A framework for multivariable algebraic loops in linear anti-windup implementations

Abstract

This brief paper addresses the implementation and well-posedness aspects of multivariable algebraic loops which arise naturally in many anti-windup control schemes. Using the machinery of linear complementarity problems, a unified framework is developed for establishing well-posedness of such algebraic loops. Enforcing well-posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti-windup design stage. Several existing anti-windup implementations appear as special cases of the unified framework presented in this brief paper.

Fixed-Dynamics Antiwindup Design: Application to Pitch-Limited Position Control of Multirotor Unmanned Aerial Vehicles

“…where x := (x a , x rm , w) ∈ R n a +n cl +n w =: R n x and Considering system (12), the design of the AW compensator can be associated with the solutions to the following problem.…”

“…Proof. The proof combines the steps used to derive the proof of the continuous-time version in [5] and some ideas borrowed from [10] to show that under the generalized sector condition used, e.g., in [6], one can guarantee a decrease of a quadratic Lyapunov function along the dynamics of system (12). Before proceeding, note that the algebraic-loop is well-posed by virtue of the inequality −2U + D yq U +UD yq < 0 (which is implied by (17)) and let us recall the following Lemma from [10], which will be exploited in the next steps.…”

“…) is inside the region of attraction of the origin (12). In other words, the region of attraction contains a convex set whose vertices represent initial conditions corresponding to reference signals each made by a step of a given amplitude along one principal direction.…”

Performance and Configuration Analysis of Tracking Time Anti-Windup PID Controllers

“…This characteristic is referred to as integral windup and it is the actual factor that is responsible for unchanged output of a system despite increase in error value. Efforts to solve the windup problem have led to the emergence of several methods to prevent windup in any given system [6]…”

Development of an Antiwindup Technique for a Cascade Control System

“…16 , 17 Only a few antiwindup techniques have been proposed to manipulate the cascade-type integral windup phenomenon in a cascade PID control system. 18 − 21 However, these techniques require an additional process model and cannot systematically manipulate the time delay. Furthermore, they are considerably complicated and necessitate the application of a heavy computation load, eliminating the advantage associated with the use of the PID controller.…”