Anti-windup for exponentially unstable linear systems

摘要

An algorithm for combining arbitrary linear and nonlinear controllers is specialized to the control design problem for exponentially unstable linear systems with input saturation. The algorithm solves an anti-windup problem: first, the linear controller operates without assistance as long as it does not encounter input saturation; second, under natural restrictions on the initial conditions of the exponentially unstable modes and on the eventual behaviour of the linear response, the nonlinear response is guaranteed to converge to the linear response. There is no restriction on the transient behaviour of the linear response nor on the initial conditions of the modes that are not exponentially unstable. The linearized model of the inverted pendulum with input saturation is used to illustrate the capabilities of the algorithm.