Fick’s Law Algorithm Based-Nonlinear Model Predictive Control of Twin Rotor MIMO System

Omar Y. Ismael; Mohanad N. Noaman; Ismael Kh. Abdullah

doi:10.18196/jrc.v5i3.21725

Fick’s Law Algorithm Based-Nonlinear Model Predictive Control of Twin Rotor MIMO System

Omar Y. Ismael, Mohanad N. Noaman, Ismael Kh. Abdullah

Abstract

Nowadays, controlling a Twin Rotor MIMO System (TRMS) is a considerable challenge for engineers due to its high non-linear attributes. The controller's design goals are to achieve the appropriate pitch and yaw angles when there is cross-coupling between its main and tail rotors while minimizing both the angular position error and controller effort. Performance measures can be utilized to evaluate the performance of the controller including integral square error, total variation, and integral absolute control action. In this paper, a Nonlinear Model Predictive Control (NMPC) is proposed to control TRMS rotors, which refer to the vertical and horizontal planes. Fick’s Law Algorithm (FLA) has been utilized to offline obtain the best selection for NMPC parameters. That includes best weighting matrices, shorter time steps, and shorter prediction horizons, by minimizing a novel penalty function called robust integral square error. FLA is used due to its flexibility, the ability to avoid suboptimal regions, and simplicity of implementation. The effectiveness of the proposed controller is examined using simulation-based tests conducted with MATLAB, which makes use of the CasADi Toolbox. In comparison to Cross Coupled PID (CC-PID) controller, the simulation results prove that FLA-based-NMPC has better performance and can track trajectories (step, square, and sine) even when there is ±30% in TRMS parameters perturbation. This work has come up with new contributions such as the new tuning strategy, extra state variable consideration, and a new FLA engineering application.

Keywords

TRMS; Nonlinear Model Predictive Control (NMPC); Trajectory Tracking; Parameters Uncertainty; Robust Control; FLA; CasADi Toolbox; Cross Coupled PID.

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References

R. Raghavan and S. Thomas, “Practically Implementable Model Predictive Controller for a Twin Rotor Multi-Input Multi-Output System,” Journal of Control, Automation and Electrical Systems, vol. 28, no. 3, pp. 358–370, Mar. 2017, doi: 10.1007/s40313-017-0311-5.

T. Roy and R. Kumar Barai, “LFT modelling and H∞ control of a non-linear MIMO system with cross coupled dynamics,” International Journal of Automation and Control, vol. 7, no. 1-2, pp. 105-133, Jul. 2014, doi: 10.1504/IJAAC.2013.055099.

M. Twin Roto. System Control Experiments 33-949S Feedback Instruments Ltd. East susex, UK, 2006.

M. Qasim and O. Y. Ismael, “Shared Control of a Robot Arm Using BCI and Computer Vision,” Journal Européen des Systèmes Automatisés, vol. 55, no. 1, pp. 139–146, Feb. 2022, doi: 10.18280/jesa.550115.

M. N. Alghanim, M. Qasim, K. P. Valavanis, M. J. Rutherford, and M. Stefanovic, “Comparison of Controller Performance for UGV-Landing Platform Self-Leveling,” 2020 28th Mediterranean Conference on Control and Automation (MED), pp. 471-478, 2020, doi: 10.1109/med48518.2020.9182837.

M. N. Noaman, M. Qasim, and O. Y. Ismael, "Landmarks exploration algorithm for mobile robot indoor localization using VISION sensor," Journal of Engineering Science & Technology, vol. 16, no. 4, pp. 3165-3184, 2021.

M. N. Alghanim, M. Qasim, K. P. Valavanis, M. J. Rutherford, and M. Stefanovic, “Passivity-Based Adaptive Controller for Dynamic Self-Leveling of a Custom-Built Landing Platform on Top of a UGV,” 2020 28th Mediterranean Conference on Control and Automation (MED), 2020, doi: 10.1109/med48518.2020.9182807.

S. Zeghlache, L. Benyettou, A. Djerioui, and M. Z. Ghellab, “Twin Rotor MIMO System Experimental Validation of Robust Adaptive Fuzzy Control Against Wind Effects,” IEEE Systems Journal, vol. 16, no. 1, pp. 409–419, Mar. 2022, doi: 10.1109/jsyst.2020.3034993.

