zbMATH — the first resource for mathematics

Development of a fuzzy-LQR and fuzzy-LQG stability control for a double link Rotary inverted pendulum. (English) Zbl 1450.93031
Summary: In this paper, a fuzzy based linear quadratic regulator (FLQR) and linear quadratic Gaussian (FLQG) controllers are developed for stability control of a double link rotary inverted pendulum (DLRIP) system. The aim of this work is to study dynamic performance analysis of both FLQR and FLQG controllers and to compare them with the classical LQR and LQG controllers, respectively. A dynamic mechanical simulation model of the DLRIP was obtained using both the numerically SimMechanics toolbox in MATLAB and the analytically dynamic nonlinear equations. To determine the control performance of the controllers, settling time \((\boldsymbol{T}_{\boldsymbol{s}})\), peak overshoot (PO), steady-state error \((\boldsymbol{E}_{\boldsymbol{ss}})\), and the total root mean squared errors (RMSEs) of the joint positions are computed. Furthermore, the dynamic responses of the controllers were compared based on robustness analysis under internal and external disturbances. To show the control performance of the controllers, several simulations were conducted. Based on the comparative results, the dynamic responses of both FLQR and FLQG controllers produce much better results than the dynamic responses of the classical LQR and LQG controllers, respectively. Moreover, the robustness results indicate that the FLQR and FLQG controllers under the internal and external disturbances were effective.
93C42 Fuzzy control/observation systems
49N10 Linear-quadratic optimal control problems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
70Q05 Control of mechanical systems
Matlab; SimMechanics
Full Text: DOI
[1] Knut, G.; Treuer, M.; Zeitz, M., Swing-up of the double pendulum on a cart by feedforward and feedback control with experimental validation, Automatica, 43, 1, 63-71 (2007) · Zbl 1140.93368
[2] Nenad, M.; Tovornik, B., Swinging up and stabilization of a real inverted pendulum, IEEE Trans. Ind. Electron., 53, 2, 631-639 (2006)
[3] Ramírez, M., Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum, ISA Trans, 53, 4, 920-928 (2014)
[4] Gisela, P.; Acho, L., Stabilization of the Furuta Pendulum with backlash using H∞‐LMI technique: experimental validation, Asian J. Control, 12, 4, 460-467 (2010)
[5] Hazem, Z. B.; Fotuhi, M. J.; Bingül, Z., A Comparative study of the joint neuro-fuzzy friction models for a triple link rotary inverted pendulum, IEEE Access, 8, 49066-49078 (2020)
[6] Casanova, V., Controlling the double rotary inverted pendulum with multiple feedback delays, Int. J. Comput. Commun. Control, 7, 1, 20-38 (2012)
[7] Jadlovský, S.; Sarnovský, J., Modelling of classical and rotary inverted pendulum systems-a generalized approach, J. Electr. En., 64, 1, 12-19 (2013)
[8] MMehedi, I., Stabilization of a double inverted rotary pendulum through fractional order integral control scheme, Int. J. Adv. Robot. Syst., 16, 4, Article 1729881419846741 pp. (2019)
[9] Baumann; Rugh, W., Feedback control of nonlinear systems by extended linearization, IEEE Trans. Automat. Control, 31, 1, 40-46 (1986) · Zbl 0582.93031
[10] El-Bardini, M.; El-Nagar, A. M., Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system, ISA Trans., 53, 3, 732-743 (2014)
[11] Tao, J., Asynchronous filtering of nonlinear Markov jump systems with randomly occurred quantization via T-S fuzzy models, IEEE Trans. Fuzzy Syst., 26, 4, 1866-1877 (2017)
[12] Tao, J., Dissipativity-based reliable control for fuzzy Markov jump systems with actuator faults, IEEE Trans. Cybern., 47, 9, 2377-2388 (2016)
[13] Tao, J., et al. “Filtering of T-S fuzzy systems with nonuniform sampling”, IEEE Trans. Syst., Man Cybern. Syst., 48, 12, 2442-2450 (2017)
[14] Zhang, M., Static output feedback control of switched nonlinear systems with actuator faults, IEEE Trans. Fuzzy Syst. (2019)
[15] Zhang, M., Dissipative filtering for switched fuzzy systems with missing measurements, IEEE Trans. Cybern., 50, 5, 1931-1940 (2019)
[16] Zhang, M., PID passivity-based control of port-Hamiltonian systems, IEEE Trans. Automat. Control, 63, 4, 1032-1044 (2017) · Zbl 1390.93652
[17] El-Hawwary, Mohamed I., Adaptive fuzzy control of the inverted pendulum problem, IEEE Trans. Control Syst. Technol., 14, 6, 1135-1144 (2006)
[18] Prasad, L. B.; Tyagi, B.; Gupta, Hari Om, Optimal control of nonlinear inverted pendulum system using PID controller and LQR: performance analysis without and with disturbance input, Int. J. Autom. Comput., 11, 6, 661-670 (2014)
[19] Yi, Jianqiang; Yubazaki, Naoyoshi; Hirota, Kaoru, Upswing and stabilization control of inverted pendulum system based on the SIRMs dynamically connected fuzzy inference model, Fuzzy Sets Syst., 122, 1, 139-152 (2001) · Zbl 0978.93530
[20] Tao, Chin-Wang, Design of a fuzzy controller with fuzzy swing-up and parallel distributed pole assignment schemes for an inverted pendulum and cart system, IEEE Trans. Control Syst. Technol., 16, 6, 1277-1288 (2008)
[21] Tao, Chin-Wang; Taur, Jin-Shiuh; Chen, Y. C., Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system, Fuzzy Sets Syst., 161, 15, 2081-2103 (2010) · Zbl 1194.93119
[22] Adeli, Mahdieh, et al. “Anti-swing control for a double-pendulum-type overhead crane via parallel distributed fuzzy LQR controller combined with genetic fuzzy rule set selection.”, Proceedings of the IEEE International Conference on Control System, Computing and Engineering, IEEE(2011).
