TABLE OF CONTENTS The review given in this appendix covers the essential background on linear parameter varying control theory. The emphasis is on the design tools and some aspects of controller implementation.
The main motivation behind gain scheduling is the extension of the well established linear control design tools to the nonlinear and time-varying systems. Gain scheduling techniques encompass a wide variety of design methods. Here, we will associate the term gain scheduling with the adjustment of the controller as function of some variables, which can be internal or external to the plant. These so-called scheduling variables have information about the nonlinearities of the plant.
In general, the design of a gain-scheduled controller can be organised into three steps:
In the first step, a set of operating points is selected. Next, a linear time-invariant (LTI) description of the nonlinear or time-varying system is derived for each operating point previously selected. Thus, a family of LTI models parametrised by the scheduling variables is obtained.
Then, an LTI controller is designed for each member of the family of models such that stability and performance are guaranteed at the corresponding operating point. Any available tool for linear control design can be used in this step.
The third step is the planning of the gain scheduling, i.e., the formulation of an algorithm that modifies the controller according to the value of the scheduling variables.
A commonly cited disadvantage of gain scheduling techniques is the lack of stability and performance...
