(469c) Static Anti-Windup Controller Synthesis Using Simulations Convex Design

The behavior of linear, time-invariant (LTI) system subject to actuator saturation has been extensively studied over the past several decades. During this time, a natural division has occurred wherein two general methodologies have emerged for handling input saturation; those methods that account for saturation a priori and those which account for saturation a posteriori. Among theses techniques, the term anti-windup has been used extensively to describe a large class of input constrained control methodologies. A majority of these methods remained a posteriori techniques, following a two step design methodology: Design first the linear controller ignoring effects of any control input nonlinearity and then add anti-windup compensation to minimize the adverse effects of any control input nonlinearities on closed loop performance. The main advantage of this design methodology is that no restrictions are placed on the original linear controller design. The main disadvantage it that although the linear controller and anti-windup compensator both affect the closed loop performance under saturation is completely ignored, by definition.

In this paper, we propose a control law with the structure of the traditional anti-windup design: a linear controller and static anti-windup compensation. Unlike the traditional two-step design procedure for anti-windup, however, we propose a method for the simultaneous synthesis of both the linear and static anti-windup compensator. There are several instances where the anti-windup retrofits to existing linear controller which involve not only the addition of ant-windup compensation but also retuning/detuning of the original linear controller parameters. Such retuning/detuning of the original linear controller during anti-windup retrofitting is currently carried out using as-hoc guidelines involving an intuitive understanding of the interactions and trade-offs between linear and constrained closed loop responses. The proposed method provides a systematic framework for carrying out these trade-offs in a multi-objective settings.

In designing an anti-windup control system, the designer must choose which control channel to optimize and moreover, in what sense to optimize the chosen channel. Some authors have proposed directly minimizing the gain from reference and disturbance signal to the output error or state error while other authors have suggested minimizing the gain from the controller output error to the output or state error. In our framework, all forms can be handled directly by appropriately defining w and z. Moreover, when deciding in what sense to minimize a particular input-output channel, several choices have been suggested, although the induced L2 gain is a popular choice. Here, we wish to present in detail two possible performance objectives, the induced L2 gain and the peak-to-peak gain, for the saturating closed-loop that can be used in an over-all possibly multi-objective synthesis. In this paper,

We present a framework for the synthesis of a constrained linear control law which incorporates both traditional linear output-feedback controller and static anti-windup compensator. However, our work differs from the traditional anti-windup synthesis where the output-feedback controller is synthesized first, followed by the anti-windup compensator. In our method, all controller parameters are synthesized simultaneously. Thus, our simultaneous approach provides:

* A systematic framework for the synthesis of a control law where the effect of all controller parameters can be utilized to design the unconstrained and constrained closed-loop performance.

* A framework for the synthesis of a control law which provides, a priori, bounds on multiple unconstrained/constrained performance objectives and allows insight into the trade-off between each objectives.

* A method for bounding constrained performance with a choice of several objectives. Previously reported LMI anti-windup synthesis techniques are limited to only L2 gain (or closely related) performance objectives.

Moreover, synthesis is achieved through optimization over Linear Matrix Inequalities(LMIs). Thus, our method provides a practical and effective method for the control of LTI plants subject to actuator saturation.