Robust disturbance rejection for discrete-time systems having Magnitude and rate bounded inputs

Abstract

The design of a robust controller for uncertain discrete-time systems subject to bounded disturbances and having magnitude and rate bounded actuators is considered. To tackle the problem, the proposed method utilises nested ellipsoids and employs an incremental (velocity) form of the state-space model of the system. By using modified full block S-procedure, the proposed robust control design approach is applicable to any uncertain system with rational parameter dependence which cannot be managed by the existing approaches without introducing some extra conservatism. Finally, an algorithm that allows the method to be used as a gain-scheduling controller is also noted in the study.

Robust gain-scheduling H∞ control of uncertain continuous-time systems having magnitude- and rate-bounded actuators: An application of full block S-procedure

“…In this work, we employed Pólya relaxation for checking the feasibility of the infinite-dimensional MI condition (35). The details of the application is presented in Section 5.1.2 of the paper by [26].…”

“…Again, they did not touch on the robustness problem of the controller in their study. Other techniques that deal with the problem include use of saturation blocks in nested configuration [6,43,51,33], nested and attractive ellipsoids [26], MPCs [31] and representation of the actuator with low order sluggish model [25,23,9]. Particularly, [26] considers a GS stabilisation problem in the discrete-time domain by utilising nested and invariant ellipsoids without considering any performance objectives.…”

“…Other techniques that deal with the problem include use of saturation blocks in nested configuration [6,43,51,33], nested and attractive ellipsoids [26], MPCs [31] and representation of the actuator with low order sluggish model [25,23,9]. Particularly, [26] considers a GS stabilisation problem in the discrete-time domain by utilising nested and invariant ellipsoids without considering any performance objectives. On the other hand, the GS technique introduced in this reference is based on a switching mechanism in which the controller changes its feedback gain depending on the existence of saturation.…”

“…If a saturation occurs, the supervisory mechanism switches to a lower pre-determined gain ensuring that a highest gain that is not saturated would be the one to be used at all times. Therefore, the technique used in [26] works in a way similar to the working principle of an anti wind-up (AW) mechanism and, therefore, prone to ringing problems.…”

“…Therefore, a smooth operation is always achieved. Compared to its AW counterparts and [26], the proposed technique of this present paper does not contain any ringing problem which may lead to a discontinuity in the control signal. Hence, the proposed technique is well suited for use in mechanical systems which are prone to damage because of stringent working conditions and exposition to excessive usage.…”