Design of Robust Reset Controller Based on Optimal After Reset Performance to Improve the Performance of an Industrial Robot Control

Subject Areas : Renewable energy

Maryam  Jeddi-Golfazani ¹ (Department of Electrical Engineering- Saveh Branch, Islamic Azad University, Saveh, Iran)
Mohammad  Vahedi ² (Department of Electrical Engineering- Saveh Branch, Islamic Azad University, Saveh, Iran)
Majid  Gandomkar ³ (Department of Electrical Engineering- Saveh Branch, Islamic Azad University, Saveh, Iran)

Received: 2022-02-21 Accepted : 2022-07-25 Published : 2023-11-22

Keywords: Reset control, robot with two degrees of freedom, robust combination control, optimal output feedback control, systematic after reset method,

Abstract :

Standard PID controllers are one of the most desirable controllers for industrial automation and the most widely used control in feedback systems. However, linear controllers have limitations that represent­tation controllers can be used to overcome these limitations. In this paper, a robust reset control based on optimal output feedback to control a robot with two degrees of freedom. In general, the behavior of reset controllers is similar to that of linear controllers, in other words, they are easy to implement. In this regard, in this paper, by introducing a special combination control called robust reset output feedback control, the disadvantages of the linear controller are eliminated and its main purpose is to reduce overexposure and increase the response speed and better stability of the controlled system. Therefore, this paper introduces a systematic method for reset optimal output feedback controller. To do this, an optimal output feedback controller is first designed without the reset action, so that the poles of the closed-loop system are located in a predefined area. This area is selected to ensure the stability of the exponential and the arrival time of the closed loop in a finite time. Then, the reset value at reset times is designed to minimize a cost-effective function for better performance. In this paper, for the first time, the reset value is specified only with the system output information and then the stability of the system will be guaranteed. The robot used in this article is a practical and industrial example that has two arms and two joints with separate control capability. The position and behavior of the arms based on the governing equations and mathematical relations indicate its direct effect on each other. Finally, to prove the proposed design, numerical simulation will be performed using Matlab software and a comparison between the proposed controller and a similar controller will be performed.

References:

[1] K.J. Aström, T. Hägglund, "The future of PID control", Control Engineering Practice, vol. 9, no. 11, pp. 1163-1175, May 2001 (doi: 10.1016/S0967-0661(01)00062-4).

[2] A. Baños, A. Barreiro, "Reset control systems (Advances in Industrial Control)", London: New York: Springer, Aug. 2012 (ISBN-13: 978-1447122166).

[3] J.C. Clegg, "A nonlinear integrator for servomechanisms", Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry, vol. 77, no. 1, pp. 41-42, Jan. 1958 (doi: 10.1109/TAI.1958.6367399).

[4] N. Popescu, M. Ivanescu, D. Popescu, "A note on observer-based frequency control for a class of systems described by uncertain models", Journal of Dynamic Systems, Measurement, and Control, vol. 140, no. 2, February 2018 (doi: 10.1115/1.4037528).

[5] R. Sakthivel, K. Raajananthini, P. Selvaraj, Y. Ren, "Design and analysis for uncertain repetitive control systems with unknown disturbances", Journal of Dynamic Systems, Measurement, and Control, vol. 140, no. 12, Article Number: 121007, December 2018 (doi: 10.1115/1.4040663).

[6] K.A. Alattas, J. Mostafaee, A. Sambas, A.K. Alanazi, S. Mobayen, A. Zhilenkov, "Nonsingular integral-type dynamic finite-time synchronization for hyper-chaotic systems", Mathematics, vol. 10, no. 1, Article Number: 115, December 2022 (doi: 10.3390/math10010115).

[7] F. Rahmanian, M.H. Asemani, M. Dehghani, S. Mobayen, "Robust dynamic output feedback control of blood glucose level in diabetic rat with robust descriptor Kalman filter", Biomedical Signal Processing and Control, vol. 71, Article Number: 103088, Nov. 2022 (doi: 10.1016/j.bspc.2021.103088).

[8] S. Gao, B. Ning, H. R. Dong, "Fuzzy dynamic surface control for uncertain nonlinear systems under input saturation via truncated adaptation approach", Fuzzy Sets and Systems, vol. 290, pp. 100-117, May 2016 (doi: 10.1016/j.fss.2015.02.013).

