Author :
Tiwari, Pradeep Y. ; Mulder, Eric F. ; Kothare, Mayuresh V.
Abstract :
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.
Keywords :
Lyapunov methods; bilinear systems; continuous time systems; control system synthesis; iterative methods; linear matrix inequalities; linear systems; optimisation; stability; actuator saturation; antiwindup controller synthesis; bilinear matrix inequality; commercial software; iterative approach; linear time-invariant system; optimisation; piecewise affine system; piecewise quadratic Lyapunov function theory; stability; Automatic control; Convergence; Low-frequency noise; Lyapunov method; Noise robustness; Nonlinear control systems; Partial differential equations; Robust control; Stochastic resonance; Stochastic systems; Actuator saturation; antiwindup; bilinear matrix inequalities (BMI); constrained control; optimal control; piecewise linear system;
