On construction of control that stabilizes the movement of a nonlinear TORA model





Translational Oscillator with Rotating Actuator, underactuated mechanical system, dynamic surface control, asymptotical stability


The law of rotation of the electric motor, which provides asymptotic direction of the trajectory of the TORA model to its equilibrium state, is obtained in the work. In contrast to usual approach, the nonlinear dependence of the force, arising from the deformation of the elastic element of the model, on the amount of deformation is considered. The use of DSC (Dynamic Surface Control) technics allows to get the desired control. The development of the DSC method, which consists of the specific choice of parameters and filter constants, is proposed. This avoids the growth of the order of the auxiliary system, as well as the phenomenon of significant complication of the form of both the auxiliary system of differential equations and the law of control, the socalled. “Explosion of terms”. Reducing the order of the system of differential equations and simplifying its form allowed in this case to obtain an explicit corresponding auxiliary function and with its help to prove that the proposed control low solves the control problem. The obtained results are illustrated on the example of a specific mechanical model.


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Hall, C. D. (1995). Resonance capture in axial gyrostats. J. Astronaut. Sci., 43, No. 2, pp. 127-138.

Yee, R. K. (1981). Spinup dynamics of a rotating system with limiting torque. (Extended abstract of M. S. thesis). University of California, Los Angeles, USA.

Liu, Y. & Yu, H. (2013). A survey of underactuated mechanical systems. IET Control Theory Appl., 7, No. 7, pp. 921-935. https://doi.org/10.1049/iet-cta.2012.0505


Olfati-Saber, R. (2001). Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. (Extended abstract of Ph. D. Thesis). Massachusetts Institute of Technology, Cambridge, USA.

Kinsey, R. J., Mingori, D. L. & Rand, R. H. (1992, December). Nonlinear controller to reduce resonance effects during despin of a dual-spin spacecraft through precession phase lock. Proceedings of the 31st IEEE Conference on Decision and Control (pp. 3025-3030). Tucson, AZ, USA. https://doi.org/10.1109/CDC.1992.371254


Swaroop, D., Hedrick, J. K., Yip, P. P. & Gerdes, J. C. (2000). Dynamic surface control for a class of nonlinear systems. IEEE Trans. Automat. Control., 45, No. 10, pp. 1893-1899. https://doi.org/10.1109/TAC.2000.880994




How to Cite

Khoroshun А. . (2022). On construction of control that stabilizes the movement of a nonlinear TORA model. Reports of the National Academy of Sciences of Ukraine, (3), 20–28. https://doi.org/10.15407/dopovidi2022.03.020