Dynamic anti-windup design for a class of nonlinear systems

ABSTRACT

This work addresses the dynamic anti-windup design problem for a class of nonlinear systems subject to actuator saturation. The considered class regards the systems that can be cast in a differential algebraic representation (DAR), such as rational and polynomial systems. Considering that a nonlinear dynamic output feedback controller, which can also be written as a DAR, has been designed to stabilise the nonlinear system disregarding the saturation effects, LMI-based conditions are proposed to compute a stabilising dynamic anti-windup compensator. Two problems are considered: the first one regards the regional internal stabilisation; and the second one, assuming that an energy-bounded disturbance acts on the system, concerns the ${\mathcal{L}}_2$ input-to-state stability. The derived conditions can therefore be incorporated in convex optimisation problems that allow to compute the anti-windup compensator in order to maximise the region of guaranteed asymptotic stability, to maximise a bound on the admissible ${\mathcal{L}}_2$-norm of the disturbance or even to minimise a bound on the ${\mathcal{L}}_2$-gain between the disturbance and the output. Numerical examples illustrate the proposed methods.

Keywords:

• Anti-windup
• nonlinear systems
• rational systems
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of M.B. Longhi was supported by CAPES (MSc. Scholarship), Brazil. J.M. Gomes da Silva Jr. was partially supported by CNPq (grants PQ 306210/2009-6, UNIV. 480638/2012-8), Brazil.