Positive μ modification as an anti-windup mechanism

This paper proposes a simple anti-windup mechanism for a model reference adaptive control scheme subject to saturation constraints. The anti-windup compensator has, in essence, the same structure as positive μ modification for the same class of systems. It is shown how this structure can, under certain circumstances, display characteristics similar to anti-windup schemes proposed for linear control systems. In particular, it is shown that if the (unknown) ideal control signal eventually lies within the control constraints, then the response of the adaptive control system will converge to that of the reference system—provided certain conditions are satisfied. The paper illustrates the challenge of designing anti-windup compensators for model-reference adaptive control systems

Anti-windup compensation for systems with sensor saturation: a study of architecture and structure

This article proposes a linear dynamic anti-windup strategy for the alleviation of performance and stability problems in systems which are linear apart from saturating sensors. Unlike anti-windup compensation for systems subject to actuator saturation, there is no agreed architecture for applying anti-windup to systems with sensor saturation and therefore attention is devoted to the discussion of various candidate configurations which can be interpreted as a particular choice of a static non-linear map. The main results of the article give existence conditions for compensators which yield global exponential stability and finite L2 gain of the overall non-linear closed-loop system. The existence conditions are different to those which have appeared hitherto in the literature

Lyapunov functions and L-2 gain bounds for systems with slope restricted nonlinearities

The stability and L2L2 performance analysis of systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static nonlinear element which is Lipschitz, slope restricted and sector bounded is revisited. The main thrust of the paper is to improve and extend an existing result in the literature to enable (i) concise and correct conditions for asymptotic stability of the interconnection and (ii) reasonably tight bounds on the L2L2 gain between an exogenous input and a given output to be obtained. Numerical examples indicate that the proposed algorithm performs well compared to competing results in the literature

Analysis of Systems With Slope Restricted Nonlinearities Using Externally Positive Zames–Falb Multipliers

This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames-Falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive non-causal transfer function. By restricting attention to a sub-set of these multipliers, a set of pure LMI conditions is obtained which requires no initial paramterisation by the user. A useful by-product of using externally positive systems is that the results are applicable to non-odd slope restricted nonlinearities, which is not the case for all classes of Zames-Falb multipliers

Nonlinear regulation in constrained input discrete-time linear systems

The use of composite linear and non-linear feedback laws for the control of constrained input discrete-time linear systems is re-examined. By making use of the delta operator formulation of a discrete-time system, an apparent restriction on the magnitude of the non-linear control law is removed, and the similarities between the continuous and discrete-time solutions to the problem are elucidated. In order to develop the results, unconstrained systems are treated initially, but it is shown that, locally, the sufficient conditions for the stabilization of such systems are actually equivalent to those for the stabilization of the corresponding constrained systems

A new perspective on static and low-order anti-windup synthesis

By viewing the anti-windup problem as a decoupled set of subsystems and relating this configuration to a general static anti-windup set-up, LMI conditions are established which guarantee stability and performance of the resulting closed-loop system. The approach taken, and the mapping used for the performance index, are logical and intuitive--and, it is argued, central to the 'true' anti-windup objective. The approach enables one to construct static anti-windup compensators in a systematic and numerically tractable manner. The idea is extended to allow low-order anti-windup compensators to be synthesized, which, while being sub-optimal, can improve transient performance and possess several desired properties (such as low computational overhead and sensible closed-loop pole locations). In addition, low-order anti-windup synthesis is often feasible when the corresponding static synthesis is not

Improved Circle and Popov Criteria for systems containing magnitude bounded nonlinearities

This paper presents improved versions of the Circle and Popov Criteria for Lure systems in which the nonlinear element is both sector and magnitude bounded. The main idea is to use the fact that if the nonlinearity is magnitude bounded and the linear system is asymptotically stable, then its state will be ultimately bounded. When the state enters this set of ultimate boundedness, it will satisfy a narrower sector condition which can then be used to prove stability in a wider set of cases than the standard Circle and Popov Criteria. The results are illustrated with some numerical examples

Anti-windup design: an overview of some recent advances and open problems

The anti-windup technique which can be used to tackle the problems of stability and performance degradation for linear systems with saturated inputs is dealt with. The anti-windup techniques which can be found in the literature today have evolved from many sources and, even now, are diverse and somewhat disconnected from one another. In this survey, an overview of many recent anti-windup techniques is provided and their connections with each other are stated. The anti-windup technique is also explained within the context of its historical emergence and the likely future directions of the field are speculated. The focus is on so-called `modern' anti-windup techniques which began to emerge during the end of the 20th century and which allow a priori guarantees on stability to be made. The survey attempts to provide constructive LMI conditions for the synthesis of anti-windup compensators in both global and local contexts. Finally, some interesting extensions and open problems are discussed, such as nested saturations, the presence of time delays in the state or the input, and anti-windup for non-linear systems

A non-square sector condition and its application in deferred-action anti-windup compensator design

A sector condition for two connected deadzone nonlinearities is provided. By introducing an additional non-square operator which exploits their connectivity, a more general set of sector-like matrix inequalities is obtained. This “non-square” matrix inequality condition is applied to an anti-windup (AW) problem in which the AW compensator is not activated until the unconstrained control signal reaches a well-defined level beyond that of the physical actuator limits. The non-square sector condition allows such “deferred-action” AW synthesis to be performed in a manner much closer to traditional (“immediate”) sector-based AW with either lowered conservatism or decreased computational effort in contrast to recent work. The non-square condition is applicable to other AW problems

Output Violation Compensation for Systems with Output Constraints

The problem of output constraints in linear systems is considered, and a new methodology which helps the closed loop respect these limits is described. The new methodology invokes ideas from the antiwindup literature in order to address the problem from a practical point of view. This leads to a design procedure very much like that found in antiwindup design. First, a linear controller ignoring output constraints is designed. Then, an additional compensation network which ensures that the output limits are, as far as possible, respected is added. As the constraints occur at the output, global results can be obtained for both stable and unstable plants