Coprime factor anti-windup for systems with sensor saturation

Abstract

This paper considers the design of anti-windup compensators for linear systems with saturated sensor measurements. The architecture used for the anti-windup (AW) compensators resembles that commonly used in fault-detection and high performance control, rather than the traditional antiwindup approach. Stability of the system is examined and it transpires that the design problem reduces to choosing appropriately a coprime factorisation of the plant, and its associated Bezout complement. In turn, this new problem has a statespace interpretation which requires the choice of appropriate state-feedback and observer gains such that a certain nonlinear matrix inequality (NLMI) is feasible. Although this NLMI is not easily linearised, it is shown that, providing the plant under consideration is detectable and controllable, there always exists a choice of parameters such that this inequality is satisfied and therefore, there always exists an anti-windup compensator (of this particular form) such that the overall closed-loop system with sensor saturation is asymptotically stable.

Prevention of windup in output constrained minimum-phase systems

“…Though this does not lead to an unstable behaviour, it opens the loop and leads to more prolonged disturbance transients. Choosing insteadD(s) = D(s) and ∆(s) = ∆ r (s)N (s) with ∆ r (s) = (s + 50) 2 the transfer function of the resulting compensator has the form G C (s) = 7500(s + 1) 3 2(s + 2)(s + 100)s (11) leading to aḠ L (s) = −2500/(s + 50) 2 which also satisfies the circle criterion. The broken line in Figure 3 shows the disturbance step response resulting with the compensator (11) which is considerably improved in relation to the one resulting with the compensator (10).…”

“…In [10] the rejection of disturbances has been investigated, but only for L 2 -bounded signals. An interesting approach which allows for persistent disturbances was presented in [11]. It does not assure, however, linear performance recovery and it leads to eigenvalues of the closed loop whose real parts tend towards minus infinity.…”

Windup in Control Owing to Sensor Saturation

“…Anti-windup control for output-constrained systems is considered in the following papers. In [23], persistent disturbances were allowed, but the scheme does not assure Linear Performance Recovery (LPR) and it leads to eigenvalues of the closed loop whose real parts tend to minus infinity. In [24], various possible configurations of anti-windup systems are discussed, but the authors state that there is no agreed architecture for applying anti-windup to systems with sensor saturation so far.…”

Vermeidung von Windup bei Ausgangsbegrenzung / Prevention of Windup in the Presence of Output Constraints

“…Der Nenner N L (s) + D L (s) von G mod L (s) ist nun das charakteristische Polynom 1 wenn y s ≥ y 0 > 0 0 wenn -y 0 < y s < y 0 1 wenn y s ≤ -y 0 (13) zum Einsatz, das einen Sättigungsindikator darstellt.…”

“…In [2] wurde die Ausregelung von Störungen untersucht, jedoch nur für L 2 beschränkte Signale. Einen interessanten Ansatz, der ständig einwirkende Störungen erlaubt, findet man in [13]. Er verändert aber das Verhalten des nominellen Reglers, d. h., er garantiert nicht die sogenannte "Linear Performance Recovery" (LPR) und er führt zu Eigenwerten des Regelkreises bei minus Unendlich.…”