Advanced and Optimization Based Sliding Mode Control

This monograph on control theory explores advanced methods for sliding mode control and optimized algorithms for special sliding mode control applications. Sliding mode control is a nonlinear method in control theory designed to drive a system’s state onto a special subset of state space called the sliding manifold. Once the sliding manifold is reached, sliding mode control is designed to keep future states near it. A sliding mode controller then has two parts: design of the sliding manifold so that the system’s subsequent evolution satisfies the design specifications, and design of the control law that makes the switching manifold an attractor in state space.

 

The advantages of a sliding move controller are several. The method gives closed-loop control of the system while reducing sensitivity to uncertainties in model parameters, external disturbances, and nonlinearities. One of the most interesting parts of sliding mode control is the discontinuous nature of the control action whose primary role is to switch between two system components that are distinctly different. A very simple example is a control system whose controls are limited to “on” or “off”. Of course, most are a good deal more sophisticated. Among the several applications of sliding mode are anti-lock brake control and electronic throttle control. 

 

Although sliding mode control is very promising and has been successful in several applications, its greatest challenge has been to deal with the phenomenon of chattering. Chattering appears as rapid motion that oscillates about the sliding manifold. It can arise because fast dynamics (high-frequency switching, for example) appear in the control loop that are not anticipated in the system model, or because digital implementations of controllers with fixed sampling rates are not fast enough to match the dynamics. The authors offer several methods for higher=order sliding control that can alleviate chattering.

 

Much of the book is devoted to a description of advanced, optimized and specialized sliding mode control. Among the issues the authors consider are minimum-time convergence to the sliding manifold, algorithms for systems with input and state constraints, event-triggered and model-based control, and control for networked systems. One of the most interesting applications of advanced sliding mode control is distributed and decentralized control of electric power generation by solar or wind power.

 

This book requires significant background in control theory and the design of control algorithms. It is based in large part on a collection of the authors’ more recent published results. A reader with only a casual interest in control theory would find it tough going.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications ranging from speech recognition and network modeling to optical films and material science. He did his PhD work in dynamical systems and celestial mechanics.