A well-known problem called the windup phenomenon has been comprehensively investigated by control system designers that derate the performance of closed-loop systems using controllers having integral action. In simulation-based tuning, if the windup phenomenon is ignored, even a stable design can yield an unstable system. The main cause of the windup phenomenon is control effort saturation-a very realistic and almost ubiquitously encountered constraint. Several techniques for mitigating the windup phenomenon have been proposed in literature. An exclusive class of techniques called anti-windup techniques has also been described. Such techniques involve the use of internal loops for partial compensation that use the difference between the unsaturated control effort at the controller output and the effective saturated control effort applied at the actuator. Some of these techniques are relatively complex and of higher orders; in some cases, the techniques employ dynamic compensation of the same order as that of the plant. In this paper, we propose a simple feedforward scheme as an anti-windup technique in which the integral operator is deformed; this technique is inspired from the so-called deformed calculus-a generalization of the integrals and derivatives based on the nonextensive statistical mechanics of Tsallis. With regard to deformed integral action, we have prepared a computational method for tuning the q-parameter on the basis of the minimization of an integral square error root square criterion. The proposed scheme has been simulated using examples of feedback systems; the simulation results demonstrate the advantages of the proposed technique in comparison to techniques proposed in related works. Further, a preliminary stability study is formulated in order to investigate the impact of the proposed method on system design.

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