Design of PID controllers using Filippov's method for stable operation of DC–DC converters

Abstract

SummaryA lot of work has taken place into the design and control of DC–DC converters, and various methodologies have been proposed. While traditionally only P or PI controllers have been employed, recent applications that require a fast transient performance impose the usage of the derivative, D, term. As it is well known, using the D‐term can cause numerous problems in such converters that greatly downgrade their performance and lifetime. Having said that, in this paper, we first prove that by using the D‐term, it is possible to increase the stability margin (and hence keep a low current ripple), and then, we present a novel method to tune the PID controller that guarantees a fast and stable response over a wide range of parameter values without using an unreasonably high value of the derivative gain that magnifies the presence of noise in the system. The controller is designed utilising Filippov's method, and a simple and easy to implement strategy is proposed. Furthermore, an adaptive PID controller is designed whose gains are changed depending on the value of the supply voltage or output load. Another important contribution of this work is the derivation of the saltation matrix when the switching manifold is discontinuous, the complete proof is presented, and the results validated. Copyright © 2015 John Wiley & Sons, Ltd.