CDM Based Servo State Feedback Controller with Feedback Linearization for Magnetic Levitation Ball System

Alfian Ma'arif, Adha imam Cahyadi, Oyas Wahyunggoro


This paper explains the design of Servo State Feedback Controller and Feedback Linearization for Magnetic Levitation Ball System (MLBS). The system uses feedback linearization to change the nonlinear model of magnetic levitation ball system to the linear system. Servo state feedback controller controls the position of the ball. An integrator eliminates the steady state error in servo state feedback controller. The parameter of integral gain and state feedback gains is achieved from the concept of Coefficient Diagram Method (CDM). The CDM requires the controllable canonical form, because of that Matrix Transformation is needed. Hence, feedback linearization is applied first to the MLBS then converted to a controllable form by a transformation matrix. The simulation shows the system can follow the desired position and robust from the position disturbance. The uncertainty parameter of mass, inductance, and resistance of MLBS also being investigated in the simulation. Comparing CDM with another method such as Linear Quadratic Regulator (LQR) and Pole Placement, CDM can give better response, that is no overshoot but a quite fast response. The main advantage of CDM is it has a standard parameter to obtain controller’s parameter hence it can avoid trial and error.


magnetic levitation ball system; nonlinear; feedback linearization; servo state feedback; coefficient diagram method.

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A. Nayak and B. Subudhi, “Discrete backstepping control of magnetic levitation system with a nonlinear state estimator,†in 2016 IEEE Annual India Conference (INDICON), 2016, pp. 1–5.

T. Kumar and S. Shimi, “Modeling, simulation and control of single actuator magnetic levitation system,†… (RAECS), 2014 Recent …, no. June, pp. 1–6, 2014.

C. Peng, G. Zhaoyu, and L. Jie, “Study on two feedback linearization control methods for the magnetic suspension system,†in 2015 34th Chinese Control Conference (CCC), 2015, pp. 1059–1063.

N. Patel and M. N. Uddin, “Design and performance analysis of a magnetically levitated vertical axis wind turbine based axial flux PM generator,†in 2012 7th International Conference on Electrical and Computer Engineering, 2012, pp. 741–745.

M. Mehrtash and M. B. Khamesee, “Optimal motion control of magnetically levitated microrobot,†in 2010 IEEE International Conference on Automation Science and Engineering, 2010.

P. V. S. Sobhan, G. V. N. Kumar, and J. Amarnath, “Rotor levitation by Active Magnetic Bearings using Fuzzy Logic Controller,†2010 Int. Conf. Ind. Electron. Control Robot., pp. 197–201, 2010.

M. Simi, G. Sardi, P. Valdastri, A. Menciassi, and P. Dario, “Magnetic Levitation camera robot for endoscopic surgery,†in 2011 IEEE International Conference on Robotics and Automation, 2011, pp. 5279–5284.

G. G. Sotelo, R. A. H. de Oliveira, F. S. Costa, D. H. N. Dias, R. de Andrade, and R. M. Stephan, “A Full Scale Superconducting Magnetic Levitation (MagLev) Vehicle Operational Line,†IEEE Trans. Appl. Supercond., vol. 25, no. 3, pp. 1–5, Jun. 2015.

Jaewon Lim, Chang-Hyun Kim, Jong-Min Lee, Hyung-suk Han, and Doh-Young Park, “Design of magnetic levitation electromagnet for High Speed Maglev train,†in 2013 International Conference on Electrical Machines and Systems (ICEMS), 2013, pp. 1975–1977.

P. Šuster and A. Jadlovská, “Modeling and Control Design of Magnetic Levitation System,†Appl. Mach. Intell. Informatics (SAMI), 2012 IEEE 10th Int. Symp., pp. 295–299, 2012.

M. Ahsan, N. Masood, and F. Wali, “Control of a magnetic levitation system using non-linear robust design tools,†in 2013 3rd IEEE International Conference on Computer, Control and Communication (IC4), 2013, pp. 1–6.

M. A. Akram, I. Haider, H.-U.-R. Khalid, and V. Uddin, “Sliding mode control for electromagnetic levitation system based on feedback linearization,†in 2015 Pattern Recognition Association of South Africa and Robotics and Mechatronics International Conference (PRASA-RobMech), 2015, pp. 78–82.

Huann-Keng Chiang, Wen-Te Tseng, Chun-Chiang Fang, and Chien-An Chen, “Integral backstepping sliding mode control of a magnetic ball suspension system,†in 2013 IEEE 10th International Conference on Power Electronics and Drive Systems (PEDS), 2013, pp. 44–49.

A. M. Benomair, A. R. Firdaus, and M. O. Tokhi, “Fuzzy sliding control with non-linear observer for magnetic levitation systems,†in 2016 24th Mediterranean Conference on Control and Automation (MED), 2016, pp. 256–261.

T. Namerikawa and H. Kawano, “A passivity-based approach to wide area stabilization of magnetic suspension systems,†in 2006 American Control Conference, 2006, p. 6 pp.

S. K. Verma, S. Yadav, and S. K. Nagar, “Optimal fractional order PID controller for magnetic levitation system,†in 2015 39th National Systems Conference (NSC), 2015, pp. 1–5.

I. Ahmad, M. Shahzad, and P. Palensky, “Optimal PID control of Magnetic Levitation System using Genetic Algorithm,†in 2014 IEEE International Energy Conference (ENERGYCON), 2014, pp. 1429–1433.

N. Magaji and J. L. Sumaila, “Fuzzy logic controller for magnetic levitation system,†in 2014 IEEE 6th International Conference on Adaptive Science & Technology (ICAST), 2014, pp. 1–5.

A. M. Benomair and M. O. Tokhi, “Control of single axis magnetic levitation system using fuzzy logic control,†in 2015 Science and Information Conference (SAI), 2015, pp. 514–518.

A. M. Benomair, F. A. Bashir, and M. O. Tokhi, “Optimal control based LQR-feedback linearisation for magnetic levitation using improved spiral dynamic algorithm,†in 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015, 2015, pp. 558–562.

K. Ogata, Modern control engineering. Prentice-Hall, 2010.

S. Manabe, “Coefficient diagram method,†in Proceedings of the 14th IFAC Symposium on Automatic Control in Aerospace, 1998, pp. 199–210.

S. Manabe, “Importance of coefficient diagram in polynomial method,†in 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp. 3489–3494.

R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation, vol. 29. 1994.

J.-J. E. Slotine and W. Li, Applied nonlinear control. Prentice Hall, 1991.

H. K. Khalil, Nonlinear Systems. Upper Saddle River: Prentice Hall, 2001.



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