Gain Scheduling: Potential Hazards and Possible Remedies

A concept for implementation of multivariable controllers is presented in this paper. The concept is based on the Youla–Jabr–Bongiorno–Kucera (YJBK) parameterization of all stabilizing controllers. Using this scheme for implementation of multivariable controllers, it is shown how it is possible to smoothly switch between multivariable controllers with guaranteed closed‐loop stability. This includes also the case where one or more controllers are unstable.The concept for smooth on‐line changes of multivariable controllers based on the YJBK architecture can also handle the start‐up and shut down of multivariable systems. Furthermore, the start‐up of unstable multivariable controllers can be handled as well. Finally, implementation of (unstable) controllers as a stable Q parameter in a Q‐parameterized controller can also be achieved. Copyright © 2004 John Wiley & Sons, Ltd.

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“…Using the Bezout equation, the controller given either by (11) or by (12) can be realized as an LFT in the parameter Q;…”

Section: The Yjbk Parameterizationmentioning

confidence: 99%

Switching between multivariable controllers

Niemann

Stoustrup

Abrahamsen³

2004

Optim Control Appl Methods

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“…The controller parameter that determines selection of the appropriate operating region is called the scheduling variable. Despite the popularity of gain scheduling techniques, they are sometimes considered in a class of ad hoc methodologies, since the robustness, performance, or even stability properties of the overall design are not explicitly addressed (Shamma & Athans, 1992). However, we can infer these properties via extensive simulations.…”

Section: Gain Scheduled Controlmentioning

confidence: 99%

“…The basic idea behind gain-scheduled control is to choose various desired operating points, model the system at these points, and apply an appropriate controller (in this case, linear) for each of these ranges. Gain scheduling is a common engineering practice used to control nonlinear systems in many engineering applications, such as flight control and process control (Shamma & Athans, 1992). The main idea is that one algorithm from several different control designs is chosen based on some operating conditions.…”

Section: Gain Scheduled Controlmentioning

confidence: 99%

“…Many heuristic rules-of-thumb have emerged in guiding successful gain scheduled design; however, the most important guideline is to ensure "slow" variation in the scheduling variable. In (Shamma & Athans, 1992), "slow" is defined for situations wherein the scheduling variable changes slower than the slowest time constant of the closed loop system.…”

Section: Gain Scheduled Controlmentioning

confidence: 99%

See 1 more Smart Citation

On the Control of Automotive Traction PEM Fuel Cell Systems

Al‐Durra¹,

Yurkovich²,

Guezennec³

2011

New Trends and Developments in Automotive System Engineering

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“…However, while intuitively appealing, this idea has several pitfalls [Shamma and Athans (1992)]. Motivated by these shortcomings, during the past few years considerably attention has been devoted to the problem of synthesizing controllers for Linear Parameter Varying Systems, where the statespace matrices of the plant depend on time-varying parameters whose values are not known a priori, but can be measured by the controller.…”

Section: Introductionmentioning

confidence: 99%

Risk Adjusted Receding Horizon Control of Constrained Linear Parameter Varying Systems

Sznaier

Lagoa

et al.

Lecture Notes in Control and Information Sciences

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Summary. In the past few years, control of Linear Parameter Varying Systems (LPV) has been the object of considerable attention, as a way of formalizing the intuitively appealing idea of gain scheduling control for nonlinear systems. However, currently available LPV techniques are both computationally demanding and (potentially) very conservative. In this chapter we propose to address these difficulties by combining Receding Horizon and Control Lyapunov Functions techniques in a risk-adjusted framework. The resulting controllers are guaranteed to stabilize the plant and have computational complexity that increases polynomially, rather than exponentially, with the prediction horizon.

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Gain Scheduling: Potential Hazards and Possible Remedies

Cited by 136 publications

References 2 publications

Switching between multivariable controllers

Switching between multivariable controllers

On the Control of Automotive Traction PEM Fuel Cell Systems

Risk Adjusted Receding Horizon Control of Constrained Linear Parameter Varying Systems

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