Eric F. Mulder

Synthesis of Stabilizing Antiwindup Controllers Using Piecewise Quadratic Lyapunov Functions

We consider the problem of antiwindup controller synthesis based on the general antiwindup framework presented in Kothare (Automatica, vol. 30, no. 12, pp. 1869-1883, 1994) applicable to linear time-invariant systems (LTI) subject to a saturating actuator. Our synthesis approach takes advantage of the fact that the antiwindup system is a piecewise affine system and thus, we can utilize piecewise quadratic Lyapunov function theory Johansson and Rantzer (IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 555-559, Apr. 1998), Rantzer and Johansson (IEEE Trans. Autom. Control, vol. 45, no. 4, pp. 629-637, Apr. 2000), and Johansson (Proc. 14th World Congr., Beijing, China, 1999, pp. 521-5260) to determine a stabilizing antiwindup control law. The synthesis problem is expressed in terms of bilinear matrix inequalities (BMIs) and is solved using an iterative approach as well as using commercial software. The performance of the system is optimized by minimizing an upper bound on the induced gain of the system. The proposed approach is demonstrated using examples.

Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions

We consider the problem of multivariable anti-windup bumpless transfer (AWBT) controller synthesis based on the general AWBT framework presented by Kothare et al. (1994). Specifically, we propose a method for synthesizing AWBT compensators which stabilize linear time-invariant systems subject to saturating actuators. Our synthesis approach takes advantage of the fact that the AWBT system is a piecewise affine system and thus, we can utilize piecewise quadratic Lyapunov function theory to determine a stabilizing control law. The synthesis problem is solved via iteration between a set of linear matrix inequalities. The utility of the approach is demonstrated on a simple example where our method is shown to be less conservative.

Multivariable Anti-windup Controller Synthesis Using Bilinear Matrix Inequalities

We consider the problem of multivariable anti-windup bumpless transfer (AWBT) controller synthesis based on the general A WBT framework presented in (M.V. Kothare et al., Automatica 1994; 30(12): 1869–1883). We review several recent A WBT synthesis techniques. Next, we give a completely general formulation of the A WBT controller synthesis problem and show how this problem can be solved in terms of bilinear matrix inequalities (BMIs). For two simple examples, we demonstrate that an induced L 2 norm objective function is a sufficient performance indicator. Moreover, the objective minimum leads to multiple solutions for the static output feedback AWBT parameters, all of which provide equivalent output responses and graceful performance degradation under saturation. We also demonstrate the superior performance of the two parameter framework over an otherwise equivalent one parameter framework.

Multivariable Anti-Windup Controller Synthesis incorporating Multiple Convex Constraints

We study the problem of multivariable anti-windup controller synthesis that incorporates trade-offs between unconstrained linear performance and constrained anti- windup performance. In our previous work [13], we presented a framework for simultaneous design of a linear output feedback controller and a static anti-windup compensator using Linear Matrix Inequalities (LMIs). This framework deviated from the conventional two step paradigm of anti-windup by proposing a one-step synthesis while still maintaining the anti-windup structure. However, the work in [13] did not provide conclusive demonstration of the efficacy of this formulation through realistic practical examples. In this paper, we further study the framework in [13] and explicitly demonstrate its capability in providing effective constrained anti-windup controller performance for two benchmark problems, viz. a vibration isolation table and a multivariable model for the longitudinal dynamics of an F8 aircraft.