Designing a Robust Memory State Feedback Controller Leveraging LMI on DC Motor Under Time Delays and Norm-Bounded Disturbances

Document Type : Research Paper

Authors

1 Department of Electrical Engineering, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran.

2 Department of Electrical Engineering, Yadegar -e- Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran.

Abstract

This paper investigates the performance of a predictor-based  H_∞controller applied to a first-order DC motor system under significant input-time delays. Alongside the proposed predictor-based H_∞ controller, an LQR controller has been implemented to serve as a benchmark for effectively comparing and evaluating the performance of the proposed method. This study specifically focuses on scenarios involving time delays exceeding one second and external disturbances such as constant, sinusoidal, and stochastic disruptions. The proposed controller employs a robust memory-state feedback mechanism to ensure closed-loop stability and minimize the impact of disturbances. Using Linear Matrix Inequality (LMI) conditions, the controller compensates for input delays of up to five seconds while guaranteeing disturbance attenuation. A delay-dependent Lyapunov stability analysis is conducted to validate the proposed approach. Comprehensive simulation results and evaluations based on key performance metrics, such as settling time and overshoot, indicate that the predictor-based H_∞  controller outperforms both the open-loop configuration and the LQR controller. Notably, the proposed approach achieves a reduced overshoot, a faster transient response, and superior disturbance attenuation compared to the LQR method. Furthermore, this controller significantly enhances the overall system robustness and control precision in scenarios with prolonged delays. The predictor-based H_∞ controller suggests an innovative solution for mitigating the effects of long input delays in DC motor systems, thereby overcoming a pivotal challenge in robust control.

