Uppsala universitet

Systematic Anti-Windup Compensator Design for Multivariable Systems

Jonas Öhr, Mikael Sternad and Anders Ahlén

Swedish Control Meeting ``Reglermöte'',
Luleå, Sweden, June 6-7, 1996.

The aim of anti-windup compensation is to modify the dynamics of a control loop when control signals saturate, so that a good transient behaviour is attained after desaturation, while avoiding nonlinear oscillations and repeated saturations. Model-based anti-windup compensation is here considered for multiple-input multiple-output (MIMO) systems.

We assume a model of a multivariable plant and a nominal controller structure to be given as rational fractional representations. A modified controller structure is proposed, which leaves the nominal closed-loop dynamics unchanged, as long as none of the control signals saturate.

By diagonalizing the loop gain around the saturation nonlinearity, the problem of modifying the behaviour during and after saturation is reduced to separate scalar design problems, one for each control signal. The multivariable control problem can then be solved by utilizing two concepts widely taught in basic control education: scalar loop gains and describing functions.

The design aim of obtaining a fast desaturation transient is sometimes contradictory to the aim of avoiding repeated resaturations, due to nonlinear oscillations. A H-2 optimization criterion is proposed as a tool for developing reasonable compromises.

The proposed approach is applicable to continuous-time as well as discrete-time systems. Although it is developed for systems in input-output form, it can be used for systems and controllers described in state-space form as well.

Related publications:
Conference paper (ECC 1997), which presents the methodology.
Internal Report, with details and examples.
Scalar case, described in a report by Rönnbäck and Sternad 1993.

Pdf, 287K.

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