Abstract
The steady-state operation and controlled position tracking in ball balancer applications are largely affected due to their nonlinear and underactuated behavior. To overcome these drawbacks, this paper develops a wavelet-based fuzzy controller which operates in closed loop with the system by measuring the ball position and the plate angle. The proposed approach adapts discrete wavelet transform for denoising the error signal and tuning the weights of the fuzzy controller. To test the effectiveness of the proposed approach, numerical simulations are performed by modeling a two degree of freedom ball balancer system. The eminence of the controller is assessed by comparing its operation on the modeled system with conventional fuzzy logic controller and by calculating the root mean square error, and time response analysis. The results showed a steady and precise response of the proposed approach to the framework of positioning ball on the plate.
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Murray, R.M., Astrom, K.J., Boyd, S.P., Brockett, R.W., Stein, G.: Future directions in control in an information-rich word. IEEE Control Syst Mag. 23, 20–33 (2003). https://doi.org/10.1109/MCS.2003.1188769
Nelles, O.: Nonlinear System Identification. Springer, Berlin Heidelberg, Berlin, Heidelberg (2001)
Boubaker, O.: The inverted pendulum: A fundamental benchmark in control theory and robotics. Int. Conf. Educ. e-Learning Innov. (2012)
Chalupa, P., Přikryl, J., Novák, J.: Modelling of Twin Rotor MIMO System. Proc. 2015 20th Int. Conf. Process Control. PC 2015. 2015-July, 314–319 (2015). https://doi.org/https://doi.org/10.1109/PC.2015.7169982
Nowopolski, K.: Ball-and-beam laboratory system controlled by Simulink model through dedicated microcontrolled-Matlab data exchange protocol. Comput. Appl. Electr. Eng. 11, 310–320 (2013)
Aranda, J., Chaos, D., Dormido-Canto, S., Muñoz, R., Díaz, J.M.: Benchmark control problems for a non-linear underactuated hovercraft: A simulation laboratory for control testing. IFAC Proc. 7, 463–468 (2006). https://doi.org/10.3182/20060621-3-ES-2905.00080
Acosta, J.Á.: Furuta’s pendulum: A conservative nonlinear model for theory and practise. Math. Probl. Eng. 2010, (2010). https://doi.org/https://doi.org/10.1155/2010/742894
Awtar, S., Bernard, C., Boklund, N., Master, A., Ueda, D., Craig, K.: Mechatronic design of a ball-on-plate balancing system. Mechatronics 12, 217–228 (2002). https://doi.org/10.1016/S0957-4158(01)00062-9
Aguilar-Avelar, C., Moreno-Valenzuela, J.: New feedback linearization-based control for arm trajectory tracking of the furuta pendulum. IEEE/ASME Trans Mechatronics. 21, 638–648 (2016). https://doi.org/10.1109/TMECH.2015.2485942
Rudra, S., Barai, R.K., Maitra, M.: Block Backstepping Control of the Underactuated Mechanical Systems. In: Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems. pp. 31–52. Springer Singapore, Singapore (2017)
Moreno-Valenzuela, J., Aguilar-Avelar, C.: Feedback Linearization Control of the Furuta Pendulum. Presented at the (2018)
Spong, M.W.: Partial feedback linearization of underactuated mechanical systems. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’94). pp. 314–321. IEEE
Ortega, R., Spong, M.W., Gomez-Estern, F., Blankenstein, G.: Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002). https://doi.org/10.1109/TAC.2002.800770
Sun, S., Li, L.: The Study of Ball and Plate System Based on Non-linear PID. Appl. Mech. Mater. Vol. 187 pp 134–137. 187, 134–137 (2012). https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.187.134
Mochizuki, S., Ichihara, H.: Generalized Kalman-Yakubovich-Popov Lemma Based I-PD Controller Design for Ball and Plate System. J. Appl. Math. 2013, 1–9 (2013). https://doi.org/10.1155/2013/854631