M. Z. Ghellab, S. Zeghlache, A. Djerioui, and L. Benyettou, “Experimental validation of adaptive RBFNN global fast dynamic terminal sliding mode control for twin rotor MIMO system against wind effects,” Measurement, vol. 168, p. 108472, Jan. 2021, doi: 10.1016/j.measurement.2020.108472.

L. Dutta and D. K. Das, “A New Adaptive Explicit Nonlinear Model Predictive Control Design for a Nonlinear MIMO System: An Application to Twin Rotor MIMO System,” International Journal of Control, Automation and Systems, vol. 19, no. 7, pp. 2406–2419, Mar. 2021, doi: 10.1007/s12555-020-0272-5.

D. M. Ezekiel, R. Samikannu, and M. Oduetse, “Modelling of the Twin Rotor MIMO System (TRMS) Using the First Principles Approach,” 2020 International Conference on Computer Communication and Informatics (ICCCI), pp. 1-7, 2020, doi: 10.1109/iccci48352.2020.9104156.

R. Roman, M. Radac, and R. Precup, “Multi‐input–multi‐output system experimental validation of model‐free control and virtual reference feedback tuning techniques,” IET Control Theory & Applications, vol. 10, no. 12, pp. 1395–1403, Aug. 2016, doi: 10.1049/iet-cta.2016.0028.

L. Belmonte, R. Morales, A. Fernández-Caballero, and J. Somolinos, “Robust Decentralized Nonlinear Control for a Twin Rotor MIMO System,” Sensors, vol. 16, no. 8, p. 1160, Jul. 2016, doi: 10.3390/s16081160.

D. E. Konovalov, S. A. Vrazhevsky, I. B. Furtat, and A. S. Kremlev, “Modified Backstepping Algorithm with Disturbances Compensation for Nonlinear MIMO Systems,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 6012–6018, 2020, doi: 10.1016/j.ifacol.2020.12.1665.

V. K. Singh, S. Kamal, and S. Ghosh, “Prescribed-time constrained feedback control for an uncertain twin rotor helicopter,” Aerospace Science and Technology, vol. 140, p. 108483, Sep. 2023, doi: 10.1016/j.ast.2023.108483.

S. Zacher, “Multivariable Control and Management,” Closed Loop Control and Management, pp. 317–353, 2022, doi: 10.1007/978-3-031-13483-8_10.

S. K. Pandey, J. Dey, and S. Banerjee, “Design of Optimal PID Controller for Control of Twin Rotor MIMO System (TRMS),” Advances in Power and Control Engineering, pp. 93–106, Nov. 2019, doi: 10.1007/978-981-15-0313-9_7.

F. Gopmandal and A. Ghosh, “LQR-based MIMO PID control of a 2-DOF helicopter system with uncertain cross-coupled gain,” IFAC-PapersOnLine, vol. 55, no. 22, pp. 183–188, 2022, doi: 10.1016/j.ifacol.2023.03.031.

A. T. Azar, A. S. Sayed, A. S. Shahin, H. A. Elkholy, and H. H. Ammar, “PID Controller for 2-DOFs Twin Rotor MIMO System Tuned with Particle Swarm Optimization,” Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2019, pp. 229–242, Oct. 2019, doi: 10.1007/978-3-030-31129-2_22.

S. Sengupta and C. Dey, “Optimal Auto-Tuned PID Controller for Twin Rotor MIMO System,” Lecture Notes in Mechanical Engineering, pp. 591–601, 2023, doi: 10.1007/978-981-19-9285-8_56.

V. Mihaly, M. Şuşcă, and E. H. Dulf, “μ-Synthesis FO-PID for Twin Rotor Aerodynamic System,” Mathematics, vol. 9, no. 19, p. 2504, Oct. 2021, doi: 10.3390/math9192504.

S. K. Pandey and V. Laxmi, “Optimal Control of Twin Rotor MIMO System Using LQR Technique,” Smart Innovation, Systems and Technologies, pp. 11–21, Dec. 2014, doi: 10.1007/978-81-322-2205-7_2.

S. K. Valluru, M. Singh, Ayush, and A. Dharavath, “Design and Experimental Implementation of Multi-loop LQR, PID, and LQG Controllers for the Trajectory Tracking Control of Twin Rotor MIMO System,” Intelligent Communication, Control and Devices, pp. 599–608, Aug. 2019, doi: 10.1007/978-981-13-8618-3_62.

K. R. Palepogu and S. Mahapatra, “Design of sliding mode control with state varying gains for a Benchmark Twin Rotor MIMO System in Horizontal Motion,” European Journal of Control, p. 100909, Oct. 2023, doi: 10.1016/j.ejcon.2023.100909.

