Sage Journals: Discover world-class research

Abstract

In this paper, we consider the problem of stabilization of a translational oscillator with a rotational actuator (TORA) system. In practical applications, TORA systems usually suffer from parametric uncertainties. Moreover, existing control methods for TORA systems cannot guarantee the rotational scope of the actuator and often lead to unwanted unwinding behaviour. To handle these issues, we present an adaptive control strategy for TORA systems with uncertain or unknown parameters, which is robust to parameter uncertainties and can guarantee that the rotational actuator rotates in a preset range. Specifically, a Lyapunov function is elegantly constructed on the basis of the nonlinear interaction between the translational oscillator and the eccentric rotational proof mass. Then an adaptive control method, along with an online estimation mechanism, is proposed straightforwardly and the stability of the closed-loop system is proven, invoking Lyapunov techniques and LaSalle’s invariance principle. Simulation results are provided to demonstrate the performance of the presented method.

Keywords

Lyapunov method adaptive control state constraint underactuated mechatronics

Get full access to this article

View all access options for this article.

References

Aguilar-Avelar

Moreno-Valenzuela

(2015) A composite controller for trajectory tracking applied to the Furuta pendulum. ISA Transactions 57: 286–294.

Aguilar-Ibáñez

Suarez-Castanon

Cruz-Cortés

(2012) Output feedback stabilization of the inverted pendulum system: a Lyapunov approach. Nonlinear Dynamics 70(1): 767–777.

Avis

Nersesov

Nathan

et al . (2010) A comparison study of nonlinear control techniques for the RTAC system. Nonlinear Analysis: Real World Applications 11(4): 2647–2658.

Behal

Setlur

Dixon

et al . (2005) Adaptive position and orientation regulation for the camera-in-hand problem. Journal of Robotic Systems 22(9): 457–473.

Bupp

Bernstein

Coppola

(1995) A benchmark problem for nonlinear control design: problem statement, experimental testbed, and passive nonlinear compensation. In: American control conference, Seattle, WA, USA, 21–23 June 1995, pp. 4363–4367. Piscataway, NJ: IEEE.

Bupp

Bernstein

Coppola

(1998) A benchmark problem for nonlinear control design. International Journal of Robust Nonlinear Control 8(4–5): 307–310.

Celani

(2011) Output regulation for the TORA benchmark via rotational position feedback. Automatica 47(3): 584–590.

Escobar

Ortega

Sira-Ramírez

(1999) Output-feedback global stabilization of a nonlinear benchmark system using a saturated passivity-based controller. IEEE Transactions on Control Systems Technology 7(2): 289–293.

Fang

Sun

(2015) Anti-sway control of an overhead crane with persistent disturbances by Lyapunov method. In: 34th Chinese control conference, Hangzhou, China, 28–30 July 2015, pp. 889–894. Piscataway, NJ: IEEE.

10.

Jankovic

Fontaine

Kokotović

(1996) TORA example: cascade- and passivity-based control designs. IEEE Transactions on Control Systems Technology 4(3): 292–297.

11.

Khalil

(2002) Nonlinear Systems, 3rd ed. Upper Saddle River, NJ: Prentice Hall.

12.

Moreno-Valenzuela

Aguilar-Avelar

(2018) Motion Control of Underactuated Mechanical Systems. Cham: Springer.

13.

Nazrulla

Khalil

(2008) A novel nonlinear output feedback control applied to the TORA benchmark system. In: 47th IEEE conference on decision and control, Cancun, Mexico, 9–11 December 2008, pp. 3565–3570. Piscataway, NJ: IEEE.

14.

Ngo

Mahony

(2005) Integrator backstepping using barrier functions for systems with multiple state constraints. In: 44th IEEE conference on decision and control. Seville, Spain, 15 December 2005, pp. 8306–8312. Piscataway, NJ: IEEE.

15.

Pavlov

Janssen

van de

Wouw N

et al . (2007) Experimental output regulation for a nonlinear benchmark system. IEEE Transactions on Control Systems Technology 15(4): 786–793.

16.

Pomet

J-B

Praly

(1992) Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Transactions on Automatic Control 37(6): 729–740.

17.

Quan

Cai

K-Y

(2013) Additive-state-decomposition-based tracking control for TORA benchmark. Journal of Sound and Vibration 332(20): 4829–4841.

18.

She

Zhang

Lai

et al . (2012) Global stabilization of 2-DOF underactuated mechanical systems – an equivalent-input-disturbance approach. Nonlinear Dynamics 69(1): 495–509.

19.

Sun

Fang

et al . (2017) Nonlinear stabilization control of multiple-RTAC systems subject to amplitude-restricted actuating torques using only angular position feedback. IEEE Transactions on Industrial Electronics 64(4): 3084–3094.

20.

Tee

Tay

(2009) Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4): 918–927.

21.

Wan

C-J

Bernstein

Coppola

(1994) Global stabilization of the oscillating eccentric rotor. In: 33rd IEEE conference on decision and control. Lake Buena Vista, FL, USA, 14–16 December 1994, vol. 4, pp. 4024–4029. Piscataway, NJ: IEEE.

22.

Wan

C-J

Bernstein

Coppola

(1996) Global stabilization of the oscillating eccentric rotor. Nonlinear Dynamics 10(1): 49–62.

23.

(2017) Nonlinear energy-based regulation control of three dimensional overhead cranes. IEEE Transactions on Automation Science and Engineering 39(12): 1763–1770.

24.

Sun

Fang

(2017) An increased nonlinear coupling motion controller for underactuated multi-TORA systems: theoretical design and hardware experimentation. IEEE Transactions on Systems, Man, and Cybernetics: Systems. Epub ahead of print 21 July 2017. DOI: 10.1109/TSMC.2017.2723478.

Adaptive control of the TORA system with partial state constraint

Abstract

Keywords

Get full access to this article

References