Swing-up control strategies for a reaction wheel pendulum

Abstract

Control of a reaction wheel pendulum, a prototype of an under-actuated system, is easily done using switching control strategies, which combines swing-up control and balancing control schemes. In this article, two novel swing-up control strategies for a reaction wheel pendulum have been proposed. The first swing-up control strategy treats the oscillations of the pendulum as perturbations from the bottom equilibrium point. The second swing-up control is based on interconnection and damping assignment-passivity based control (IDA-PBC). IDA-PBC preserves Euler Lagrangian structure of the system and gives more physical insight about any mechanical system. Any balancing controller can be coupled with the proposed swing-up control strategies to stabilise the pendulum at the top unstable equilibrium position. The control task of balancing the pendulum in top upright position is completed by switching from swing-up scheme to the balancing scheme at the point where the pendulum is very near to the top equilibrium point. Proposed swing-up control strategies have been implemented in real time in switching mode. The two proposed swing-up control schemes provide fast responses as compared to existing energy based schemes.

Keywords:

• Under-actuated system
• reaction wheel pendulum
• swing-up control strategies
• IDA-PBC

Acknowledgements

The authors are thankful to Bonagiri Bapiraju, Subhas Chandra Das and Prem Kumar P. for their technical suggestions.

Notes

Notes

1. The reader may refer to Slotine (1988) and Ortega, Schaft, Mareels, and Maschke (2001) for detailed discussions on IDA.

2. During experimentation, the balancing control is able to stabilise whenever the pendulum is within ±0.08 rad.

3. The swings of the pendulum represent transient state of the system.

4. The magnitude of (m₁₂/m₁₁)q₂ response is very small as compared to (x₁/m₁₁).

5. The tapping can be avoided by improving transient response of the swing-up controller.

6. In Ortega, et al. (2002b), the control law is designed for unconstrained control input. Since it is a regulation problem, for constrained control input the control law cannot stabilise the pendulum at the upright position.

7. M ⁻¹ + N = [I + J ₁(x _q )⁻¹]M ⁻¹.

8.  represents the potential energy of H _a .

9. Algebraic manipulations are given in Appendix.

10. for swing-up control of the pendulum, energy shaping term has to shape both kinetic energy and potential energy of the RWP system. To make design procedure simple, swing-up control can be easily achieved using only positive damping injection. The controlled oscillations can be achieved by selecting the free parameters such as a and d.