## Journal of Applied Mathematics

### Dynamical Analysis and Stabilizing Control of Inclined Rotational Translational Actuator Systems

#### Abstract

Rotational translational actuator (RTAC) system, whose motions occur in horizontal planes, is a benchmark for studying of control techniques. This paper presents dynamical analysis and stabilizing control design for the RTAC system on a slope. Based on Lagrange equations, dynamics of the inclined RTAC system is achieved by selecting cart position and rotor angle as the general coordinates and torque acting on the rotor as general force. The analysis of equilibriums and their controllability yields that controllability of equilibriums depends on inclining direction of the inclined RTAC system. To stabilize the system to its controllable equilibriums, a proper control Lyapunov function including system energy, which is used to show the passivity property of the system, is designed. Consequently, a stabilizing controller is achieved directly based on the second Lyapunov stability theorem. Finally, numerical simulations are performed to verify the correctness and feasibility of our dynamical analysis and control design.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 598384, 9 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305867

Digital Object Identifier
doi:10.1155/2014/598384

#### Citation

Gao, Bingtuan; Ye, Fei. Dynamical Analysis and Stabilizing Control of Inclined Rotational Translational Actuator Systems. J. Appl. Math. 2014 (2014), Article ID 598384, 9 pages. doi:10.1155/2014/598384. https://projecteuclid.org/euclid.jam/1425305867

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