Composite Disturbance Rejection Control for Ball Balancer System: Pinagapani, A.K., Mani, G., K R, C., Pandian, K. Procedia Comput. Sci. 133, 124–133 (2018). https://doi.org/10.1016/j.procs.2018.07.016
Ali, H.I., Jassim, H.M., Hasan, A.F.: Optimal Nonlinear Model Reference Controller Design for Ball and Plate System. Arab. J. Sci. Eng. 44, 6757–6768 (2019). https://doi.org/10.1007/s13369-018-3616-1
Bang, H., Lee, Y.S.: Implementation of a ball and plate control system using sliding mode control. IEEE Access. 6, 32401–32408 (2018). https://doi.org/10.1109/ACCESS.2018.2838544
Das, A., Roy, P.: Improved performance of cascaded fractional-order smc over cascaded smc for position control of a ball and plate system. IETE J. Res. 63, 238–247 (2017). https://doi.org/10.1080/03772063.2016.1258336
Kao, S.-T., Ho, M.-T.: Second-Order Sliding Mode Control for Ball-Balancing System. In: 2018 IEEE Conference on Control Technology and Applications (CCTA). pp. 1730–1735. IEEE (2018)
Bang, H., Lee, Y.S.: Embedded model predictive control for enhancing tracking performance of a ball-and-plate system. IEEE Access. 7, 39652–39659 (2019). https://doi.org/10.1109/ACCESS.2019.2907111
Zhang, Z., Yuan, D.: Modelling and control scheme of the ball–plate trajectory-tracking pneumatic system with a touch screen and a rotary cylinder. IET Control Theory Appl. 4, 573–589 (2010). https://doi.org/10.1049/iet-cta.2008.0540
Marco A. Moreno-Armendariz,Cesar A. Perez-Olvera, Floriberto Ortiz Rodrıguez, E.R.: Indirect hierarchical FCMAC control for the ball and plate system. Neurocomputing. 73, 2454–2463 (2010). https://doi.org/https://doi.org/10.1016/j.neucom.2010.03.023
Dong, X., Zhao, Y., Xu, Y., Zhang, Z., Shi, P.: Design of PSO fuzzy neural network control for ball and plate system. Int J Innov Comput Inf Control. 7, 7091–7103 (2011)
Singh, R., Bhushan, B.: Real-time control of ball balancer using neural integrated fuzzy controller. Artif Intell Rev. (2018). https://doi.org/10.1007/s10462-018-9658-7
Shahriari-Kahkeshi, M.: Dead-zone model-based adaptive fuzzy wavelet control for nonlinear systems including input saturation and dynamic uncertainties. Int J Fuzzy Syst. 20, 2577–2592 (2018). https://doi.org/10.1007/s40815-018-0515-2
Huynh, T.-T., Le, T.-L., Lin, C.-M.: Self-organizing recurrent wavelet fuzzy neural network-based control system design for MIMO uncertain nonlinear systems using TOPSIS method. Int J Fuzzy Syst. 21, 468–487 (2019). https://doi.org/10.1007/s40815-018-0550-z
Tafti, B.E.F., Teshnehlab, M., Khanesar, M.A.: Recurrent interval type-2 fuzzy wavelet neural network with stable learning algorithm: application to model-based predictive control. Int J Fuzzy Syst. 22, 351–367 (2020). https://doi.org/10.1007/s40815-019-00766-z
Sugiyama, M.: Statistical Reinforcement Learning, Modern Machine Learning Approaches, (2015)
Electronics, M.: Faulhaber DC-Micromotors Series 2338.
Quanser Inc.: Peripherals to Accelerate Control System Design and Implementation. 12 (2010)
Chaumette, F., Hutchinson, S.: Visual servo control. I. Basic approaches. IEEE Robot. & Autom. Mag. 13, 82–90 (2006). https://doi.org/https://doi.org/10.1109/MRA.2006.250573
Quanser educational solutions: 2D Ball Balancer User Manual. , Markham, Ontario. (2013)
Singh, R., Bhushan, B.: Improved ant colony optimization for achieving self-balancing and position control for balancer systems. J. Ambient Intell. Humaniz, Comput (2020)
https://doi.org/https://doi.org/10.1007/s12652-020-02566-y
Pinagapani, A.K., Mani, G., Chandran, K.R., Pandian, K.: Composite disturbance rejection control for ball balancer system. Procedia Comput Sci. 133, 124–133 (2018). https://doi.org/10.1016/j.procs.2018.07.016
Sarkar, T.K., Adve, R., Salazar, M., Garcia, L.: Engineering Perspective, Part 1: Discrete Wavelet Techniques’. IEEE Antennas Propag Mag. 40, 49–70 (1998). https://doi.org/10.1109/74.735965
