Experimental implementation of nonlinear TORA system and adaptive backstepping controller design

LESO-Based Nonlinear Continuous Robust Stabilization Control of Underactuated TORA Systems

In this paper, we consider the robust stabilization control problem of underactuated translational oscillator with a rotating actuator (TORA) system in the presence of unknown matched disturbances by employing continuous control inputs. A nonlinear continuous robust control approach is proposed by integrating the techniques of backstepping and linear extended state observer (LESO). Specifically, based on the backstepping design methodology, a hyperbolic tangent virtual control law is designed for the first subsystem of the cascaded TORA model, via which an integral chain error subsystem is subsequently constructed and the well-known LESO technique is easy to implement. Then, an LEO is designed to estimate the lumped matched disturbances in real-time, and the influence of the disturbances is compensated by augmenting the feedback controller with the disturbance estimation. The convergence and stability of the entire control system are rigorously proved by utilizing Lyapunov theory and LaSalle’s invariance principle. Unlike some existing methods, the proposed controller is capable of generating robust and continuous control inputs, which guarantee that both the rotation and translation of TORA systems are stabilized at the origin simultaneously and smoothly, attenuating the influence of disturbances. Comparative simulation results are presented to demonstrate the effectiveness and superior control performance of the proposed method.

A Model-Free Output Feedback Control Approach for the Stabilization of Underactuated TORA System with Input Saturation

The horizontal translational oscillator with a rotational actuator (TORA) is a typical underactuated mechanical system, whose control problem is still open and theoretically challenging. At present, the existing control methods are structurally complicated and require an exact knowledge of the system parameters. Moreover, few works have considered the output feedback stabilization of the TORA system subject to practical constraints of input saturation and angular velocity unmeasurement. To address these problems, this paper proposes a novel model-free amplitude-limited control approach to stabilize the TORA system at the origin using only angle feedback. Firstly, the passivity of the horizontal TORA system is analyzed, based on which a novel Lyapunov function augmented with an auxiliary signal is constructed by taking the input saturation into account. Then, an amplitude-limited control law is derived in a straightforward manner. In order to make the control law independent of velocity feedback, the auxiliary signal is designed in terms of the ball rotational angle and an output of a dynamic system. The asymptotic stability of the entire control system is rigorously guaranteed by utilizing Lyapunov theory and LaSalle’s invariance principle. Finally, simulation results with comparisons to existing methods demonstrate the effectiveness and superiority of the proposed control approach.

Dynamical Modelling and Controllability Analysis of an Underactuated 2-Dimensional TORA System on a Slope

The 2-Dimensional Translational Oscillators with Rotating Actuator (2DTORA) is a novel underactuated system which has one actuated rotor and two unactuated translational carts. This paper focuses on dynamical modelling and simulation analysis of the underactuated 2DTORA on a slope. Based on Lagrange equations, the dynamics of the 2DTORA is achieved by selecting a transverse position of a cart, a travelling position of a cart, and the rotor angle as the general coordinates and torque acting on the rotor as the general force. When the slope angle is set to zero, the dynamics of 2DTORA on a slope is reduced to that of 2DTORA on the horizontal plane. Moreover, by eliminating one degree of translational cart motion, the dynamics of 2DTORA is reduced to that of TORA which is a benchmark of underactuated systems. In addition, the equilibrium and controllability of the 2DTORA system on a slop are discussed. Finally, numerical simulations are performed to verify the feasibility of the developed dynamic models.