Stabilization of an arbitrary order transfer function with time delay H2 Controller

Main Article Content

Muhammad Nasir
Muhammad Muzamil Aslam
Zahoor Ahmed

Abstract

Cyber physical system (CPS) has become the new generation of control industry because of the rapid advancement in computers and communications. Despite the advantages, the computations and manipulations have increased because of the complex network. This creates a lot of uncertainties such as input time delay and communication time delay which cause the performance degradation of a system. This paper proposed a robustH2 controller to overcome these effects in frequency domain. An enhanced way for linear time invariant stabilization of any order transfer function with time delay is adapted. Studied method is based on stability limit computation withH2 performance index. A numerical example is provided to illustrate the efficiency of the proposed method.

Article Details

How to Cite
Nasir, M. ., Aslam, M. M. ., & Ahmed, Z. (2022). Stabilization of an arbitrary order transfer function with time delay H2 Controller. Pakistan Journal of Emerging Science and Technologies (PJEST), 2(2), 1–11. https://doi.org/10.58619/pjest.v2i2.25
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Articles

References

P. So and E. Ott, “Controlling chaos using time delay coordinates via stabilization of periodic orbits,” Phys. Rev. E, vol. 51, no. 4, pp. 2955–2962, 1995, doi: 10.1103/PhysRevE.51.2955.

L. S. Block and W. A. Coppel, “Controlling chaos using time delay coordinates via stabilization of periodic orbits,” vol. 51, no. 4, pp. 5–23, 1992, doi: 10.1007/bfb0084764.

M. M. Aslam, L. Du, Z. Ahmed, M. N. Irshad, and H. Azeem, “A Deep Learning-Based Power Control and Consensus Performance of Spectrum Sharing in the CR Network,” vol. 2021, p. 7125482, 2021.

X. Yu, S. Member, G. Chen, Y. Xia, Y. Song, and Z. Cao, “An Invariant-Manifold-Based Method for,” vol. 48, no. 8, pp. 930–937, 2001.

Z. Ahmed, M. Mansoor, and M. Abid, “Consensus control of multi-agent systems with input and communication delay : A frequency domain perspective,” ISA Trans, 2020, doi: 10.1016/j.isatra.2020.02.005.

T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M. Spano, and J. A. Yorke, “Using the sensitive dependence of chaos (the eebutterfly effectee) to direct trajectories in an experimental chaotic system,” Phys. Rev. Lett., vol. 68, no. 19, pp. 2863–2866, 1992, doi: 10.1103/PhysRevLett.68.2863.

A. Jnifene, “Active vibration control of flexible structures using delayed position feedback,” Syst. Control Lett., vol. 56, no. 3, pp. 215–222, 2007, doi: 10.1016/j.sysconle.2006.10.005.

T. Vyhlídal and P. Zítek, “Analysis of infinite spectra of time delay systems using quasipolynomial root finder implemented in matlab,” Computing, no. 4, 2006.

Z. Ahmed, M. A. Saeed, A. Jenabzadeh, and Z. Weidong, “Frequency domain analysis of resilient consensus in multi-agent systems subject to an integrity attack,” ISA Trans., vol. 111, pp. 156–170, 2021, doi: 10.1016/j.isatra.2020.11.014.

M. M. Aslam, L. Du, X. Zhang, Y. Chen, and B. Qureshi, “Sixth Generation ( 6G ) Cognitive Radio Network ( CRN ) Application , Requirements , Security Issues , and Key Challenges,” Wirel. Commun. Mob. Comput., vol. Under revi, pp. 1–29, 2021.

D. Roose, T. Luzyanina, K. Engelborghs, and W. Michiels, “Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization,” pp. 167–181, 2004, doi: 10.1007/978-3-642-18482-6_12.

D. Breda, S. Maset, and R. Vermiglio, “Pseudospectral differencing methods for characteristic roots of delay differential equations,” SIAM J. Sci. Comput., vol. 27, no. 2, pp. 482–495, 2006, doi: 10.1137/030601600.

M. M. Aslam, M. N. Irshad, H. Azeem, and M. Ikram, “Cost Effective & Energy Efficient Intelligent Smart Home System Based on IoT, Afyon Kocatepe Univ. Int. J. Eng. Technol. Appl. Sci., vol. 3, no. 1, 2020.

V. A. Oliveira, M. C. M. Teixeira, and L. úcia Cossi, “Stabilizing a class of time delay systems using the Hermite-Biehler theorem,” Linear Algebra Appl., vol. 369, no. SUPP., pp. 203–216, 2003, doi: 10.1016/S0024-3795(02)00721-8.

M. M. Aslam, J. Zhang, B. Qureshi, and Z. Ahmed, “Beyond6G- Consensus Traffic Management in CRN , Applications , Architecture and key Challenges,” 2021 IEEE 11th Int. Conf. Electron. Inf. Emerg. Commun., pp. 182–185, 2021, doi: 10.1109/ICEIEC51955.2021.9463832.

N. Tan, “Computation of stabilizing PI and PID controllers for processes with time delay,” ISA Trans., vol. 44, no. 2, pp. 213–223, 2005, doi: 10.1016/S0019-0578(07)90000-2.

M. M. Aslam, L. Du B, Z. Ahmed, H. Azeem, and M. Ikram, Consensus Performance of Traffic Management System for Cognitive Radio Network : An Agent Control Approach, vol. 1. Springer Singapore, 2019.

K. Okano, S. Hara, and H. Ishii, Characterization of a complementary sensitivity property in feedback control: An information theoretic approach, vol. 41, no. 2. IFAC, 2008.

A. Vasičkaninová and M. Bakošová, “Application of H2 and H∞ approaches to the robust controller design for a heat exchanger,” Chem. Eng. Trans., vol. 35, pp. 463–468, 2013, doi: 10.3303/CET1335077.

G. E. Piper et al., “AIAA 2003-5510 ON THE IMPACT OF CROSS-LINK DELAYS ON SPACECRAFT FORMATION CONTROL American Institute of Aeronautics and Astronautics American Institute of Aeronautics and Astronautics,” Control, no. August, pp. 1–10, 2003.

M. Nasir, M. F. Hayat, A. Jamal, and Z. Ahmed “Frequency domain consensus control analysis of the networked multi-agent system with controller area network bus–induced delay,” J. Vib. Control, no. p. 107754632110224, 2021.

M. Zhang, M. Diao, and L. Guo, “Convolutional Neural Networks for Automatic Cognitive Radio Waveform Recognition,” IEEE Access, vol. 5, pp. 11074–11082, 2017, doi: 10.1109/ACCESS.2017.2716191.