Synthesis of Digital PID Controllers for Discrete-Time Systems With Guaranteed Non-Overshooting Transient Response
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In this paper, we present a new method of synthesizing digital PID controllers for discrete-time, Linear Time Invariant (LTI) Systems satisfying a class of transient response specifications. The problem of synthesizing a controller to achieve desirable transient specifications, such as requiring the transient response to be within an allowable range of overshoot, can be carried out as a problem of guaranteeing the impulse response of an appropriate closed loop error transfer function to be non-negative. An earlier result by the authors provides necessary and sufficient conditions for the impulse response of a discrete-time transfer function to be non-negative in terms of the requirement of a sequence of polynomials to be sign-invariant on the interval [1,∞). An application of this result to the error transfer function yields a sequence of polynomials which are required to be sign-invariant on [1,∞) but whose coefficients are polynomial functions of the controller gains k1,k2 and k3. Copyright © 2011 by ASME.
author list (cited authors)
Mohsenizadeh, N., Darbha, S., & Bhattacharyya, S. P.