A Simple Anti-Windup Strategy for State Constrained Linear Control

Rojas, Osvaldo J.; Goodwin, Graham C.

doi:10.3182/20020721-6-es-1901.01089

Cited by 14 publications

(10 citation statements)

References 9 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other possible and very useful methods [8], [11], [12] address output constraints problems for nonlinear systems of special form and/or try to escape the constraints while L. Burlion is with Onera -The French Aerospace Lab, F-31055 Toulouse, France. (Laurent.Burlion(at)onera.fr) our design can be applied to a broad class of nonlinear system (for instance, thanks to our design, we can saturate any nonlinear function of the state if it is controllable) and enables to remain on the constraints limitations offering thus the possibility to use anti-windup loops as in [2], [1]. This paper is organized as follows : the basic notations and our two main results are given in Section 2 : the first one shows how one can transform an output constraint into an input constraint for a perfectly known general nonlinear system whereas the second one addresses the same problem in presence of disturbances.…”

Section: Introductionmentioning

confidence: 98%

“…Concerning Linear systems, not only future prediction is easier but we can also apply some dedicated LMI-based methods [6], [2]. Moreover, state and input constraints problems are very close since it is possible to apply a relationship between a constrained output and an induced constrained input (whose constraints are state dependent) when the system is perfectly known and discretized [3], [1]. In this paper, we propose to generalize this idea to nonlinear systems by transforming an output constrained nonlinear system into an input constrained nonlinear system whose constraints are state dependent.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new Saturation function to convert an output constraint into an input constraint

Burlion

2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

View full text Add to dashboard Cite

The main result of our new method is to convert an output constraint into an input constraint for a nonlinear system. Then, standard saturated input design can be used as an anti-windup design for instance which is known to be efficient to enlarge a closed-loop system stability domain in presence of control saturations. We only address the single input single 'saturated' output problem in this paper. I. INTRODUCTIONOutput and Input hard constraints problems arise in most of the control applications because achieving good performance often requires to reach the inherent physical and safety limitations of a concrete system. Even if one has to cope with possible future destabilizing effects, the application of a saturation placed just after an input is a simple and sure strategy to handle an input constraint whereas there does not exist an equivalent element for an output limitation. That's probably why the input constraint problem has received more attention in the past few decades (see for instance [4]). Existing solutions to these problems can be divided into two groups : those who predict the future of the closed loop trajectory and check if the constraints will be violated and the other, which at each time 'do their best' to avoid the constraints. Concerning Linear systems, not only future prediction is easier but we can also apply some dedicated LMI-based methods [6], [2]. Moreover, state and input constraints problems are very close since it is possible to apply a relationship between a constrained output and an induced constrained input (whose constraints are state dependent) when the system is perfectly known and discretized [3], [1]. In this paper, we propose to generalize this idea to nonlinear systems by transforming an output constrained nonlinear system into an input constrained nonlinear system whose constraints are state dependent. As we will see our method can still be applied when some disturbances are applied to the nonlinear system and does not require to discretize the system but contrary to the linear case it can be slightly conservative. By comparison to existing results based on nonlinear model predictive control [5], [9], [7], [10] (to cite a few), our method does not use prediction and can thus be easily implemented ; however, it is fair to say that we do not address several output constraints problems (where the number of inputs is inferior to the number of constrained outputs) in this preliminary work. Other possible and very useful methods [8], [11], [12] address output constraints problems for nonlinear systems of special form and/or try to escape the constraints while

show abstract

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A new Saturation function to convert an output constraint into an input constraint

Burlion

2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

View full text Add to dashboard Cite

show abstract

“…These strategies often include the control law design, especially when an optimising scheme is used. Alternative schemes including anti-windup systems were proposed for example in Turner and Postlethwaite (2002) and Rojas and Goodwin (2002). Compared to the aforementioned results, the anti-windup design is interesting because the nominal control law remains unchanged when acting far from the constraints.…”

Section: Introductionmentioning

confidence: 99%

Time-response shaping using output to input saturation transformation

Chambon¹,

Burlion²,

Apkarian³

2017

International Journal of Control

View full text Add to dashboard Cite

For linear systems, the control law design is often performed so that the resulting closed-loop meets specific frequency-domain requirements. However, in many cases, it may be observed that the obtained controller does not enforce time-domain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert prescribed bounds on an output variable into time-varying saturations on the synthesized linear control law. This transformation uses some well-chosen time-varying coefficients so that the resulting time-varying saturations do not overlap in the presence of disturbances. Using an anti-windup approach, it is demonstrated that the origin of the resulting closed-loop is globally asymptotically stable and that the regulated variable satisfies the time-domain constraints in the presence of an unknown finite-energy bounded disturbance. An application to a linear ball and beam model is presented.

show abstract

“…The output-to input-saturation transformation (OIST) theory was first detailed in [1], [2] and proposes to find a remedy to this by reformulating 'saturations' (or expected bounds) on the regulated variable α into saturations on the controller output u. Other strategies include [3], [4] which use anti-windup loops to constrain the state or outputs in the time-domain. OIST is illustrated on the bottom of Fig.…”

Section: Introductionmentioning

confidence: 99%

Output to input saturation transformation: Demonstration and application to disturbed linear systems

Chambon¹,

Burlion²,

Apkarian³

2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

In the case of linear systems, control law design is often performed so that the resulting closed-loop meets specific frequency requirements. However, in many cases, it may be observed that the obtained controller does not enforce timedomain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert expected bounds on an output variable into time-varying saturations on the synthesized linear control law. It is demonstrated that the resulting closedloop is stable and satisfies time-domain constraints in the presence of unknown bounded disturbance. An application to a linear ball and beam model is presented.

show abstract

A Simple Anti-Windup Strategy for State Constrained Linear Control

Cited by 14 publications

References 9 publications

A new Saturation function to convert an output constraint into an input constraint

A new Saturation function to convert an output constraint into an input constraint

Time-response shaping using output to input saturation transformation

Output to input saturation transformation: Demonstration and application to disturbed linear systems

Contact Info

Product

Resources

About