K. Raj, S. K. Choudhary, and V. Muthukumar, “Robust finite-time sliding mode control of twin rotor MIMO system,” International Journal of Modelling, Identification and Control, vol. 35, no. 1, p. 1, 2020, doi: 10.1504/ijmic.2020.113292.

O. Y. Ismael, M. Qasim, and M. N. Noaman, “Equilibrium Optimizer-Based Robust Sliding Mode Control of Magnetic Levitation System,” Journal Européen des Systèmes Automatisés, vol. 54, no. 1, pp. 131–138, Feb. 2021, doi: 10.18280/jesa.540115.

K. R. Palepogu and S. Mahapatra, “Pitch orientation control of twin-rotor MIMO system using sliding mode controller with state varying gains,” Journal of Control and Decision, pp. 1–11, Jan. 2023, doi: 10.1080/23307706.2023.2165977.

M. Panda, N. K. Peyada, and A. Ghosh, “Saturated adaptive backstepping control of uncertain nonlinear systems with validation using twin rotor system,” Journal of the Franklin Institute, vol. 357, no. 18, pp. 13477–13510, Dec. 2020, doi: 10.1016/j.jfranklin.2020.10.003.

Y. Li, H. Zhang, Z. Wang, C. Huang, and H. Yan, “Hybrid adaptive bionic fuzzy control method for MIMO systems with dead-zone input,” Journal of the Franklin Institute, vol. 360, no. 10, pp. 6804–6826, Jul. 2023, doi: 10.1016/j.jfranklin.2023.04.029.

B. Loutfi, Z. Samir, D. Ali, and G. M. Zinelaabidine, “Real Time Implementation of Type-2 Fuzzy Backstepping Sliding Mode Controller for Twin Rotor MIMO System (TRMS),” Traitement du Signal, vol. 36, no. 1, pp. 1–11, Apr. 2019, doi: 10.18280/ts.360101.

J.-G. Juang, W.-K. Liu, and R.-W. Lin, “A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation,” ISA Transactions, vol. 50, no. 4, pp. 609–619, Oct. 2011, doi: 10.1016/j.isatra.2011.06.006.

H. R. Karimi and M. R. J. Motlagh, “Robust Feedback Linearization Control for a non Linearizable MIMO Nonlinear System in the Presence of Model Uncertainties,” 2006 IEEE International Conference on Service Operations and Logistics, and Informatics, pp. 965-970, 2006, doi: 10.1109/soli.2006.328881.

O. Y. Ismael, M. Qasim, M. N. Noaman, and A. Kurniawan, “Salp Swarm Algorithm-Based Nonlinear Robust Control of Magnetic Levitation System Using Feedback Linearization Approach,” Proceedings of the 3rd International Conference on Electronics, Communications and Control Engineering, pp. 58-64, 2020, doi: 10.1145/3396730.3396734.

K. U. Ebirim, A. Lecchini-Visintini, M. Rubagotti, and E. Prempain, “Constrained Model Predictive Control With Integral Action for Twin Rotor MIMO Systems,” Journal of Dynamic Systems, Measurement, and Control, vol. 145, no. 8, Jul. 2023, doi: 10.1115/1.4062735.

L. Dutta and D. K. Das, “Nonlinear Disturbance Observer Based Adaptive Explicit Nonlinear Model Predictive Control Design for a Class of Nonlinear MIMO System,” IEEE Transactions on Aerospace and Electronic Systems, pp. 1–12, 2022, doi: 10.1109/taes.2022.3211252.

S. V. Raković and W. S. Levine, Handbook of Model Predictive Control. Springer International Publishing, 2019. doi: 10.1007/978-3-319-77489-3.

N. Wu, D. Li, Y. Xi, and B. de Schutter, "Distributed Event-Triggered Model Predictive Control for Urban Traffic Lights," in IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 8, pp. 4975-4985, Aug. 2021, doi: 10.1109/TITS.2020.2981381.

M. H. Moradi, “Predictive control with constraints, J.M. Maciejowski; Pearson Education Limited, Prentice Hall, London, 2002, pp. IX+331, price £35.99,” International Journal of Adaptive Control and Signal Processing, vol. 17, no. 3, pp. 261–262, Mar. 2003, doi: 10.1002/acs.736.

