Optimization of Energy for Tracking of the ‎Magnetic Levitation Ball Using the SDRE ‎Technique

Document Type : Original Article

Author

Department of Electrical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul ,Iran,

Abstract

This paper was dealt with the optimization of energy for tracking the magnetic levitation ball by using the technique of State-Dependent Riccati Equation. The magnetic levitation ball is widely used in various fields. This system includes a steel ball suspended by electromagnetic force. The differential equations of this system are nonlinear. Generally, first, these nonlinear equations are linearized around an equilibrium point. Then, a Linear Quadratic Tracker controller is designed for this system. Note that this system has a non-zero equilibrium point. However, in the technique of State-Dependent Riccati Equation, the nonlinear equations are linearized by using the method of State-Dependent Coefficients. If the system is pointwise stabilizable and detectable, the State-Dependent Riccati Equation has an answer. Then, an optimal control law is extracted so that the energy of tracking is minimized. In the end, it has been shown that four different trajectories are tracked appropriately using the proposed method.

Keywords


[1] Scott C. Beeler,State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities: National Institute of Aerospace, Hampton, Virginia, Report No. 2004-08.
[2] Saeed Mohammad-Hosseini, Ali-Reza Alfie, Mohammad Farrokhi, Mohammad-Reza Jahed-Motlagh, “Fuzzy sliding state feedback control of nonlinear ball suspension system”, IFAC Proceedings Volumes,Vol.35, No.1, 2002, pp 229-234.
[3] Mária Hypiusová, Jakub Osuský, “PID controller design for magnetic levitation model”,in Proceedings of International Conference cybernetics and informatics,Feb. 2010.
[4] Bharat Bhushan, Sudarshan K.Valluru, Madhusudan Singh, “Takagi-Sugeno Fuzzy System based Stable Direct Adaptive Control of Nonlinear Systems”, International Journal of Computer Applications, Vol.68, No.15, Apr. 2013.
[5] Bharat Bhushan, “Direct Adaptive Control of Robot Manipulator and Magnetic Ball Suspension System”, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol.2, No.11, Nov. 2013.
[6] Shibly Ahmed Al-Samarraie, “Variable Structure Control Design for a Magnetic Levitation System”, Journal of Engineering, Mechanical and Energy Engineering, Vol.24, No.12,Dec. 2018.
[7] Ahmed A. Oglah, Samara H. Abed Al-Hady, “Design and implementation of an interval Type-2 Fuzzy Logic and type-1 fuzzy logic controls for Magnetic Levitation System”, American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), Vol.46, No1,Aug. 2018.
[8] Muhammad Junaid Khan, Muhammad Junaid,, Sahibzada Bilal, Sadia Jabeen Siddiqi,Haseeb Ahmad Khan, “Modelling, Simulation & Control of NonLinear Magnetic Levitation System”, in Proceedings of IEEE, 21st International Multi-Topic Conference (INMIC),Nov. 2018,
[9] Chih-Min Lin,Ming-Hung Lin, Chun-Wen Chen, “SoPC-Based Adaptive PID Control System Design for Magnetic Levitation System”, IEEE Systems Journal, Vol.5, No.2, Jun. 2011.
[10] Fernando Ornelas-Tellez, J. Jesus Rico-Melgoza, Edgar N. Sanchez, “Optimal tracking for a class of nonlinear systems based on the state-dependent Riccati equation”, in Proceedings of 10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE),Mexico city, Mexico,Sep. 2013.
[11] Raghuwansh Sing, “Nonlinear control of a magnetic levitation system using feedback linearization”, Journal of Technology Research & Innovation, Vol.4, No.2, July 2016.
[12] Guimei Qi,Zhaojing Wu, “Filter-based tracking of magnetic levitation ball system”,in Proceedings of Chinese Control And Decision Conference (CCDC), June 2018.
[13] Mohammad Divandari, Mehdi Hashemi-Tilehnoee, Masoud Khaleghi, Mohammadreza Hosseinkhah, “A novel control-rod drive mechanism via electromagnetic levitation in MNSR”, NUKLEONIKA, Vol.59, No.2:73−79, June2014.