Tracking Iterative Learning Control of TRMS using Feedback Linearization Model with Input Disturbance
DOI:
https://doi.org/10.18196/jrc.v6i1.25579Keywords:
Feedback Linearization Control, Uncertain Parameters, Iterative Learning, TRMS, Euler-Lagrange Form, Input DisturbancesAbstract
This paper presents a method for angular trajectory tracking control of the Twin Rotor Multi-Input Multi-Output System (TRMS) experimental model using linearized feedback control with nonlinear compensation and iterative learning-based angular trajectory tracking control. First, the dynamic model of the Twin Rotor MIMO System (TRMS) is developed in the form of Euler-Lagrange (ELF), including descriptions of uncertain parameters and input disturbances such as energy dependence related to the mass of components, friction forces, the effect of the TRMS flat cable, and the impact of the main rotor and tail rotor speeds on horizontal and vertical movements. Based on the nonlinear acceleration equations for the pitch and yaw angles of the TRMS, a compensator is designed to address the nonlinearity of the EL model. Notably, this compensator self-adjusts the compensation signal so that the closed-loop system, consisting of the TRMS and the compensator, becomes a predetermined linear model. Therefore, the structure of the compensator does not need to be designed based on the nonlinear model of the TRMS. After incorporating the compensator, the ELF becomes nearly linear with sufficient accuracy as designed. This system is then controlled using a predefined trajectory tracking controller based on iterative learning with proportional-type learning parameters. By adjusting a sufficiently small optional time parameter, the trajectory tracking error of the pitch and yaw angles of the closed-loop system can be reduced to a desired small-radius neighborhood. Simulation and experimental results demonstrate the trajectory-tracking capability of the closed-loop system. Although the convergence rate depends on the complexity of the TRMS dynamics, the robustness of this method with varying initial conditions is always ensured. The computational complexity is slightly higher compared to other methods, Still, this study contributes a straightforward yet effective trajectory control method under conditions of noise depending on the position, velocity, pitch and yaw angles and unmeasured kinematic model parameters for the TRMS system.
References
TRMS 33-949S, User Manual. Feedback instruments Ltd., East Sussex, U. K, 1998.
S. K. Pandey, J. Dey, and S. Banerjee, "Design and real-time implementation of robust PID controller for Twin Rotor MIMO System (TRMS) based on Kharitonov's theorem," in IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), pp. 1-6, 2016, doi: 10.1109/ICPEICES.2016.7853106.
A. A. Patel, P. M. Pithadiya, and H. V. Kannad, “Control of Twin Rotor MIMO System (TRMS) Using PID Controller,” in National Conference on Emerging Trends in Computer, Electrical & Electronics (ETCEE-2015) International Journal of Advance Engineering and Research Development (IJAERD), pp. 2348-4470, 2015.
Fahmizal, H. A. Nugroho, A. I. Cahyadi and I. Ardiyanto, "Twin Rotor MIMO System Control using Linear Quadratic Regulator with Simechanics," in 7th International Conference on Electrical, Electronics and Information Engineering (ICEEIE), pp. 301-306, 2021, doi: 10.1109/ICEEIE52663.2021.9616893.
A. Rahideh and M. H. Shaheed, "Mathematical dynamic modelling of a twin-rotor multiple input-multiple output system," in Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 221, no. 1, pp. 89-101, 2007.
A. K. Ekbote, N. S. Srinivasan, and A. D. Mahindrakar, “Terminal sliding mode control of a Twin rotor multiple-input multiple Output System,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 10952-10957, 2011.
S. Sajjad Moosapour, H. Mehdipour, and M. Keramatzadeh, "Sliding Mode Disturbance Observer-Based Control of a Laboratory Twin Rotor Multi Input-Multi Output System," in IEEE Access, vol. 13, pp. 394-406, 2025, doi: 10.1109/ACCESS.2024.3523850.
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, 2019.
