A Frequency Domain Approach to Anti-windup Compensator Design

Mikael Sternad and Stefan Rönnbäck

Internal Report UPTEC 93024R, Dept. of Technology, Uppsala University.

Outline:

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 single-input single-output (SISO) systems and controllers in polynomial form.

Abstract:

The effect of input saturation in linear time invariant control systems is addressed. We utilize a controller in polynomial form, with a three degrees of freedom structure. This makes it possible to add a saturation compensator (an anti-windup filter) separately, after tuning of the controller properties for unsaturated signals.

Our aim is that the effect of a saturation event should decay as quickly as possible after desaturation, while the tendency for repeated re-saturations, due to nonlinear oscillations, should be suppressed. This is achieved by modifying the relevant loop gain by a safety margin. The modified loop gain is then adjusted, so that it touches the describing function of the saturation nonlinearity. The construction of the safety margin takes the magnitude of exogenous signals into account. The method requires only simple calculations. It can be automated, using a one-dimensional numerical search. Furthermore, the effect of D/A-quantization in digital feedback systems is also controlled by the same antiwindup scheme. The presence of unstructured errors in a linear plant model can be taken into account.

We also provide a discussion on how the frequency domain viewpoint can improve the understanding of previously suggested anti-windup methods, such as the observer-based approach, and the conditioning technique.

Related publications:

PhD Thesis by Jonas Öhr, 2003.

Conference paper (ECC'97) on the corresponding design for multivariable control systems.
Internal Report, with more details on the multivariable case.

Source:

Pdf 3000K.