A control design methodology for SISO linear time-delay systems

Lei Zhang; Qingwei Chen; R. Ramjug-Ballgobin; R. T.F. Ah King; K. Busawon

doi:10.1109/ELECOM49001.2020.9297003

A control design methodology for SISO linear time-delay systems

Lei Zhang, Qingwei Chen, R. Ramjug-Ballgobin, R. T.F. Ah King, K. Busawon

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper illustrates a control technique for single-input linear systems with delay in the state. We first proceed by introducing a novel definition of stability called Ω-stability which translate the fact that a system is stable in the Krasovskii sense over a set Ω derived from the negative real side of the complex plane. In other words, all the eigenvalues of the system lies inside the set Ω with a given stability margin. Then, for the control design, the system's model is transformed into an extended Jordan controllable canonical form (JCCF). Based on the JCCF, we proposed a systematic construction of the controller gain such that the system under consideration becomes Ω-stable. The effectiveness of the controller is shown, via simulation, by using a typical academic example.

Original language	English
Title of host publication	2020 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Proceedings
Editors	Sameerchand Pudaruth, Avinash Mungur, Robert T. F. Ah King, Tulsi Pawan Fowdur, Zoran Bojkovic, Dragorad Milovanovic, Visham Hurbungs
Place of Publication	Picataway, NJ
Publisher	IEEE
Pages	6-11
Number of pages	6
ISBN (Electronic)	9781728157078
DOIs	https://doi.org/10.1109/ELECOM49001.2020.9297003
Publication status	Published - 25 Nov 2020
Event	3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Balaclava, Mauritius Duration: 25 Nov 2020 → 27 Nov 2020

Conference

Conference	3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020
Country/Territory	Mauritius
City	Balaclava
Period	25/11/20 → 27/11/20

Keywords

controller gain
Jordan controllable canonical form (JCCF)
Krasovskii stability
Time delay systems

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10.1109/ELECOM49001.2020.9297003

Cite this

Zhang, L., Chen, Q., Ramjug-Ballgobin, R., Ah King, R. T. F., & Busawon, K. (2020). A control design methodology for SISO linear time-delay systems. In S. Pudaruth, A. Mungur, R. T. F. Ah King, T. P. Fowdur, Z. Bojkovic, D. Milovanovic, & V. Hurbungs (Eds.), 2020 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Proceedings (pp. 6-11). Article 9297003 IEEE. https://doi.org/10.1109/ELECOM49001.2020.9297003

Zhang, Lei ; Chen, Qingwei ; Ramjug-Ballgobin, R. et al. / A control design methodology for SISO linear time-delay systems. 2020 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Proceedings. editor / Sameerchand Pudaruth ; Avinash Mungur ; Robert T. F. Ah King ; Tulsi Pawan Fowdur ; Zoran Bojkovic ; Dragorad Milovanovic ; Visham Hurbungs. Picataway, NJ : IEEE, 2020. pp. 6-11

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title = "A control design methodology for SISO linear time-delay systems",

abstract = "This paper illustrates a control technique for single-input linear systems with delay in the state. We first proceed by introducing a novel definition of stability called Ω-stability which translate the fact that a system is stable in the Krasovskii sense over a set Ω derived from the negative real side of the complex plane. In other words, all the eigenvalues of the system lies inside the set Ω with a given stability margin. Then, for the control design, the system's model is transformed into an extended Jordan controllable canonical form (JCCF). Based on the JCCF, we proposed a systematic construction of the controller gain such that the system under consideration becomes Ω-stable. The effectiveness of the controller is shown, via simulation, by using a typical academic example.",

keywords = "controller gain, Jordan controllable canonical form (JCCF), Krasovskii stability, Time delay systems",

author = "Lei Zhang and Qingwei Chen and R. Ramjug-Ballgobin and \{Ah King\}, \{R. T.F.\} and K. Busawon",

note = "Funding Information: This work was supported by the National Natural Science Foundation of China [grant numbers 61673214, 61673217, 61673219]; the Innovation Fund Project for Graduate Student of Jiangsu Province [grant number KYLX16 0450]; Jiangsu Key research and development plan (Modem Agriculture) [grant number BE2017370-2], ; 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 ; Conference date: 25-11-2020 Through 27-11-2020",