R. G. Tiwalkar, S. S. Vanamane, S. S. Karvekar, and S. B. Velhal, “Model predictive controller for position control of twin rotor MIMO system,” 2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI), pp. 952-957, 2017, doi: 10.1109/icpcsi.2017.8391852.

U. M. Nath, C. Dey, and R. K. Mudi, “Controlling of Twin Rotor MIMO System (TRMS) based on Multivariable Model Predictive Control,” Lecture Notes in Electrical Engineering, pp. 493–499, Nov. 2020, doi: 10.1007/978-981-15-7486-3_44.

D.-A. Dutescu, M.-B. Radac, and R.-E. Precup, “Model predictive control of a nonlinear laboratory twin rotor aero-dynamical system,” 2017 IEEE 15th International Symposium on Applied Machine Intelligence and Informatics (SAMI), pp. 000037-000042, 2017, doi: 10.1109/sami.2017.7880339.

A. Rahideh and M. H. Shaheed, “Constrained output feedback model predictive control for nonlinear systems,” Control Engineering Practice, vol. 20, no. 4, pp. 431–443, Apr. 2012, doi: 10.1016/j.conengprac.2011.12.003.

A. Rahideh and M. Hasan Shaheed, “Stable model predictive control for a nonlinear system,” Journal of the Franklin Institute, vol. 348, no. 8, pp. 1983–2004, Oct. 2011, doi: 10.1016/j.jfranklin.2011.05.015.

M. T. Milojkovic, A. D. Djordjevic, S. Lj. Peric, M. B. Milovanovic, Z. H. Peric, and N. B. Dankovic, “Model Predictive Control of Nonlinear MIMO Systems Based on Adaptive Orthogonal Polynomial Networks,” Elektronika ir Elektrotechnika, vol. 27, no. 2, pp. 4–10, Apr. 2021, doi: 10.5755/j02.eie.28780.

F. A. Hashim, R. R. Mostafa, A. G. Hussien, S. Mirjalili, and K. M. Sallam, “Fick’s Law Algorithm: A physical law-based algorithm for numerical optimization,” Knowledge-Based Systems, vol. 260, p. 110146, Jan. 2023, doi: 10.1016/j.knosys.2022.110146.

J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, “CasADi: a software framework for nonlinear optimization and optimal control,” Mathematical Programming Computation, vol. 11, no. 1, pp. 1–36, Jul. 2018, doi: 10.1007/s12532-018-0139-4.

A. Wächter and L. T. Biegler, “Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 1–31, Jan. 2005, doi: 10.1137/s1052623403426556.

L. Grüne and J. Pannek. Nonlinear Model Predictive Control. Springer International Publishing, 2017, doi: 10.1007/978-3-319-46024-6.

E. F. Camacho and C. Bordons. Model Predictive control. Springer London, 2007, doi: 10.1007/978-0-85729-398-5.

O. Y. Ismael, M. Almaged, and A. I. Abdulla, "Nonlinear Model Predictive Control-based Collision Avoidance for Mobile Robot," Journal of Robotics and Control (JRC), vol. 5, no. 1, pp. 142-151, doi: 10.18196/jrc.v5i1.20615.

J. B. Rawlings and K. R. Muske, “The stability of constrained receding horizon control,” IEEE Transactions on Automatic Control, vol. 38, no. 10, pp. 1512–1516, 1993, doi: 10.1109/9.241565.

L. Grüne and J. Pannek. Nonlinear Model Predictive Control. Springer London, 2011, doi: 10.1007/978-0-85729-501-9.

S. Li, H. Chen, M. Wang, A. A. Heidari, and S. Mirjalili, “Slime mould algorithm: A new method for stochastic optimization,” Future Generation Computer Systems, vol. 111, pp. 300–323, Oct. 2020, doi: 10.1016/j.future.2020.03.055.

A. G. Hussien, A. E. Hassanien, E. H. Houssein, M. Amin, and A. T. Azar, “New binary whale optimization algorithm for discrete optimization problems,” Engineering Optimization, vol. 52, no. 6, pp. 945–959, Jun. 2019, doi: 10.1080/0305215x.2019.1624740.

S. M. Ahmad, A. J. Chipperfield, and M. O. Tokhi, “Dynamic modelling and linear quadratic Gaussian control of a twin-rotor multi-input multi-output system,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 217, no. 3, pp. 203–227, May 2003, doi: 10.1177/095965180321700304.

DOI: https://doi.org/10.18196/jrc.v5i3.21725

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