M. Derakhshannia, S. B. F. Asl, and S. S. Moosapour, "Backstepping Terminal Sliding Mode Control Design for a TRMS," 2021 7th International Conference on Control, Instrumentation and Automation (ICCIA), pp. 1-5, 2021, doi: 10.1109/ICCIA52082.2021.9403545.
N. Abbas, Z. Abbas, and X. Liu, "Adaptive recursive sliding mode control (ARSMC)-Based UAV control for future smart cities," in Applied Sciences, vol. 13, no. 11, pp. 6790, 2023.
X. Yang et al., "Input shaping enhanced active disturbance rejection control for a twin rotor multi-input multi-output system (TRMS)," in ISA transactions, vol. 62, pp. 287-298, 2016.
G. Shivani, A. Jamodkar, and B. J. Pandian, "Modeling and Implementation of Adaptive Control Technique on a TRMS Model," in International Journal of Innovative Technology and Exploring Engineering, vol. 8, no. 8, pp. 1015-1020, 2019.
A. Rahideh, M. H. Shaheed, and A. H. Bajodah, "Adaptive Nonlinear Model Inversion Control of a Twin Rotor System Using Artificial Intelligence," in IEEE International Conference on Control Applications, pp. 898-903, 2007, doi: 10.1109/CCA.2007.4389347.
F. Faris, A. Moussaoui, B. Djamel, and T. Mohammed, “Design and real-time implementation of a decentralized sliding mode controller for twin rotor multi-input multi-output system,” in Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 231, no. 1, pp. 3-13, 2017, doi: 10.1177/0959651816680457
E. S. Ghith and F. A. A. Tolba, "Design and optimization of PID controller using various algorithms for micro-robotics system," in Journal of Robotics and Control (JRC), vol. 3, no. 3, pp. 244-256, 2022.
M. H. Shaheed, "Feedforward neural network based non‐linear dynamic modelling of a TRMS using RPROP algorithm," in Aircraft Engineering and Aerospace Technology, vol. 77, no. 1, pp. 13-22, 2005.
A. Rahideh, M. H. Shaheed, and H. J. C. Huijberts, "Dynamic modelling of a TRMS using analytical and empirical approaches," in Control Engineering Practice, vol. 16, no. 3, pp. 241-259, 2008.
G. S. Rao et al., "Evaluating and optimizing surface roughness using genetic algorithm and artificial neural networks during turning of AISI 52100 steel," in International Journal on Interactive Design and Manufacturing (IJIDeM), vol. 18, no. 8, pp. 6151-6160, 2024.
M. H. Shaheed, "Performance analysis of 4 types of conjugate gradient algorithms in the nonlinear dynamic modelling of a TRMS using feedforward neural networks," 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583), vol. 6, pp. 5985-5990, 2004, doi: 10.1109/ICSMC.2004.1401153.
A. Jain, S. Sheel, and P. Kuchhal, “Fuzzy logic-based real-time control for a twin-rotor MIMO system using GA-based optimization,” World Journal of Engineering, vol. 15, no. 2, pp. 192-204, 2018.
S. Bandyopadhyay, P. Pramanick, and C. Dey, "Fuzzy Rule-Based supervisory PID Auto-Tuner for TRMS process," in Proceedings of the Fourth International Conference on Microelectronics, Computing and Communication Systems: MCCS 2019, pp. 655-669, 2021.
S. K. Valluru, R. Kumar, and R. Kumar, "Design and Real Time implementation of fmincon, MOGA tuned IO-PID and FO-PIλDμ Controllers for Stabilization of TRMS," in Procedia Computer Science, vol. 171, pp. 1241-1250, 2020.
K. Kalyani and S. Kanagalakshmi, "Control of Trms using Adaptive Neuro Fuzzy Inference System (ANFIS)," 2020 International Conference on System, Computation, Automation and Networking (ICSCAN), pp. 1-5, 2020, doi: 10.1109/ICSCAN49426.2020.9262417.
F. L. Lewis, D. M. Dawson, and C. T. Abdallah, Robot manipulator control: theory and practice. CRC Press, 2003.
E. D. Sontag and Y. Wang, “On characterizations of the input-to-state stability property,” Systems & Control Letters, vol. 24, no. 5, pp. 351-359, 1995.
