Stabilization strategy for unstable first order linear systems with large time‐delay

Márquez‐Rubio, Juan Francisco; Muro-Cuéllar, Basilio del; Velasco-Villa, M.; Alvarez-Ramı́rez, José

doi:10.1002/asjc.415

Cited by 6 publications

(4 citation statements)

References 22 publications

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“…Proof. The proof of this lemma is provided in Appendix A, and it is carried out as a slight modification of the one presented for a system of the form described in eq , without considering the splitting strategy described by eq .…”

Section: Splitting Time-delay and Observer Strategymentioning

confidence: 99%

“…Then, there exist constants g 1 and g 2 such that the closed-loop system, is stable if and only if τ 2 < 2/a.■ Proof. The proof of this lemma is provided in Appendix A, and it is carried out as a slight modification of the one presented for a system of the form described in eq 1, 19 without considering the splitting strategy described by eq 4.…”

Section: ■ Introductionmentioning

confidence: 99%

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Observer–PID Stabilization Strategy for Unstable First-Order Linear Systems with Large Time Delay

Márquez‐Rubio

Del-Muro-Cuellar

Velasco-Villa

et al. 2012

Ind. Eng. Chem. Res.

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This work considers the stabilization and control of a class of unstable first-order linear systems subject to a relatively large input−output time delay. As a first step, a particular observer scheme is proposed in order to predict a specific internal signal in the process. Conditions to ensure the adequate prediction convergence of the signals are formally stated. In a second step, the internal predicted signal is used to implement classical P, PI, and PID controllers providing stability conditions for the resulting closed-loop system. The proposed control strategy allows one to address time delays as large as four times the unstable time constant of the open-loop system, in contrast with the reported related literature where the maximal bound has been stated until now as two times the unstable time constant of the open-loop system. The proposed observer-based control structure considers also the tracking of step reference signals and the rejection of input step disturbances.

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Section: Splitting Time-delay and Observer Strategymentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Observer–PID Stabilization Strategy for Unstable First-Order Linear Systems with Large Time Delay

Márquez‐Rubio

Del-Muro-Cuellar

Velasco-Villa

et al. 2012

Ind. Eng. Chem. Res.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In many practical systems, however, time delays are ubiquitous and unavoidable. Because the existence of time delay may not only affect the performance of the control, but also even undermine the stability of a system [12][13][14][15][16][17][18][19][20], the influence of time delay for system performance can not be ignored. Switched nonlinear delay systems are often met in practical systems such as networked control systems, drilling systems, and mechanical rotational cutting processes [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Stability Properties of Switched Nonlinear Delay Systems with Synchronous or Asynchronous Switching

Wang¹,

Sun²,

Wang³

et al. 2014

Asian Journal of Control

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This paper is concerned with the problem of input‐to‐state stability (ISS) for a class of switched nonlinear delay systems. The cases where the switching signal of the system and the switching signal of the corresponding controller are synchronous and asynchronous are both considered. To study two asynchronous switching signals in a unified framework, we adopt the technique of the merging switching signal. Based on a piecewise Lyapunov–Krasovskii functional method, some sufficient conditions are explicitly given to guarantee the ISS of the switched nonlinear delay system under the average dwell time scheme. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theory.

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“…This work was supported also by the development project of key laboratory of Liaoning Province. systems, the problem is relatively simple and general and effective techniques have been proposed mainly based on the Routh-Hurwitz criterion, such as, the Ziegler-Nichols method in [3], generalization of the Hermite-Biehler Theorem in [4], the Astrom-Hagglund method in [5], and also some new summary results in [6][7][8][9][10][11]. However, as inherent phenomena, time delays are encountered in a variety of interconnected real systems or processes, which makes the problem much more complex.…”

Section: Introductionmentioning

confidence: 99%

The τ Decomposition Method for PID Controllers of First Order Delayed Unstable Processes

Cai¹,

Zhang²,

Yang³

et al. 2014

Asian Journal of Control

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The stabilization of first‐order delayed (FOD) unstable processes with proportional–integral–derivative (PID) controllers is considered, and all the feasible PID controllers are determined. Different from the existing results which are based on the D‐partition technique and partitioning complex's real and imaginary parts, a novel procedure enlightened by the τ decomposition method is proposed to characterize the space of controller parameters. Generally speaking, the parameter space is mainly divided into four regions: delay independent stable region, delay independent unstable region, delay interval dependent stable region, and delay interval dependent unstable region. The depiction of the space partition boundaries and the determination of stable intervals become the main problems. In our work, these boundaries are related to the existence of the purely imaginary roots (PIRs) of the systems' characteristic equation, and the determination of stable intervals refers to the number and value of the PIRs. Thus, the key points are the number and calculation of PIRs. According to our discussion, analytical results on both topics are obtained in explicit form. Finally, vivid numerical simulations are given to illustrate the results.

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Stabilization strategy for unstable first order linear systems with large time‐delay

Cited by 6 publications

References 22 publications

Observer–PID Stabilization Strategy for Unstable First-Order Linear Systems with Large Time Delay

Observer–PID Stabilization Strategy for Unstable First-Order Linear Systems with Large Time Delay

Stability Properties of Switched Nonlinear Delay Systems with Synchronous or Asynchronous Switching

The τ Decomposition Method for PID Controllers of First Order Delayed Unstable Processes

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