## Analytic Feedback System Design: An Interpolation ApproachThis supplement presents the use of a technique derived from research conducted over the last 20 years. This technique, called interpolation theory in analytic design, is still not found in major introductory textbooks. Most introductory-level books teach trial and error design methods, not analytic design. Using this new technique, a mathematical existence theorem, and a solution algorithm, are posited and then used to solve a problem. Interpolation theory, which requires a minimal amount of mathematics, is the technique used to solve analytical design problems. The analytical design techniques presented in this book reflect modern approaches to problem-solving developed over the past 20 years (especially in the area of frequency domain), and are thoroughly up-to-date, as compared to the trial-and-error approach, which is now more than 30 years old. |

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### Contents

Introduction | 1 |

Design with Stable Compensators | 11 |

Design with Unstable Compensators | 29 |

Copyright | |

4 other sections not shown

### Common terms and phrases

algorithm analytic design BIBO stable function Bode plot Chapter closed-loop characteristic polynomial closed-loop poles closed-loop stability closed-loop system coefficients compensator C(s computed Consider the plant denominator polynomial denotes Dp(s DT-BIBO gain margin design given Hurwitz polynomial input internal stability interpolating SPR function interpolating unit interpolation approach interpolation conditions interpolation points interpolation problem interpolation values inverted pendulum kmax Matlab function nominal plant Note Nyquist plot Nyquist stability criterion p.i.p. condition parameterization phase margin Pi(s plant P(s plant transfer function plant with transfer poles and zeros poles of P(s Q-parameter design Q-parameterization rational function real axis referred relative degree robust stabilization root-locus root-locus plot s-plane satisfied sator sensitivity function shown in Figure simple proportional feedback Solution SPR array stability criterion stabilizes this plant stable compensator stable stabilizing compensator steady-state error strictly positive real tion transfer function P(s unit circle unit U(s unstable poles unstable zeros Youla Z-transform