# Anti-Windup Design with the SAW Library

Saturations (magnitude, rate, acceleration) are always present in control systems and must be taken into account either a priori or a posteriori to avoid loss of performance and possibly destabilization. This is classicaly achieved by an anti-windup structure as shown on, the figure below.

Figure 1: Anti-windup structure.

The anti-windup compensator $J(s)$ may be computed in several ways (see [1] for details):

• stability domain extension: the anti-windup gain is optimized so as to enlarge the stability domain against saturations, regardless of the performance level.
• performance enhancement: for a given stability domain, the anti-windup is tuned so that the nominal performance is preserved "as long as possible". This situation is clearly illustrated by the above scheme. The objective consists of minimizing the error signal between the saturated closed-loop output and a nominal linear reference model $L(s)$ output.

The tools included in the SAW library permit to set (with the Simulink interface) and solve easily the above two problems with static, fixed-order and full-order compensators. The main three routines of the library are:

• satsan: saturated systems stability/performance analyis by an LMI-based Lyapunov approach
• awlsyn:anti-windup design by a Lyapunov approach
• awhsyn:anti-windup design by a multi-objective $H_\infty$ design approach (available soon with version v2 of the library)

The best way to start with the tools is to run the examples contained in a specific folder of the package.

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