Control saturation prevention for linear parameter-varying (LPV) systems

In many applications, it is essential to limit control signals. This dissertation presents methods that process accessible control system signals (e.g., plant and compensator states, reference commands) to limit control signals. In contrast to "classical techniques" which limit variables by unnecessarily reducing control system bandwidth, the proposed methods limit variables in a nonconservative manner, reducing bandwidth only when necessary. A fundamental contribution of this work is that the methods presented are applicable to linear parameter varying (LPV) and quasi-LPV plants and controllers. This is particularly significant given the research community's acceptance of the LPV framework as an effective way to represent nonlinear plants and (gain-scheduled) controllers. The methods presented rely on appropriately "scaling back" key signals. An error governor system exploits real-time controller state and error signal measurements, a look-ahead function, and on-line optimization to appropriately "scale back" error signals entering the nominal controller. A reference governor system exploits real-time plant and controller state measurements, reference command measurements, a look-ahead function; and on-line optimization to appropriately "scale back" reference commands. It is assumed that a nominal LPV controller internally stabilizes the LPV plant when no saturation is present. The "scaling back" is done in a manner which (1) limits control signal levels, (2) ensures closed loop stability for the closed loop LPV system with saturating actuators, and (3) maintains, to the extent possible, the "directionality properties" of the original LPV control system design. As such, the methods presented provide a new systematic approach for addressing saturation issues within LPV gain scheduled control systems. The methods are conservative in that they are applicable to "slowly varying" LPV systems. Ideas for removing the associated conservatism are discussed. Computational issues are also addressed. Although the methods require access to all internal closed loop system state variables, one could use an appropriately designed LPV state estimator, if necessary. This extension is not addressed. The methods are applied to several LPV and quasi-LPV systems, including a nonlinear model for an unstable missile. It is also shown how the methods presented may be used to limit other important variables (e.g., angle-of-attack, speed, etc.).