NDLI: Synthesis of PID controllers with guaranteed non-overshooting transient response

Content Provider	IEEE Xplore Digital Library
Author	Mohsenizadeh, N. Darbha, S. Bhattacharyya, S.P.
Copyright Year	2011
Description	Author affiliation: Department of Electrical Engineering, Texas A& M University, College Station, 77843, USA (Bhattacharyya, S.P.) \|\| Department of Mechanical Engineering, Texas A & M University, College Station, 77843 USA (Mohsenizadeh, N.) \|\| Department of Mechanical Engineering, Texas A& M University, College Station, 77843, USA (Darbha, S.)
Abstract	This paper presents a new method for approximating the set of PID controllers satisfying a class of transient specifications. The problem of designing a controller to satisfy transient specifications such as the maximum allowable overshoot to a given input or the response being required to be within an envelope can be cast as a problem of guaranteeing the impulse response of an appropriate closed loop error transfer function to be non-negative. Stabilizing PID controllers for Linear Time Invariant (LTI) systems can be synthesized as a union of convex polygons in ki − kd space for kp's lying in a specific range. In this paper, we provide a method to restrict the stabilizing set for LTI systems further by using Widder's theorem and Markov-Lucaks representation for polynomials that are non-negative on the positive real axis. Widder's theorem provides necessary and sufficient conditions for the error response to be non-negative and upon an application of Widder's theorem, we obtain a sequence of polynomials, whose coefficients are polynomial functions of kp, ki and kd to be non-negative. For every polynomial in the sequence and for a specified kp, using Markov-Lucaks theorem and Minkowski's projection, we obtain a polynomial inequality in ki and kd that must be satisfied by every controller satisfying the desired transient specification. We also provide a method to arbitrarily tighten this set of desired controllers.
Starting Page	447
Ending Page	452
File Size	253603
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6161429
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Polynomials Transfer functions Transient analysis Transient response USA Councils Closed loop systems
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Modeling and Simulation Control and Optimization

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