) 0, i 1 e(t)dt 0, i 2 →∞ =∀ Effect of Open Loop Integrators Effect of Open Loop Integrators
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ME575 Handouts 2 ME575 Session 14 – Pole/Zero Effects School of Mechanical Engineering Purdue University Slide 3 Lemma 8.1 (continued) Lemma 8.1 (continued) Also, for a negative unit ramp output disturbance or a positive unit ramp reference command, the error e(t) satisfies 0 t 1 t 0 c lim e(t) , for i 1 c lim 0, i 2 e(t)dt 0, i 3 →∞ == =∀ Q: Is it possible to design a one-DOF controller to reject a ramp output disturbance that also has the property that the step response does not have any overshoot?
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14 - PoleZeroEffects14 filled - ME575 Handouts Effect of...

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