Dynamical anti-reset windup method for discrete-time saturating systems

doi:10.1016/S0005-1098(96)00208-7

Automatica

Volume 33, Issue 6, June 1997, Pages 1055-1072

https://doi.org/10.1016/S0005-1098(96)00208-7 Get rights and content

Abstract

This paper presents a dynamical anti-reset windup method for multivariable discrete-time saturating control systems. With the intention of maintaining the behavior of unsaturated linear systems as far as possible, an additional dynamical compensator is determined explicitly for the saturating system. Due to the additional compensator, the state positioning problem of saturated systems is completely resolved. The proposed method guarantees total stability of resulting systems, and asymptotic stability in the absence of exogeneous inputs can be addressed easily. The resulting dynamics of the compensated controller reflects the linear closed-loop system. The proposed method is applicable to any open-loop stable plants with saturating actuators and linear controllers. Simulation examples are included to illustrate the effectiveness of the proposed method.

References (36)

P.J. Campo et al.
Robust control of processes subject to saturation nonlinearities
Comput. Chem. Engng
(1990)
R.W. Cottle
Manifestations of the Schur complement
Linear Algebra Applies
(1974)
R. Hanus et al.
Conditioning technique, a general anti-windup and bumpless transfer method
Automatica
(1987)
M.V. Kothare et al.
A unified framework for the study of anti-windup designs
Automatica
(1994)
V.R. Saksena et al.
Singular perturbations and time-scale methods in control theory: survey 1976–1983
Automatica
(1984)
O. Agamennoni et al.
Robust controller design for a class of uncertain multivariable systems
B.D.O. Anderson et al.
K.J. Åström et al.
Integrator windup and how to avoid it
K.J. Åström et al.
P.J. Campo et al.
Multivariable anti-windup and bumpless transfer: a general theory

B.S. Chen et al.

The stability of feedback control with nonlinear saturating actuator: time domain approach

IEEE Trans. Autom. Control

(1988)

C.T. Chen

C.A. Desoer et al.

J.C. Doyle et al.

Control of plants with input saturation nonlinearities

A.H. Glattfelder et al.

Stability analysis of single loop control systems with saturation and antireset-windup circuits

IEEE Trans. Automatic Control

(1983)

A.H. Glattfelder et al.

Start up performance of different proportional integral antiwindup regulators

Int. J. Control

(1986)

P.-O. Gutman et al.

Admissible set and feedback control for discrete-time linear dynamical systems with bounded controls and states

IEEE Trans. Autom. Control

(1986)

R. Hanus et al.

Control of constrained multivariable systems using the conditioning technique

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Additional recent results within the reference governor scheme can be found in [1,2,9]. Aside from reference management, not much has been offered in the discrete-time setting for anti-windup designs that consider greater freedom in modifying the controller (a notable exception is [21]). Nevertheless, as it will be shown, if the anti-windup compensator can directly measure and modify signals within the closed-loop and the plant is not exponentially unstable, then even with disturbances1global results can be obtained. (
The anti-windup problem for discrete-time linear systems is formalized in terms of the $l_{2}$ norm of the deviation of the actual response of the system with saturation and anti-windup compensation from the (ideal) unconstrained response. We show that, paralleling continuous-time results [A.R. Teel, N. Kapoor, The $L_{2}$ anti-windup problem: its definition and solution, in: Proceedings of the 4th ECC, Brussels, Belgium, July 1997], the problem is globally solvable if and only if the plant is non-exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable. We provide a constructive solution whenever the problem is solvable. Also offered is a high-performance global solution for exponentially stable plants based on receding horizon control. Illustrative simulations are included.
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We will design the compensator M(s) so that the controller states in the presence of state constraints should keep track of those in the absence of state constraints. This concept is known to be effective in an AW compensation strategy (Hanus et al., 1987; Park & Choi, 1997; Peng et al., 1998). The objective of the proposed compensation scheme is to modify the controller in the presence of state constraints since we cannot access the plant directly.
Based on the dynamic anti-windup strategy, an alternative control methodology for state constrained systems is presented. The proposed method is an a posteriori approach for state constrained systems, which is differentiated from the usual a priori approach. That is, first a linear controller is designed to show a desirable nominal performance by ignoring state constraints. Then, an additional compensator is introduced to account for state constraints. By minimizing a reasonable performance index, a dynamic compensator is derived explicitly, which is expressed in plant and controller parameters. The proposed method not only provides a graceful performance degradation, but it also guarantees the total stability of the resulting systems. An illustrative example is given to show the effectiveness of the proposed method.
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Here we adopt an anti-windup scheme in Park et al. (2000). This scheme is based on the dynamic anti-windup method in Park and Choi (1995), and Park and Choi (1997). However this scheme also takes into account time delay in control input.
In this paper, we apply a dynamic anti-windup scheme for improving the performance of a conventional proportional–integral (PI) controller for active queue management (AQM) supporting TCP flows. When a PI controller is used for AQM, the windup phenomenon of the integral action can cause performance degradation because the packet drop probability is limited between 0 and 1. Therefore we suggest a TCP/AQM model with a saturating actuator and apply a dynamic anti-windup method for improving the performance of the conventional PI AQM scheme. The proposed scheme not only provides graceful performance degradation, but also guarantees the stability of the overall system with the linearized TCP model. We verify the performance of the proposed scheme through ns-2 simulations. The simulation results show that our scheme outperforms the conventional PI controller when the traffic load is not stationary, which is always the case in real network environment.
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Small-amplitude high-frequency noises are inevitable in practical systems and may induce adverse performance degradation, or instability, if not properly attenuated in saturation systems. This note establishes the necessary and sufficient conditions on saturation compensators for rate and amplitude constrained systems to attenuate noises in continuous time domains. For discrete systems, only necessary but not sufficient conditions can be found. Some existing compensators are analyzed using the obtained results and illustrated by a simulated example.

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^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Hassan K. Khalil under the direction of Editor Tamer Başar.

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PaperDynamical anti-reset windup method for discrete-time saturating systems☆

Abstract

Comput. Chem. Engng

Linear Algebra Applies

Automatica

Automatica

Automatica

Robust controller design for a class of uncertain multivariable systems

Integrator windup and how to avoid it

Multivariable anti-windup and bumpless transfer: a general theory

The stability of feedback control with nonlinear saturating actuator: time domain approach

IEEE Trans. Autom. Control

Control of plants with input saturation nonlinearities

Stability analysis of single loop control systems with saturation and antireset-windup circuits

IEEE Trans. Automatic Control

Start up performance of different proportional integral antiwindup regulators

Int. J. Control

Admissible set and feedback control for discrete-time linear dynamical systems with bounded controls and states

IEEE Trans. Autom. Control

Control of constrained multivariable systems using the conditioning technique

Paper
Dynamical anti-reset windup method for discrete-time saturating systems☆