A windup prevention scheme for exponentially unstable SISO plants

A linear controller for exponentially unstable plants may give rise to severe windup problems when input saturation becomes active, and this also, after the usual reset windup or controller windup has been removed by appropriate measures. This plant windup depends on how far the poles are shifted to the left, and it reduces the allowable reference step amplitudes not hazarding closed loop stability to possibly extremely small values. Reducing the amount of pole shift also reduces the windup effects, however at the expense of (input) disturbance rejection. Based on a structure proposed by Teel, a windup prevention scheme for exponentially unstable SISO plants is developed, which, given a nominal (linear) compensator, allows to apply reference steps almost within the whole amplitude region limited by input saturation, while assuring the same amount of input disturbance suppression as the controller without windup prevention. A model plant containing four exponentially unstable modes is used to demonstrate the results.