Switching linear parameter‐varying control with improved local performance and optimized switching surfaces

Summary Robust control of parameter‐dependent input delay linear parameter‐varying (LPV) systems via gain‐scheduled dynamic output‐feedback control is considered in this paper. The controller is designed to provide disturbance rejection in the context of the induced scriptL2‐norm or the scriptL2−scriptL∞ norm of the closed‐loop system in the presence of uncertainty and disturbances. A reciprocally convex approach is employed to bound the Lyapunov‐Krasovskii functional derivative and extract sufficient conditions for the controller characterization in terms of linear matrix inequalities (LMIs). The approach does not require the rate of the delay to be bounded, hence encompasses a broader family of input‐delay LPV systems with fast‐varying delays. The method is then applied to the air‐fuel ratio (AFR) control in spark ignition (SI) engines where the delay and the plant parameters are functions of the engine speed and mass air flow. The objectives are to track the commanded AFR signal and to optimize the performance of the three‐way catalytic converter (TWC) through the precise AFR control and oxygen level regulation, resulting in improved fuel efficiency and reduced emissions. The designed AFR controller seeks to provide canister purge disturbance rejection over the full operating envelope of the SI engine in the presence of uncertainties. Closed‐loop simulation results are presented to validate the controller performance and robustness while meeting AFR tracking and disturbance rejection requirements.

“…By solving the LMIs and rearranging the equations given in (29), it is then possible to calculate the controller matrices through…”

Section: Respectivelymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

Salavati

Grigoriadis

Franchek

2019

“…In particular, the issue on the inexact values of scheduling parameters has been increasingly studied in the area of LPV control. For instance, the inexact scheduling parameters have been considered in References 39 and 40 when carrying out the LPV controller design for both state‐feedback and output‐feedback cases, respectively. Moreover, a more general approach is proposed to deal with the additive and multiplicative uncertainties in Reference 41.…”

Section: Introductionmentioning

confidence: 99%

Active fault tolerant control design using switching linear parameter varying controllers with inexact fault‐effect parameters

Che

Zhu

Zhou

et al. 2022

In this article, a novel active fault-tolerant control (AFTC) design method is developed by using the switching linear parameter varying (LPV) controller with inexact fault-effect parameters. The LPV controller is not only considered as a gain-scheduled controller varying with the operating points, but also an AFTC controller varying with the fault-effect parameters, which can be obtained via the fault estimator in real-time. The inexact measurement of fault-effect parameters is considered for the first time in this article. To cover large parameters variation, a class of switched LPV fault-tolerant controller is designed to work in the multiple partitioned parameters subregions. The dynamic output feedback controller model is constructed to perform the switched LPV fault-tolerant control task under the mode-dependent average dwell time constraint. By using the multiple parameter-dependent Lyapunov function approach, sufficient conditions with less conservatism are obtained, such that the corresponding closed-loop systems are globally uniformly exponentially stable and satisfy an upper bound of weighted l 2 -gain performance indexes. Finally, effectiveness and applicability of the developed approaches are validated via an active magnetic bearing system.

“…Simultaneous design of switching surfaces and a switching LPV controller is tackled in some works. [32][33][34] On the other hand, the switched gain-scheduling control for discrete-time LPV system has been investigated by Zhao et al 35 The widely used assumption is that the exact values of the scheduling parameters are available. However, this assumption is impractical for real control applications due to the measurement errors or estimation inaccuracies.…”

Section: Introductionmentioning

confidence: 99%

“…State‐dependent switching without online measurement of varying parameters and also using online measurement of scheduling parameters are considered in the presented methods by Deaecto et al 29 and by Yang et al, 30,31 respectively. Simultaneous design of switching surfaces and a switching LPV controller is tackled in some works 32‐34 . On the other hand, the switched gain‐scheduling control for discrete‐time LPV system has been investigated by Zhao et al 35 …”

Section: Introductionmentioning

confidence: 99%

Improved multiobjective switching gain‐scheduled controller synthesis exploiting inexact scheduling parameters

Yavari

Sadeghzadeh

Shamaghdari

2020

In this article, the design problem of switching gain-scheduled output-feedback (SGSOF) controller with mixed  2 ∕ ∞ performance exploiting inexact scheduling parameters for continuous-time linear parameter-varying (LPV) systems is tackled. The absolute and proportional uncertainties on the scheduling parameters are considered. All the system matrices of the LPV plant are supposed to have polynomial dependency of arbitrary degree on the scheduling parameters. By exploiting hysteresis switching law and utilizing two independent families of parameter-dependent Lyapunov matrices and a family of slack variables, introducing additional degrees of freedom, performance improvement is achieved. A design approach, involving a two-step algorithm, is proposed in terms of solutions to a set of parameter-dependent linear matrix inequalities (LMIs) including parameter searches for two scalar values. The merit of the proposed method lies in its less conservativeness in comparison with the available approaches in the literature. Numerical studies are carried out to demonstrate the effectiveness of the presented method.