Stability analysis and design of model predictive reset control for nonlinear time-delay systems with application to a two-stage chemical reactor system

Pourdehi, Shabnam; Karimaghaee, Paknosh

doi:10.1016/j.jprocont.2018.09.010

Cited by 21 publications

(14 citation statements)

References 27 publications

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“…In summary, we establish a nonlinear system model and reduced the dimension of the mathematical model to obtain system (9), which is improved to obtain system (14). To verify the validity of the established model, we will next prove the positive definiteness and boundedness of all of the solutions of system (14).…”

Section: Improvement Of Nonlinear Systemmentioning

confidence: 99%

“…Because P 1 and P 2 are the same when E 0 ¼ B 0 , we can regard P 2 as a special case of P 1 ; hence, we mainly consider the stability of the system at P 1 . First, we move the equilibrium point P 1 of system (14) to the origin,…”

Section: Model Simplificationmentioning

confidence: 99%

“…When a 1 < 0, Es is an invariant stable subspace. The central manifold theorem is utilized to analyse the stability of system (14). The central manifold theorem [28,29] is summarized as follows: Consider a nonlinear system:…”

Section: Model Simplificationmentioning

confidence: 99%

“…To better analyse the process of biochemical reactions, it is essential to establish a nonlinear system model based on chemical reactions. Many experts and scholars have worked on the modelling methods of nonlinear systems [12][13][14][15][16][17][18]. Biochemical reaction modelling methods have been introduced [7,12,19].…”

Section: Introductionmentioning

confidence: 99%

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Modelling and analysis of haemoglobin catalytic reaction kinetic system

Liu

Wang

et al. 2020

Mathematical and Computer Modelling of Dynamical Systems

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In order to study whether haemoglobin (Hb) can replace peroxidase and has good catalytic properties. The key to exploring the characteristics of Hb peroxidase is to establish a suitable kinetic model, which is studied in this paper. First, according to the Hb catalytic reaction, a nonlinear system is established and improved. It is proved that the established system is in line with the practical significance. The stability of the original system is judged by analysing the stability of the simplified system. Then, considering the effect of time delay on Hb catalytic reaction, a nonlinear timedelay catalytic reaction system is obtained. For convenient application, the system is linearized using Taylor's formula, and the dynamic characteristics of Hopf bifurcation are analysed. The response diagrams of three system are plotted by setting perturbation parameters, and their variations are observed to analyse the differences among them. The results show that the nonlinear timedelay system can better describe the characteristics of the catalytic reaction.

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Section: Improvement Of Nonlinear Systemmentioning

confidence: 99%

Section: Model Simplificationmentioning

confidence: 99%

Section: Model Simplificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling and analysis of haemoglobin catalytic reaction kinetic system

Liu

Wang

et al. 2020

Mathematical and Computer Modelling of Dynamical Systems

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“…The research on the control of systems with input delay has received sustained attention in the past decades because of the wide array of physical problems they cover: chemical processes, reactors, quadruple tank process, automotive speed control, and teleoperation (see References and ). The early frequency domain proposals of Smith for stable systems and its modification for unstable systems were followed by the so‐called reduction approach, and the finite spectrum assignment resulting from the feedback of predicted state values obtained from the Cauchy formula.…”

Section: Introductionmentioning

confidence: 99%

Dynamic predictor for systems with state and input delay: A time‐domain robust stability analysis

Juárez

Mondié

Kharitonov

2020

Intl J Robust & Nonlinear

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Summary The robust stability of linear systems with both state and input delay in closed loop with dynamic predictor‐based controller is analyzed. The problem of time‐varying matrix uncertainty is studied in the Lyapunov‐Krasovskii framework. The complete type functional with prescribed derivative expressed in terms of the delay Lyapunov matrix associated with the nominal system is a key piece of our analysis. The robust stability conditions depend on the delay Lyapunov matrix whose computation is carried out. An illustrative example is presented.

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Optimal reset law design based on guaranteed cost control method for Lipschitz nonlinear systems

Shahbazzadeh

Sadati

HosseinNia

2022

Intl J Robust & Nonlinear

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This article proposes a systematic approach for optimal reset law design of a class of nonlinear systems. By using the guaranteed cost control method, sufficient conditions for the design of optimal reset law are derived in terms of linear matrix inequalities. In an offline design procedure, the reset law is computed that minimizes the upper bound of a quadratic cost function. The proposed method can be implemented for real-time applications even with small sampling time. The simulation results verify the efficacy and effectiveness of the proposed theoretical results.

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Stability analysis and design of model predictive reset control for nonlinear time-delay systems with application to a two-stage chemical reactor system

Cited by 21 publications

References 27 publications

Modelling and analysis of haemoglobin catalytic reaction kinetic system

Modelling and analysis of haemoglobin catalytic reaction kinetic system

Dynamic predictor for systems with state and input delay: A time‐domain robust stability analysis

Optimal reset law design based on guaranteed cost control method for Lipschitz nonlinear systems

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