Robust model reference control of linear parameter‐varying systems with disturbances

Abdullah, Ali A.

doi:10.1049/iet-cta.2017.0717

Cited by 11 publications

(13 citation statements)

References 37 publications

(100 reference statements)

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“…The main contributions of this article are as follows: The model following control system is designed for LPV descriptor systems, where the design problem has not been tackled in the literature to the best of our knowledge. The proposed

H_{\infty}

model following control of LPV descriptor systems is an extension to the method used for LPV systems 32 . The extended design to LPV descriptor systems is not straightforward due to the algebraic equation constraints and the impulsive behavior of descriptor systems 33 …”

Section: Introductionmentioning

confidence: 99%

H∞ model following control of linear parameter‐varying descriptor systems

Abdullah

2022

Optim Control Appl Methods

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The topic of H ∞ model following control of linear parameter-varying (LPV) descriptor systems is considered in this article. The main objective of using the H ∞ model following control system is to ensure that the outputs of the LPV descriptor system track robustly the reference model outputs in the presence of bounded energy disturbances. The H ∞ model following control system consists of three subsystems: an LPV feedforward controller, an LPV reference model, and an LPV H ∞ descriptor dynamic output-feedback controller. The design matrices of these three subsystems are obtained by solving a set of tractable LPV matrix equations and inequalities. Two descriptor systems: an electrical circuit and a DC motor with an unbalanced disc are modeled as LPV descriptor systems and then used to show the design steps. The simulation results show the effectiveness of the proposed H ∞ model following control system.

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H_{\infty}

Section: Introductionmentioning

confidence: 99%

H∞ model following control of linear parameter‐varying descriptor systems

Abdullah

2022

Optim Control Appl Methods

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“…The main objective of robust model reference control is to regulate the system output to a desired output of the reference model in the presence of system model uncertainties, external disturbances, measurement noises, time delays and so on. Robust model reference control techniques are applied to different types of systems, such as multivariable linear systems with parameter uncertainties (Duan et al, 2001; Gerardo et al, 2016; Huang and Jia 2017), descriptor linear systems with parametric uncertainties (Duan and Zhang, 2007), linear parameter-varying systems (Abdullah, 2018; Abdullah and Zribi, 2009), Markov jump systems with unknown transition probabilities (Boukas, 2009; Zhang and Boukas, 2009), non-linear systems (Zhang et al, 2018; Qin et al 2018) and uncertain network-based control systems (Gao and Chen, 2008). To improve the transient response caused by uncertain dynamics, a robust model reference control design is proposed in Yang et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

Tian

Duan

2021

Transactions of the Institute of Measurement and Control

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This paper is devoted to designing the robust model reference controller for uncertain second-order descriptor linear systems subject to parameter uncertainties. The parameter uncertainties are assumed to be norm-bounded. The design of a robust controller can be divided into two separate problems: a robust stabilization problem and a robust compensation problem. Based on the solution of generalized Sylvester matrix equations, we obtain some sufficient conditions to guarantee the complete parameterization of the robust controller. The parametric forms are expressed by a group of parameter vectors which reveal the degrees of freedom existing in the design of the compensator and can be utilized to solve the robust compensation problem. In order to reduce the effect of parameter uncertainties on the tracking error vector, the robust compensation problem is converted into a convex optimization problem with a set of linear matrix equation constraints. A simulation example is provided to illustrate the effectiveness of the proposed technique.

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“…The subject of designing model reference control systems has been studied by many researchers in recent years that mainly aim to regulate the output of the system to a desired output of the reference model. Various types of systems have been studied for the model reference control, such as multivariable linear systems (De La Torre et al, 2016;Duan et al (2001), second-order linear system (Duan and Huang, 2008;Tian and Duan, 2020), constrained linear systems (Di Cairano and Borrelli, 2016), multi-agent systems (Liu and Jia, 2012), networked control systems (Sakthivel et al, 2017), switched linear parameter varying systems with parametric uncertainties (Abdullah, 2018), piecewise affine systems with input disturbances (Di Bernardo et al, 2016), markov jump systems (Boukas, 2009), uncertain dynamical systems with performance guarantees (Arabi et al, 2019) and linear timevarying systems (Liu et al, 2020). In the meantime, effective results were successfully achieved in practical application by utilizing model reference control technology, especially in the active damping of driveline vibration in power-split hybrid vehicles (Liu et al, 2019), training recurrent neural networks (Jafari and Hagan, 2018), precise speed tracking of industrial robot (Xie et al, 2019) and so forth.…”

Section: Introductionmentioning

confidence: 99%

Model reference control in quasi-linear systems with a parametric feed-forward compensator and state-feedback stabilization controller

Liu

Duan

2021

Transactions of the Institute of Measurement and Control

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In this paper, a parametric feed-forward compensator and a parametric state-feedback stabilization controller are proposed for the model reference control to a class of quasi-linear systems. Quasi-linear systems are a special type of nonlinear systems whose coefficient matrices contain the state variables and also a time-varying parameter vector. The parametric state-feedback stabilization controller guarantees the stability of the closed-loop system and the parametric feed-forward compensator compensates the effect of the reference model state to the tracking error. The complete parametrization of the parametric feed-forward compensator is established based on a complete parametric solution to a class of generalized Sylvester matrix equations and solution of a coefficient matrix such that two matrix equations are satisfied. The established parametric state-feedback stabilization controller only needs a complete parametric solution to the same generalized Sylvester matrix equations but with different sets of freely designed parameters that represent the degrees of design freedom and may be further utilized to improve the system performance. A linear closed-loop form with the desired eigenstructure can be derived with the proposed parametric feed-forward compensator and parametric state-feedback stabilization controller, and a constant linear can even be obtained in certain cases. A numerical example and the application in spacecraft rendezvous are provided to illustrate the effectiveness of the proposed approach.

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Robust model reference control of linear parameter‐varying systems with disturbances

Cited by 11 publications

References 37 publications

H∞ model following control of linear parameter‐varying descriptor systems

H∞ model following control of linear parameter‐varying descriptor systems

Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

Model reference control in quasi-linear systems with a parametric feed-forward compensator and state-feedback stabilization controller

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