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doi = "10.1109/ELECOM49001.2020.9297003",

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Zhang, L, Chen, Q, Ramjug-Ballgobin, R, Ah King, RTF & Busawon, K 2020, A control design methodology for SISO linear time-delay systems. in S Pudaruth, A Mungur, RTF Ah King, TP Fowdur, Z Bojkovic, D Milovanovic & V Hurbungs (eds), 2020 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Proceedings., 9297003, IEEE, Picataway, NJ, pp. 6-11, 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020, Balaclava, Mauritius, 25/11/20. https://doi.org/10.1109/ELECOM49001.2020.9297003

A control design methodology for SISO linear time-delay systems. / Zhang, Lei; Chen, Qingwei; Ramjug-Ballgobin, R. et al.
2020 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Proceedings. ed. / Sameerchand Pudaruth; Avinash Mungur; Robert T. F. Ah King; Tulsi Pawan Fowdur; Zoran Bojkovic; Dragorad Milovanovic; Visham Hurbungs. Picataway, NJ: IEEE, 2020. p. 6-11 9297003.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ah King, R. T.F.

AU - Busawon, K.

N1 - Funding Information: This work was supported by the National Natural Science Foundation of China [grant numbers 61673214, 61673217, 61673219]; the Innovation Fund Project for Graduate Student of Jiangsu Province [grant number KYLX16 0450]; Jiangsu Key research and development plan (Modem Agriculture) [grant number BE2017370-2],

PY - 2020/11/25

Y1 - 2020/11/25

N2 - This paper illustrates a control technique for single-input linear systems with delay in the state. We first proceed by introducing a novel definition of stability called Ω-stability which translate the fact that a system is stable in the Krasovskii sense over a set Ω derived from the negative real side of the complex plane. In other words, all the eigenvalues of the system lies inside the set Ω with a given stability margin. Then, for the control design, the system's model is transformed into an extended Jordan controllable canonical form (JCCF). Based on the JCCF, we proposed a systematic construction of the controller gain such that the system under consideration becomes Ω-stable. The effectiveness of the controller is shown, via simulation, by using a typical academic example.

AB - This paper illustrates a control technique for single-input linear systems with delay in the state. We first proceed by introducing a novel definition of stability called Ω-stability which translate the fact that a system is stable in the Krasovskii sense over a set Ω derived from the negative real side of the complex plane. In other words, all the eigenvalues of the system lies inside the set Ω with a given stability margin. Then, for the control design, the system's model is transformed into an extended Jordan controllable canonical form (JCCF). Based on the JCCF, we proposed a systematic construction of the controller gain such that the system under consideration becomes Ω-stable. The effectiveness of the controller is shown, via simulation, by using a typical academic example.

KW - controller gain

KW - Jordan controllable canonical form (JCCF)

KW - Krasovskii stability

KW - Time delay systems

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A2 - Ah King, Robert T. F.

A2 - Fowdur, Tulsi Pawan

A2 - Bojkovic, Zoran

A2 - Milovanovic, Dragorad

A2 - Hurbungs, Visham

PB - IEEE

CY - Picataway, NJ

T2 - 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020

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Zhang L, Chen Q, Ramjug-Ballgobin R, Ah King RTF, Busawon K. A control design methodology for SISO linear time-delay systems. In Pudaruth S, Mungur A, Ah King RTF, Fowdur TP, Bojkovic Z, Milovanovic D, Hurbungs V, editors, 2020 3rd International Conference on Emerging Trends in Electrical, Electronic and Communications Engineering, ELECOM 2020 - Proceedings. Picataway, NJ: IEEE. 2020. p. 6-11. 9297003 doi: 10.1109/ELECOM49001.2020.9297003

A control design methodology for SISO linear time-delay systems

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