CONTROLLER DESIGNS FOR NONLINEAR SYSTEMS WITH APPLICATION TO 3 DOF HELICOPTER MODEL

Abstract

The paper introduces different control design methods for nonlinear systems with their application to the nonlinear mathematical model of a 3 DOF helicopter. Recent studies on the control design approaches, such as State Dependent Riccati Equation based optimal controller, Model Reference Adaptive Control and Sliding Mode Control, are reviewed and design methodologies are given. Then the mathematical model of a 3 DOF helicopter dynamics is derived and simplified with the software called CIFER. By using the simplified mathematical model of the 3 DOF helicopter, the control algorithms are applied to the model in order to explore the performances of the controllers. The results are given in the simulation environment. The paper is presented in a tutorial manner in order to explain the applications of the proposed nonlinear control methodologies.

Keywords

• Nonlinear Systems,Controller Design,State Dependent Riccati Equations,Sliding Mode Control,Model Reference Adaptive Control

References

1. [1] Ishutkina, M.A., "Design and Implementation of a Supervisory Safety Controller for a 3DOF Helicopter", MSc. Thesis, Massachusetts Institute of Technology Department of Aeronautics and Astronautics, Massachusetts, (2004).
2. [2] Choudhary, S.K., "LQR Based PID Controller Design for 3-DOF Helicopter System", International Journal of Computer, Electrical, Automation, Control and Information Engineering, 8(8): 1498-1503, (2014).
3. [3] Zhai, Y., Nounou, M., Nounou, H. and Al-Hamidi, Y., "Model Predictive Control of a 3-DOF Helicopter System Using Successive Linearization", International Journal of Engineering, Science and Technology, 2(10): 9-19, (2010).
4. [4] Liu, Z., el haj, Z. C. and Shi, H., "Control Strategy Design Based on Fuzzy Logic and LQR for 3-DOF Helicopter Model", International Conference on Intelligent Control and Information Processing, Dalian, (2010).
5. [5] Zhang, J., Cheng, X. and Zhu, J., "Control of a Laboratory 3-DOF Helicopter: Explicit Model Predictive Approach", International Journal of Control, Automation and Systems, 14(2): 389-399, (2016).
6. [6] Nishi, M., Ishitobi, M. and Nakasaki, K., "Nonlinear Adaptive Control System Design and Experiment for a 3-DOF Model Helicopter", Artif Life Robotics, 13: 50-53, (2008).
7. [7] Boby, R.I., Mansor, H., Gunawan, T.S. and Khan, S., "Robust Adaptive LQR Control of Nonlinear System Application to 3-Dof Flight Control System", IEEE International Conference on Smart Instrumentation, Measurement and Applications (ICSIMA), Kuala Lumpur, (2014).
8. [8] Pearson, J.D., "Approximation Methods in Optimal Control", Journal of Electronics and Control, 13: 453-469, (1962).

9. [9] Çimen, T., "Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis", Journal of Guidance, Control, and Dynamics, 35(4): 1025-1047, (2012).
10. [10] Itik, M., Salamci M.U. and Banks, S.P., "SDRE Optimal Control of Drug Administration in Cancer Treatment", Turkish Journal of Electrical and Computer Engineering, 5: 715-729, (2010).
11. [11] Çimen, T., "Systematic and Effective Design of Nonlinear Feedback Controllers via the State-Dependent Riccati Equation (SDRE) Method" Annual Reviews in Control, 34(1): 32-51, (2010).
12. [12] DeCarlo, R.A., Zak, R.A. and Matthews, G.P., "Variable Structure Control of Nonlinear Multivariable Systems", A Tutorial. Proc. IEEE, 76(3): 212-232, (1998).
13. [13] Spurgeon, S.K. and Edwards, C., Sliding Mode Control: Theory and Applications, Taylor and Francis, London, (1998).
14. [14] Utkin, V.I., Sliding Modes in Control and Optimization, Springer Verlag, Berlin, (1992).
15. [15] Salamci, M.U. and Gökbilen, B., "SDRE Missile Autopilot Design Using Sliding Mode Control with Moving Sliding Surfaces", IFAC Proceedings Volumes, 40(7): 768-773, (2007).
16. [16] Babaei, N. and Salamci, M.U., "State Dependent Riccati Equation Based Model Reference Adaptive Stabilization of Nonlinear Systems with Application to Cancer Treatment", IFAC Proceedings Volumes, 47(3): 1296-1301, (2014).
17. [17] Quanser Inc., "3DOF Helicopter User Manual", (2012).
18. [18] Ogata, K., Modern Control Engineering, Prentice Hall, New Jersey, (2010).
19. [19] Babaei, N., Salamci, M.U. and Çimen, T., "State Dependent Riccati Equation Controlled Drug Delivery for Mixed Therapy of Cancer Treatment", IFAC-PapersOnline, 48(25): 265-270, (2015).
20. [20] Babaei, N. and Salamci, M.U., "Personalized Drug Administration for Cancer Treatment Using Model Reference Adaptive Control", Journal of Theoretical Biology, 371: 24-44, (2015).
21. [21] Köse, E., Abacı, K. and Aksoy, S., "Access Sub-Analysis of Different Approaches", 6th International Advanced Technologies Symposium (IATS’11), Elazığ, (2011).