DOI : https://doi.org/10.18517/ijaseit.8.3.1218

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

Alfian Ma'arif (1), Adha imam Cahyadi (2), Oyas Wahyunggoro (3)
(1) Universitas Gadjah Mada
(2) Universitas Gadjah Mada
(3) Universitas Gadjah Mada
Fulltext View | Download
How to cite (IJASEIT) :
Ma’arif, Alfian, et al. “CDM Based Servo State Feedback Controller With Feedback Linearization for Magnetic Levitation Ball System”. International Journal on Advanced Science, Engineering and Information Technology, vol. 8, no. 3, June 2018, pp. 930-7, doi:10.18517/ijaseit.8.3.1218.
Citation Format :
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.

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. Å uster and A. Jadlovskí¡, “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.

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).