[23] Kim, S.; Kwon, S., Nonlinear optimal control design for underactuated two-wheeled inverted pendulum mobile platform, IEEE/ASME Trans. Mechatron., 22, 6, 2803-2808 (2017)
[24] Mehedi, I. M., Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: design and experiments, J. Vib. Control, Article 1077546320915333 pp. (2020)
[25] Tobias, G.; Eder, A.; Kugi, A., Swing-up control of a triple pendulum on a cart with experimental validation, Automatica, 49, 3, 801-808 (2013) · Zbl 1267.93051
[26] Kumar, E.; Jerome, Jovitha, Robust LQR controller design for stabilizing and trajectory tracking of inverted pendulum, Procedia Eng., 64, 169-178 (2013)
[27] Yadav, S. K.; Sharma, S.; Singh, N., Optimal control of double inverted pendulum using LQR controller, Int. J. Adv. Res. Comput. Sci. Softw. Eng., 2, 2 (2012)
[28] Prasad, L. B.; Tyagi, B.; Gupta, H. O., Optimal control of nonlinear inverted pendulum system using PID controller and LQR: performance analysis without and with disturbance input, Int. J. Autom. Comput., 11, 6, 661-670 (2014)
[29] Wang, L.; Zhanshi, S., LQR-Fuzzy control for double inverted pendulum, (Proceedings of the International Conference on Digital Manufacturing and Automation, 1 (2010), IEEE), 900-903
[30] Kizir, S.; Bingül, Z., Fuzzy impedance and force control of a Stewart platform, Turk. J. Electr. Eng. Comput. Sci., 22, 4, 924-939 (2014)
[31] Akyüz, I. H.; Bingül, Z.; Kizir, S., “Cascade fuzzy logic control of a single-link flexible-joint manipulator.”, Turkish J. Electr. Eng. Comput. Sci., 20, 5, 713-726 (2012)
[32] Kizir, S.; Bingul, Z.; Oysu, C., Fuzzy control of a real time inverted pendulum system, J. Intell. Fuzzy Syst., 21, 1, 121-133 (2010), Volume:2 · Zbl 1211.93080
[33] Yaren, T.; Kizir, S., Stabilization Control of Triple Pendulum on a Cart, (Proceedings of the 6th International Conference on Control Engineering and Information Technology (CEIT) (2018), IEEE), 1-6
[34] Ragnar, E.; Egelid, P. M.; R. Karimi, H., “LQG control design for balancing an inverted pendulum mobile robot.”, Intell. Control Automat., 2, 02, 160 (2011)
[35] Lupian, Luis F.; Avila, R., Stabilization of a wheeled inverted pendulum by a continuous-time infinite-horizon LQG optimal controller, (Proceedings of the Latin American Robotic Symposium (2008), IEEE)
[36] Collins, G. Emmanuel; Selekwa, M. F., A fuzzy logic approach to LQG design with variance constraints, IEEE Trans. Control syst. Technol., 10, 1, 32-42 (2002)
[37] Odry, Á.; Fodor, J.; Odry, P., Stabilization of a two-wheeled mobile pendulum system using LQG and fuzzy control techniques, Int. J. Adv. Intell. Syst., 9, 1, 2 (2016)
[38] Celaya, E., Implementation of an Adaptive BDF2 Formula and Comparison with the MATLAB Ode15s, (Proceedings of the ICCS (2014))
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.