[9] C. Sun, H.Gao, Z. Liu, S. Xiang, H. Yu, N. Li, Z. Deng "Design and optimization of three-degree-of-freedom planar adaptive cable-driven parallel robots using the cable wrapping phenomenon", Mechanism and Machine Theory, vol. 166, Article Number: 104475, December 2021 (doi:10.1016/ j.mechmachtheory. 2021.104475).

[10] W. Lyu, D.H. Zhai, Y. Xiong, Y. Xia, "Predefined performance adaptive control of robotic manipulators with dynamic uncertainties and input saturation constraints", Journal of the Franklin Institute, vol. 358, no. 14, pp. 7142-7169, April 2021 (doi: 10.1016/j.jfranklin.2021.07.025).

[11] K. Shojaei, A. Kazemy, A. Chatraei, "An observer-based neural adaptive PID² controller for robot manipulators including motor dynamics with a prescribed performance", IEEE/ASME Trans. on Mechatronics, vol. 26, no. 3, pp. 1689-1699, October 2020 (doi: 10.1109/TMECH.2020.3028968).

[12] S. Mobayen, O. Mofid, S.U. Din, A. Bartoszewicz, "Finite-time tracking controller design of perturbed robotic manipulator based on adaptive second-order sliding mode control method", IEEE Access, vol. 9, pp. 71159-71169, May 2021 (doi: 10.1109/ACCESS.2021.3078760).

[13] M.A. Davó, F. Gouaisbaut, A. Baños, S. Tarbouriech, A. Seuret, "Exponential stability of a PI plus reset integrator controller by a sampled-data system approach", Nonlinear Analysis Hybrid Systems, vol. 29, pp. 133-146, August 2018 (doi: 10.1016/j.nahs.2018.01.008).

[14] D. Dinther, B. Sharif, S. Eijnden, H. Nijmeijer, M. Heertjes, W. Heemels, "Overcoming performance limitations of linear control with hybrid integrator-gain systems", IFAC-PapersOnLine, vol. 54, no. 5, pp. 289-294, March 2021 (doi: 10.1016/j.ifacol.2021.08.513).

[15] I. Hosseini, A. Khayatian, P. Karimaghaee, M. Fiacchini, M.A.D. Navarro, "LMI-based reset unknown input observer for state estimation of linear uncertain systems", IET Control Theory and Applications, vol. 13, no. 2, pp. 1872-1881, Aug. 2019 (doi: 10.1049/iet-cta.2018.5777).

[16] I. Hosseini, M. Fiacchini, P. Karimaghaee, A. Khayatian, "Optimal reset unknown input observer design for fault and state estimation in a class of nonlinear uncertain systems", Journal of the Franklin Institute, Elsevier, vol. 357, no. 5, pp. 2978-2996, Jan. 2020 (doi: 10.1016/j.jfranklin.2019.12.008).

[17] X. Xu, X. Li, P. Dong, Y. Liu, H. Zhang, "Robust reset speed synchronization control for an integrated motor-transmission powertrain system of a connected vehicle under a replay attack", IEEE Trans. on Vehicular Technology, vol. 70, no. 6, pp. 5524-5536, June 2021 (doi: 10.1109/TVT.2020.3020845).

[18] S. Pourdehi, P. Karimaghaee, "Reset observer-based fault tolerant control for a class of fuzzy nonlinear time-delay systems", Journal of Process Control, vol. 85, pp. 65-75, Feb. 2020 (doi: 10.1016/j.jpro­cont.­2019­.11.001).

[19] U.R. Nair, R. Costa-Castelló, A. Banos, "Reset control of boost converters", Proceeding of the IEEE/ACC, pp. 553-558, Milwaukee, WI, USA, July 2018 (doi: 10.23919/ACC.2018.8431380).

[20] U.R. Nair, R. Costa-Castelló, A. Banos, "Reset control for DC–DC converters: An experimental application", IEEE Access, vol. 7, pp. 128487-128497, June 2019 (doi: 10.1109/ACCESS.2019.2940140).

[21] H. Pang, S. Liu, "Robust finite time passivity and stabilization of uncertain switched nonlinear system", IEEE Access, vol. 9, pp. 36173-36180, February 2021 (doi: 10.1109/ACCESS.2021.3062661).

[22] Y. Guo, Y. Wang, L. Xie, J. Zheng, "Stability analysis and design of reset systems: Theory and an application", Automatica, vol. 45, no. 2, pp. 492-497, April 2009 (doi: 10.1016/j.automatica.2008.08.016).

[23] M.A. Davó, A. Baños, "Delay-dependent stability of reset control systems with input/output delays", Proceeding of the IEEE/CDC, pp. 2018-2023, Firenze, Italy, Dec. 2013 (doi: 10.1109/CDC.2013.6760178).