N. V. Chi and N. D. Phuoc, “Adaptive tracking control based on disturbance attenuation and ISS stabilization of Euler-Lagrange nonlinear in the presence of uncertainty and input noise,” in Proceedings of IEEE 2th Int. Conference on Electrical Engineering and Automation Control (EEAC2011), pp. 3698-3071, 2011.
N. V. Chi, “Adaptive feedback linearization control for twin rotor multiple-input multiple-output system,” in Int. J. Control Autom. Syst., vol. 15, pp. 1267–1274, 2017.
N. V. Chi, "Adaptive sliding mode tracking control for twin rotor multi-input multi-output nonlinear system," in Int. J. Control Autom. Syst., vol. 4, no. 4, pp. 9-16, 2015.
D. U. Rijalusalam and I. Iswanto, "Implementation kinematics modeling and odometry of four omni wheel mobile robot on the trajectory planning and motion control based microcontroller," in Journal of Robotics and Control (JRC), vol. 2, no. 5, pp. 448-455, 2021.
J. H. Pérez-Cruz, "Stabilization and synchronization of uncertain zhang system by means of robust adaptive control," in Complexity, vol. 2018, no. 1, pp. 4989520, 2018.
C. N. Van and P. N. Doan, “Adaptive ISS Stabilization Tracking Control Of Nonlinear Systems In The Presence Of Uncertainty And Input Noise With Guaranteed Tracking Errors,” in Journal of Computer Science and Cybernetics, vol. 29, no. 2, 2013.
A. Rahideh and M. H. Shaheed, “Mathematical dynamic modelling of a twin-rotor multiple input-multiple output system,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 221, no. 1, pp. 89-101, 2007.
D. Rotondo, F. Nejjari, and V. Puig, "Quasi-LPV modeling, identification and control of a twin rotor MIMO system," in Control Engineering Practice, vol. 21, no. 6, pp. 829-846, 2013.
D. Rotondo, Advances in gain-scheduling and fault tolerant control techniques. Springer, 2017.
X. Yang et al., "Input shaping enhanced active disturbance rejection control for a twin rotor multi-input multi-output system (TRMS)," in ISA transactions, vol. 62, pp. 287-298, 2016.
G. Srinivasarao, A. K. Samantaray, and S. K. Ghoshal, "Cascaded adaptive integral backstepping sliding mode and super-twisting controller for twin rotor system using bond graph model," in ISA transactions, vol. 130, pp. 516-532, 2022.
W. Perruquetti and J. P. Barbot, Sliding mode control in engineering. New York: Marcel Dekker, 2002.
N. D. Phuoc, Analysys and Control for nonlinear systems. Science and Technics Publishing House, Viet Nam, 2002.
H. P. Tairen Suna, Y. Pana, H. Zhoua, and C. Zhangc, “Neural network-based sliding mode adaptive control for robot manipulators,” in Neuro computing, vol. 74, no. 14–15, pp. 2377-2384, 2011.
V. I. Utkin and A. S. Poznyak, "Adaptive sliding mode control," in Advances in Sliding Mode Control: Concept, Theory and Implementation, pp. 21-53, 2013.
A. Allevato, M. Pryor, and A. L. Thomaz, "Multiparameter Real-World System Identification Using Iterative Residual Tuning," in ASME. J. Mechanisms Robotics, vol. 13, no. 3, p. 031021, 2021.
E. Spyrakos-Papastavridis and J. S. Dai, "Flexible-Joint Humanoid Balancing Augmentation via Full-State Feedback Variable Impedance Control," in ASME. J. Mechanisms Robotics, vol. 13, no. 2, p. 021014, 2021.
L. Cuvillon, X. Weber, and J. Gangloff, "Modal Control for Active Vibration Damping of Cable-Driven Parallel Robots," in ASME. J. Mechanisms Robotics, vol. 12, no. 5, p. 051004, 2020.
