A new view of anti-windup design for uncertain linear systems in the frequency domain

Abstract

Summary This paper presents a new perspective on the stability problem for uncertain LTI feedback systems with actuator input amplitude saturation. The solution is obtained using the quantitative feedback theory and a 3 DoF non‐interfering control structure. Describing function (DF) analysis is used as a criterion for closed loop stability and limit cycle avoidance, but the circle or Popov criteria could also be employed. The novelty is the combination of a controller parameterization from the literature and describing function‐based limit cycle avoidance with margins for uncertain plants. Two examples are given. The first is a benchmark problem and a comparison is made with other proposed solutions. The second is an example that was implemented and tested on an X‐Y linear stage used for nano‐positioning applications. Design and implementation considerations are given. An example is given on how the method can be extended to amplitude and rate saturation with the help of the generalized describing function, and a novel anti‐windup compensation structure inspired by previous contributions. Copyright © 2015 John Wiley & Sons, Ltd.

A New Anti-Windup Compensator Based on Quantitative Feedback Theory for an Uncertain Linear System with Input Saturation

“…Moreover, the saturation input and output are represented by U and V. The 2-DOF structure does not make it possible to avoid limit cycling in a conditionally stable system. This work is extended for the 3-DOF structure in [13], similar to the one shown in Figure 2, suggested by Horowitz [14]. In this figure, C and H represent the feedback controller and the AW controller, respectively.…”

“…The idea is to replace the nonlinear system by an equivalent frequency locus and use it jointly with the uncertain linear systems to compute the constraint region for a stabilizing controller using the QFT loop shaping. The multiplier theory is extended for a 3-DOF non-interfering control structure in [16] as shown in unlike the method in [13], in which one must take care of unstable pole-zero cancellation in designing the AW controller. 4.…”

“…4. The effectiveness of the proposed method is validated through a comparative work between the proposed method and existing methods [13,16] using a benchmark problem. It is found to perform better than the existing methods, in terms of lesser overshoot than [13] and faster response time as compared to [16].…”

“…The difficulty in searching for the multiplier (infinite dimension) [16] and the restriction involved in designing the AW controller (pole-zero cancellation, strictly proper) [13] are the main motivation for this work. In other words, the main aim of this article is to present a QFT-based AW design to alleviate the effects (divergent limit cycle for conditionally stable system) of saturation nonlinearity in uncertain linear SISO systems using the 3-DOF non-interfering structure (direct manner).…”

“…The technical novelty is the development of the proposed method directly on the 3-DOF non-interfering control structure, shown in Figure 3, as opposed to the indirect method [13]. With this framework, the proposed method does not require any restriction on the AW controller unlike the method in [13], in which one must take care of unstable pole-zero cancellation in designing the AW controller.…”