Keywords

Main Subjects

References

[1] C. Hua, L. Zhang, and X. Guan, Robust Control for Nonlinear Time-Delay Systems, Springer, 2018,
https://doi.org/10.1007/978-981-10-5131-9.
[2] H. Chen, X. Long, Y. Tang, and R. Xu, “Passive and H∞ control based on non-fragile observer for a class of uncertain nonlinear systems with input time-delay,” Journal of Vibration and Control, Aug. 2023, https://doi.org/10.1177/10775463231193458.
[3] A. K. Ali and M. M. Mahmoud, “Improved Design of Nonlinear Control Systems with Time Delay,” International Journal of Robotics and Control Systems, vol. 2, no. 2, pp. 317–331, May 2022, https://doi.org/10.31763/ijrcs.v2i2.631.
[4] L. Pekař, P. Navrátil, and R. Matušů, “Some Recent Results on Direct Delay-Dependent Stability Analysis: Review and Open Problems,” in Advances in intelligent systems and computing, 2018, pp. 25–34. https://doi.org/10.1007/978-3-319-91192-2_3.
[5] T.-Y. Cai and C. Hwang, “A Simple Procedure for the Creation of Stability Charts in Delay Parameter Space for a Class of LTI Systems with Two Delays,” IEEE Access, vol. 11, pp. 23053–23062, Jan. 2023, https://doi.org/10.1109/access.2023.3248951.
[6] J. Chen, J. H. Park, S. Xu, and B. Zhang, “A survey of inequality techniques for stability analysis of time‐delay systems,” International Journal of Robust and Nonlinear Control, vol. 32, no. 11, pp. 6412–6440, Apr. 2022, https://doi.org/10.1002/rnc.6151.
[7] X. Zhang, X. Lu, and Z. Liu, “Razumikhin and Krasovskii methods for asymptotic stability of nonlinear delay impulsive systems on time scales,” Nonlinear Analysis Hybrid Systems, vol. 32, pp. 1–9, Nov. 2018, https://doi.org/10.1016/j.nahs.2018.10.010.
[8] B. Zhou and A. V. Egorov, “Razumikhin and Krasovskii stability theorems for time-varying time-delay systems,” Automatica, vol. 71, pp. 281–291, Jun. 2016, https://doi.org/10.1016/j.automatica.2016.04.048.
[9] Y. Zhang, L. Xie, X. Xie, Z.-Y. Sun, and K. Zhang, “Fuzzy Adaptive Control for Stochastic Nonstrict Feedback Systems with Multiple Time-Delays: A Novel Lyapunov-Krasovskii Method,” IEEE Transactions on Fuzzy Systems, vol. 32, no. 6, pp. 3815–3824, Apr. 2024, https://doi.org/10.1109/tfuzz.2024.3384588.
[10] A. Pandey and D. M. Adhyaru, “Stability Analysis of Electromagnetic Levitation System Using Lyapunov-Krasovskii’s Method,” 2022 International Conference for Advancement in Technology (ICONAT), Jan. 2022, https://doi.org/10.1109/iconat53423.2022.9726080.
[11] E. Moradi, “Finite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay,” Journal of Control, vol. 14, no. 2, pp. 79–87, Jun. 2020, https://doi.org/10.29252/joc.14.2.79.
[12] E. Moradi, M. R. Jahed-Motlagh, and M. B. Yazdi, “Delay-Dependent Finite-Time Stabilization of Uncertain Switched Time-Delay Systems with Norm-Bounded Disturbance,” IETE Journal of Research, vol. 64, no. 2, pp. 195–208, Aug. 2017, https://doi.org/10. 1080/03772063.2017.1351898.
[13] S. Hao, T. Liu, and B. Zhou, “Predictor‐based output feedback control design for sampled systems with input delay subject to disturbance,” IET Control Theory and Applications, vol. 11, no. 18, pp. 3329–3340, Sep. 2017, https://doi.org/10.1049/iet-cta.2017.0504.
[14] H. D. Choi, C. K. Ahn, M. T. Lim, and M. K. Song, “Dynamic output-feedback H ∞ control for active half-vehicle suspension systems with time-varying input delay,” International Journal of Control Automation and Systems, vol. 14, no. 1, pp. 59–68, Feb. 2016, https://doi.org/10.1007/s12555-015-2005-8.
[15] X. Jin, J. Wang, Z. Yan, L. Xu, G. Yin, and N. Chen, “Robust Vibration Control for Active Suspension System of In-Wheel-Motor-Driven Electric Vehicle Via μ-Synthesis Methodology,” Journal of Dynamic Systems Measurement and Control, vol. 144, no. 5, Jan. 2022, https://doi.org/10.1115/1.4053661.
[16] V. L´echapp´e and O. Salas Jes´us de Le´on, “Predictive control of disturbed systems with input delay: experimental validation on a DC motor,” IFAC-PapersOnLine, pp. 292–297, 2015, https://doi.org/10.1016/j.ifacol.2015.09.393.
[17] N. Maleki and E. Moradi, “Robust    H∞    Control of DC Motor in the Presence of Input Delay and Disturbance by the Predictor-Based Method,” Complexity, vol. 2022, no. 1, Jan. 2022, https://doi.org/10.1155/2022/1902166.
[18] M. Liu, I. Dassios, G. Tzounas, and F. Milano, “Model-Independent Derivative Control Delay Compensation Methods for Power Systems,” Energies, vol. 13, no. 2, p. 342, Jan. 2020, https://doi.org/10.3390/en13020342.
[19] Y. Koyasako, T. Suzuki, S.-Y. Kim, J.-I. Kani, and J. Terada, “Motion Control System With Time-Varying Delay Compensation for Access Edge Computing,” IEEE Access, vol. 9, pp. 90669–90676, Jan. 2021, https://doi.org/10.1109/access.2021.3091707.
[20] D. A. Barkas, G. C. Ioannidis, C. S. Psomopoulos, S. D. Kaminaris, and G. A. Vokas, “Brushed DC Motor Drives for Industrial and Automobile Applications with Emphasis on Control Techniques: A Comprehensive Review,” Electronics, vol. 9, no. 6, p. 887, May 2020, https://doi.org/10.3390/electronics9060887.
[21] R. Silva-Ortigoza et al., “Robust Flatness-Based Tracking Control for a ‘Full-Bridge Buck Inverter–DC Motor’ System,” Mathematics, vol. 10, no. 21, p. 4110, Nov. 2022, https://doi.org/10.3390/math10214110.
[22] S. Azizi, M. H. Asemani, N. Vafamand, S. Mobayen, and M. H. Khooban, “A Linear Parameter Varying Control Approach for DC/DC Converters in All-Electric Boats,” Complexity, vol. 2021, no. 1, Jan. 2021, https://doi.org/10.1155/2021/8848904.
[23] R. J. Khlif, A. Abid, P. Melchior, and N. Derbel, “UM Shaper Command Inputs for CRONE Control: Application on a DC Motor Bench,” Mathematical Problems in Engineering, vol. 2021, pp. 1–11, May 2021, https://doi.org/10.1155/2021/9935875.
[24] Z. Qi, Q. Shi, and H. Zhang, “Tuning of Digital PID Controllers Using Particle Swarm Optimization Algorithm for a CAN-Based DC Motor Subject to Stochastic Delays,” IEEE Transactions on Industrial Electronics, vol. 67, no. 7, pp. 5637–5646, Aug. 2019, https://doi.org/10.1109/tie.2019.2934030.
[25] B. Zhu, H. R. Karimi, L. Zhang, and X. Zhao, “Neural network-based adaptive reinforcement learning for optimized backstepping tracking control of nonlinear systems with input delay,” Applied Intelligence, vol. 55, no. 2, Dec. 2024, https://doi.org/10.1007/s10489-024-05932-x.
[26] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM, 1994, https://doi.org/10.1137/1.9781611970777.
[27] K. K. Afshar, A. Javadi, and M. R. Jahed‐Motlagh, “Robust 𝐻∞ control of an active suspension system with actuator time delay by predictor feedback,” IET Control Theory and Applications, vol. 12, no. 7, pp. 1012–1023, Feb. 2018,, https://doi.org/10.1049/iet-cta.2017.0970.
[28] B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. Courier Corporation, 2007.
[29] H. Karami, N. P. Nguyen, H. Ghadiri, S. Mobayen, F. Bayat, P. Skruch, and F. Mostafavi, "LMI-Based Luenberger Observer Design for Uncertain Nonlinear Systems with External Disturbances and Time-Delays," IEEE Access, vol. 11, pp. [pages], July 2023, https://doi.org/10.1109/ACCESS.2023.3293493.
[30] A. Sassi, I. Boussaada, and S.-I. Niculescu, "Observer Design in LTI Time-Delay Systems using Partial Pole Placement with Applications," IFAC PapersOnline, vol. 55, no. 36, pp. 157–162, 2022, https://doi.org/10.1016/j.ifacol.2022.11.350.

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History

  • Receive Date: 29 November 2024
  • Revise Date: 06 March 2025
  • Accept Date: 15 March 2025

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