M. H. H. Kani, H. A. Yaghini Bonabi, H. Jalaly Bidgoly, M. Javad Yazdanpanah, and M. Nili Ahmadabadi, "Design and Implementation of a Distributed Variable Impedance Actuator Using Parallel Linear Springs," in ASME. J. Mechanisms Robotics, vol. 8, no. 2, p. 021024, 2016.
N. Olgac and R. Sipahi, "An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems," in IEEE Transactions on Automatic Control, vol. 47, no. 5, pp. 793-797, 2002.
R. Goyal, G. Parmar, and A. Sikander, "A new approach for simplification and control of linear time invariant systems," in Microsystem Technologies, vol. 25, pp. 599-607, 2019.
W. A. Malik, S. Darbha, and S. P. Bhattacharyya, "On the transient control of Linear Time Invariant systems," 2009 American Control Conference, pp. 3142-3147, 2009, doi: 10.1109/ACC.2009.5160676.
M. Pourahmadi, "Taylor expansion of and some applications," in The American Mathematical Monthly, vol. 91, no. 5, pp. 303-307, 1984.
E. M. Wright, "The asymptotic expansion of integral functions defined by Taylor series," in Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 238, no. 795, pp. 423-451, 1940.
F. J. Kraus, M. Mansour, and M. Sebek. "Hurwitz matrix for polynomial matrices," in Stability Theory: Hurwitz Centenary Conference Centro Stefano Franscini, Ascona, pp. 67-74, 1996.
W. Li, "Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix," in Applied mathematics and computation, vol. 185, no. 1, pp. 397-401, 2007.
D. A. Bristow, M. Tharayil, and A. G. Alleyne, "A survey of iterative learning control," in IEEE control systems magazine, vol. 26, no. 3, pp. 96-114, 2006.
H-. S. Ahn, Y. Q. Chen, and K. L. Moore, "Iterative learning control: Brief survey and categorization," in IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 37, no. 6, pp. 1099-1121, 2007.
Z. Bien and J-. X. Xu, Iterative learning control: analysis, design, integration and applications. in Springer Science & Business Media, 2012.
N. Amann, D. H. Owens, and E. Rogers, "Predictive optimal iterative learning control," in International Journal of Control, vol. 69, no. 2, pp. 203-226, 1998.
R. Amalrajan, R. Gunabalan, and N. Tewari, "DSPACE1103 controller for PWM control of power electronic converters," in Advances in Smart Grid Technology: Select Proceedings of PECCON 2019—Volume I, pp. 307-322, 2020.
T. Boutabba et al., "dSPACE Real-Time Implementation of Maximum Power Point Tracking Based on Kalman Filter Structure using Photovoltaic System Emulator," 2021 International Conference on Control, Automation and Diagnosis (ICCAD), pp. 1-6, 2021, doi: 10.1109/ICCAD52417.2021.9638743.
C. B. Murugan, S. Natarajan, and R. Bensraj, "dSPACE based implementation of various inverted sine carrier PWM strategies for three phase five level H-bridge inverter," in Int J Adv Engg Tech/Vol. VII/Issue I/Jan.-March, vol. 103, p. 112, 2016.
K. Lakomy et al., "Active disturbance rejection control (adrc) toolbox for matlab/simulink," in arXiv preprint arXiv:2112.01614, 2021.
V. A. Barausov, V. P. Bubnov, and S. K. Sultonov, "Simulation modeling in methods and designs for detecting ice or snow buildup on control surface in MATLAB/SIMULINK dynamic modeling environment," in Models and Methods for Researching Information Systems in Transport 2020 (MMRIST 2020), vol. 1, pp. 136-141, 2020.
L. Wang, PID control system design and automatic tuning using MATLAB/Simulink. John Wiley & Sons, 2020.
F. F. Al-Azzawi et al., "Modulation and RS-CC rate specifications in WiMAX IEEE 802.16 Standard with MATLAB Simulink model," in IOP Conference Series: Materials Science and Engineering, vol. 881, no. 1, 2020.
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