Time-response shaping using output to input saturation transformation

Abstract

For linear systems, the control law design is often performed so that the resulting closed-loop meets specific frequency-domain requirements. However, in many cases, it may be observed that the obtained controller does not enforce time-domain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert prescribed bounds on an output variable into time-varying saturations on the synthesized linear control law. This transformation uses some well-chosen time-varying coefficients so that the resulting time-varying saturations do not overlap in the presence of disturbances. Using an anti-windup approach, it is demonstrated that the origin of the resulting closed-loop is globally asymptotically stable and that the regulated variable satisfies the time-domain constraints in the presence of an unknown finite-energy bounded disturbance. An application to a linear ball and beam model is presented.

Windup in Control Owing to Sensor Saturation

“…Despite its appealing properties, the compensator is somewhat complicated to implement. Another rather different approach has been recently proposed by [26] where output constraints are interpreted, via a transformation, as constraints on plant inputs and then an (input) anti-windup compensator may be used to prevent instability. This approach is attractive because it will prevent sensor saturation from occurring, but it is potentially conservative due to this.…”

Multicontrol Surface Optimization for Blended Wing–Body Under Handling Quality Constraints

“…Moreover, it is widely used in the literature (see, for instance, [21,29,51]). Research has been done on time-domain output bounding (see, for instance, [52]); the integration of this work to our process is left for future work.…”

An Anti-Windup Mechanism for State Constrained Linear Control of Wave Energy Conversion Systems: Design, Synthesis, and Experimental Assessment

“…Contemporary approaches for the solution of this problem can be found in e.g. [13], which include rigorous closed-loop stability guarantees, though at the expense of a relatively large set of parameters for effective constraint satisfaction, and an associated iterative procedure for its synthesis. Given that the ultimate objective (and strongest advantage) of non-optimisation-based control for WEC systems, which is the main concern of this paper, is that of simplicity of implementation, we propose a state constraint handling procedure based on the strategy in [14] which, as detailed throughout this study, provides a straightforwardly implementable methodology for state constraint satisfaction for a large class of devices.…”