|Abstract:||In many applications, a controller must accommodate a plant with changing objectives, operating conditions, and behaviors. Such plants include a wide variety of complex mechanical systems including turbofan engines, aircraft, wind turbines, and internal combustion engines. Frequently, a fixed controller cannot accommodate such changes without significant deterioration in performance. A practical alternative involves switching or blending among a family of controllers in response to changing objectives and behaviors, thereby allowing improved performance over a fixed controller. Bumpless-transfer and gain scheduling are two common techniques that rely on controller switching or blending. The broad appeal of such techniques arises from addressing each situation individually rather than the entire set simultaneously. Consequently, each controller may be optimized and tuned for its respective situation without incurring trade-offs that compromise performance for the remaining situations.
However, switching and blending controllers may induce undesirable transients, which may lead to performance losses and instability. For example, switching between controllers with integrators may severely degrade performance due to a phenomenon called integrator windup. Even very simple controllers and systems can suffer ill effects from controller switching. In brief, closed loop performance degradation resulting from controller switching and blending can be attributed to "controller fighting" or improper coordination and sharing of a single set of plant inputs among the controllers.
This research focuses on designing the dynamic transition between controllers, termed controller interpolation, to meet stability and performance objectives. First, an intuitive definition of the controller interpolation problem is presented. The resulting set of controller interpolation criteria is translated into a parameterization of all stabilizing interpolated controllers leveraging a Youla controller parameterization. Second, an interpolation framework is proposed for cases that lack an appropriate controller parameterization. The proposed framework mediates the interaction among controllers and includes interpolated controller parameterizations as a special case. For a class of linear parameter-varying plants, a convex optimization problem was formulated using the framework, and the framework is applied to optimize the gain scheduled controller interpolation with respect to an H∞ norm.