Yan, R., Gao, R.X.: Tutorial 21 wavelet transform: A mathematical tool for non-stationary signal processing in measurement science part 2 in a series of tutorials in instrumentation and measurement. IEEE Instrum. Meas. Mag. 12, 35–44 (2009). https://doi.org/10.1109/MIM.2009.5270529
Poterasu, V.F.: Wavelets transform for nonlinear control of multibody systems. J. Franklin Inst. 338, 321–334 (2001). https://doi.org/10.1016/S0016-0032(00)00090-9
Mallat, S.G.: A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989). https://doi.org/10.1109/34.192463
Ngui, W.K., Leong, M.S., Hee, L.M., Abdelrhman, A.M.: Wavelet Analysis: Mother Wavelet Selection Methods. Appl Mech Mater. 393, 953–958 (2013). https://doi.org/10.4028/www.scientific.net/AMM.393.953
Sewilam, T.S.A.A.: Automated wavelet-based fault detection and diagnosis for smart distribution systems and microgrids, (2017)
Morsi, W.G., El-Hawary, M.E.: A new perspective for the IEEE standard 1459–2000 via stationary wavelet transform in the presence of nonstationary power quality disturbance. IEEE Trans Power Deliv. 23, 2356–2365 (2008). https://doi.org/10.1109/TPWRD.2008.2002660
Proakis, J.G., Manolakis, D.G.: Design of Hilbert Transformers, (1996)
Vetterli, M., Herley, C.: Wavelets and Filter Banks: Theory and Design. IEEE Trans. Signal Process. 40, 2207–2232 (1992). https://doi.org/10.1109/78.157221
Debnath, L.: The Wigner-Ville Distribution and Time-Frequency Signal Analysis. In: Wavelet Transforms and Their Applications. pp. 307–360. Birkhäuser Boston, Boston, MA (2002)
You, Y.-L.: Audio Coding: Theory and Applications. (2010)
Parvez, S., Gao, Z.: A wavelet-based multiresolution PID controller. IEEE Trans Ind Appl. 41, 537–543 (2005). https://doi.org/10.1109/TIA.2005.844378
Febin Daya, J.L., Subbiah, V., Iqbal, A., Padmanaban, S.: Novel wavelet-fuzzy ased indirect field oriented control of induction motor drives. J. Power Electron. 13, 656–668 (2013). https://doi.org/10.6113/JPE.2013.13.4.656
Febin Daya, J.L., Subbiah, V., Sanjeevikumar, P.: Robust speed control of an induction motor drive using wavelet-fuzzy based self-tuning multiresolution controller. Int J Comput Intell. Syst. 6, 724–738 (2013). https://doi.org/10.1080/18756891.2013.803741
Ho, M.-T., Rizal, Y., Chu, L.-M.: Visual Servoing Tracking Control of a Ball and Plate System: Design, Implementation and Experimental Validation. Int. J. Adv. Robot. Syst. 1 (2013). https://doi.org/https://doi.org/10.5772/56525
Kassem, A., Haddad, H., Albitar, C.: Commparison Between Different Methods of Control of Ball and Plate System with 6DOF Stewart Platform. IFAC-PapersOnLine. 48, 47–52 (2015). https://doi.org/10.1016/j.ifacol.2015.09.158
Umar, A., Haruna, Z., Musa, U., Mohammed, S.A., Muyideen, M.O.: Graphical User Interface ( GUI ) for Position and Trajectory Tracking Control of the Ball and Plate System Using H-Infinity Controller. 7, 35–56 (2019). https://doi.org/https://doi.org/10.20370/yhas-n460
Maiti, D., Acharya, A., Chakraborty, M., Konar, A., Janarthanan, R.: Tuning PID and PIλDδ Controllers using the Integral Time Absolute Error Criterion. In: 4th IEEE International Conference on Information and Automation for Sustainability, 2008. pp. 1–6 (2008)
Calcev, G.: A Passivity Result for Fuzzy Control Systems. 61, 2727–2728 (1996). https://doi.org/10.1109/CDC.1996.573518
Shin, Y.C., Chengying Xu: Stability Analysis Method. In: Automation and control engineering. pp. 225–235. , United States (2008)
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Singh, R., Bhushan, B. Improving Self-Balancing and Position Tracking Control for Ball Balancer Application with Discrete Wavelet Transform-Based Fuzzy Logic Controller. Int. J. Fuzzy Syst. 23, 27–41 (2021). https://doi.org/10.1007/s40815-020-00994-8
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DOI: https://doi.org/10.1007/s40815-020-00994-8