[24] N. Vafamand, A. Khayatian, M. H. Khooban, "Stabilisation and transient performance improvement of DC MGs with CPLs: non-linear reset control approach", IET Generation, Transmission and Distribution, vol. 13, no. 14, pp. 3169-3176, May 2019 (doi: 10.1049/iet-gtd.2018.6739).

[25] H. Wang, F. Zhu, Y. Tian, "Event-triggered optimal reset control of hard disk drive head-positioning servo systems", Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 233, no. 5, pp. 582-590, May 2019 (doi:10.1177/0959651818802097).

[26] S. Yazdi, A. Khayatian, "Performance improvement by optimal reset dynamic output feedback control based on model predictive strategy", Journal of Process Control, vol. 88, pp. 78-85, June 2020 (doi: 10.1016/j.jpro­con­t.2020.02.008).

[27] G. Zhao, J. Wang, "Stability and stabilisation of reset control systems with uncertain output matrix", IET Control Theory and Applications, vol. 9, no. 8, pp. 1312-1319, June 2015 (doi: 10.1049/iet-cta.2014.0007).

[28] V. Ghaffari, P. Karimaghaee, A. Khayatian, "Stability analysis and performance improvement of uncertain linear systems with designing of a suitable reset law", IET Control Theory and Applications, vol. 9, no. 17, pp. 2532-2540, July 2015 (doi:10.1049/iet-cta.2015.0292).

[29] V. Ghaffari, P. Karimaghaee, A. Khayatian, "Reset law design based on robust model predictive strategy for uncertain systems", Journal of Process Control, vol. 24, no. 1, pp. 261-268, Dec. 2014 (doi: 10.1016­/j.jpr­ocon­t.2013.11.017).

[30] M. Mohadeszadeh, N. Pariz, M.R. Ramezani-al, "Exponential stability and L2 gain analysis of uncertain fractional reset control systems", IMA Journal of Mathematical Control and Information, vol.39, no.1, pp. 275-294, March 2022 (doi: 10.1093/imamci/dnab043).

[31] S. Pourdehi, P. Karimaghaee, "Reset observer for a class of nonlinear time-delay systems with application to a two-stage chemical reactor system", Control Strategy for Time-Delay Systems, pp. 231-255, June 2021 (doi: 10.1016/B978-0-32-385347-7.00014-6).

[32] N. Vafamand, A. Khayatian, "Model predictive-based reset gain-scheduling dynamic control law for polyt­opic LPV systems", ISA Transactions, vol. 81, pp. 132-140, Nov. 2018 (doi:10.1016/j.isatra.2018.08.006).

[33] Y. Guo, W. Gui, C. Yang, "Quadratic stability of uncertain reset control systems", IFAC Proceedings Volumes, vol. 44, no. 1, pp. 6297-6300, June 2011 (doi: 10.3182/20110828-6-IT-1002.00120).

[34] Y. Guo, Y. Wang, L. Xie, "Robust stability of reset control systems with uncertain output matrix", Automatica, vol. 48, no. 8, pp. 1879-1884, Oct. 2012 (doi: 10.1016/j.automatica.2012.05.062).

[35] M. Chilali, P. Gahinet, "Design with pole placement constraints: An lmi approach", IEEE Trans. on Automatic Control, vol. 41, no. 3, pp. 358-367, July 1996 (doi: 10.1109/9.486637).

[36] C. Scherer, P. Gahinet, M. Chilali, "Multiobjective output-feedback control via LMI optimization", IEEE Trans. on Automatic Control, vol. 42,  no. 7, pp. 896-911, July 1997 (doi: 10.1109/9.599969).

[37] M. Lemmon, "2-degree-of-freedom robot path planning using cooperative neural fields", Neural Computation, vol. 3, no. 3, pp. 350-362, Feb. 1991 (doi: 10.1162/neco.1991.3.3.350).

[38] S. Yazdi, A. Khayatian, M.H. Asemani, "Optimal robust model predictive reset control design for performance improvement of uncertain linear system", ISA Transactions, vol. 107, pp. 78-89, July 2020 (doi: 10.1016/j.i­satr­a.2020.07.026).

[39] X.J. Li, G.H. Yang, "Robust adaptive fault-tolerant control for uncertain linear systems with actuator failures", IET Control Theory and Applications, vol. 6, no. 10, pp. 1544-1551, July 2012 (doi:10.1049/iet-cta.2011.0­599).