Energy-Based Adaptive Oscillation Control of the Electromechanical Systems

The swing-up control of the electromechanical systems is considered. Electromechanical system is the cascade system. The input subsystem is a mechanical plant. The output subsystem is the actuator which dynamics cannot be neglected in particular oscillation control problem. The energy-based objective function is used to design the energy efficient virtual control law of output subsystem. The control objectives are achieving the mechanical subsystem’s reference energy and boundedness of closed-loop cascade system trajectories.In parametric uncertainty, both energy and the control objective depends on unknown parameters of a mechanical subsystem. That complicates the design procedure. The modified Speed bi-gradient method (SBGM) to identify unknown parameters, achieve a desired energy and provide boundedness of the trajectories is proposed. Modifications of SBGM are the introduction of the output subsystem tunable model, and indirect adaptive control design. Swing-up control is calculated based on current estimation performed by the adaptation loop that is without preliminary identification. The design procedure, conditions of applicability and stability analysis are presented. The proposed method is used to design the swing-up control of pendulum under parametric uncertainty. The experimental results coтfirming the performance of a closed-loop system are demonstrated.

1. Fradkov A. L. Swinging control of nonlinear oscillations, International Journal of Control, 1996, vol. 64, no. 6, pp. 1189—1202.

2. Fantoni I., Lozano R., Spong M. W. Energy based control of the Pendubot, IEEE Transactions on Automatic Control, 2000, vol. 45, iss. 4, pp. 725 — 729.

3. Andrievskiy B. R. Stabilization of inverted reaction wheel pendulum. Control in physical-technical systems. By edit. Fradkov A. L., SPb., Nauka, 2004, pp. 52—71.

4. Spong M. W., Corke P., Lozano R. Nonlinear control of the reaction wheel pendulum, Automatica, 2001, vol. 37, no. 11, pp. 1845—1851.

5. Bobtsov A. A., Kolyubin S. A., Pyrkin A. A. Stabilization of Reaction Wheel Pendulum on Movable Support with On-line Identification of Unknown Parameters, Proc. 4th International Conference ‘Physics and Control’ (Physcon 2009), 2009.

6. Peters S. C., Bobrow J. E., Iagnemma K. Stabilizing a vehicle near rollover: An analogy to cart-pole stabilization, Robotics and Automation (ICRA), 2010 IEEE International Conference on, pp. 5194—5200.

7. Astrom K. J., Furuta K. Swinging up a pendulum by energy control. Automatica, 2000, vol. 36, no. 2, pp. 287—295.

8. Mori S., Nishihara H., Furuta K. Control of unstable mechanical systems. Control of pendulum, International Journal of Control, 1976, vol. 23, no. 5, pp. 673—692.

9. Wiklund M., Kristenson A., Astrom K. A new strategy for swinging up an inverted pendulum, Prepr. 12th IFAC World Congress, 1993, vol. 9, pp. 151—154.

10. Efimov D. V. Robust and adaptive control of nonlinear oscillatons, SPb., Nauka, 2005, 314p. (in Russian).

11. Myshlyayev Y. I. Linear system control algorithms in the case of parameter variations by sliding mode with tuning surface, Mekhatronika, Avtomatizatsiya, Upravlenie, 2009, no. 2, pp. 111—116.

12. Myshlyayev Y. I., Finoshin A. V. The speed bi-gradient method for model reference adaptive control of affine cascade systems, 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (IFAC MICNON) 2015, Saint Petersburg, Russia, 24-26 June 2015, IFACPapersOnLine, 2015, vol. 48, iss. 11, pp. 489—495.

13. Myshlyayev Y. I., Finoshin A. V. Double-speed gradient algorithms in control of Hamiltonian systems, Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy Conference), XII International Conference, Moscow, Russia, 5—8 June 2012.

14. Miroshnik I. V., Nikiforov V. O., Fradkov A. L. Nonlinear and adaptive control of comlex dynamical systems, SPb., Nauka, 2000, 549 p.

15. Fradkov A. L. Cybernetic physics: Principles and examples, SPb., Nauka, 2003, 208 p.

16. Dolgov Y. A., Zyusun A. A, Finoshin A. V., Myshlyayev Y. I. Swing-up control of the cart-pole system with drive motor by velocity bi-gradient method, Engineering Journal: Science and Innovation, Moscow, Bauman Moscow State Technical University, 2015, no. 1 (37).