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

Abstract

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.

The Non-Singular Terminal Sliding Mode Control of Underactuated Unmanned Surface Vessels Using Biologically Inspired Neural Network

“…where τdr is the disturbance value in the direction of the yaw observed by NESO, b = m 22 α u − m 11 u, λ 2 > 0 is a design constant, and the sat(x) function is chosen as shown in Equation (32). Consider the Lyapunov function:…”

“…The BINN can simplify the controller design process and increase the efficiency in calculating the system derivatives, and thus can effectively suppress the controller input saturation problem. A BINN-based bounded input control method was introduced [32] to achieve calming control for underactuated level Translational Oscillators with Rotating Actuator (TORA) systems subjected to input saturation constraints on the actuators. In [33], a robust control technique for uncertain time-delayed systems under actuator saturation was presented, the tracking control of the preset trajectory was realized by designing a Composite Nonlinear Feedback (CNF) controller, and the simulation verification showed that the proposed method is more effective than the existing CNF approaches.…”

Iterative Contraction Stability Control Strategy for Planar Prismatic-Rotational Underactuated Robot

“…(3) The robot has natural underactuated characteristic. Therefore, the research on underactuated robot in various scenarios not only enriches the control strategy, but also promotes the development of nonlinear control theory [9], [10].…”

Adaptive Neural Network Command Filtered Backstepping Control for the Underactuated TORA System

“…From the point of application, it works as an effective model for studying the despin maneuver since it can capture the major dynamical characteristics of dualspin spacecraft. Moreover, it can be used in engineering as an active mass damper for the active vibration suppression of large engineering systems [5], such as super high-rise buildings, long-span bridges, offshore floating wind turbines, etc. However, it is very difficult to realize the TORA stabilization, because it cannot be globally feedback linearized for its weak nonlinear interaction and its nonminimum phase nature.…”

“…During the past decades, the challenging control problem for TORA systems has attracted a considerable amount of attention, and many ambitious works have been published in the literature. Some focus on the intelligent design methods [5]- [7] and some focus on the nonlinear design methods [8]- [15]. Among the intelligent design methods, the fuzzy methods are proposed [4], [6] and a neural network (NN) controller is proposed with SPSA Algorithm [7].…”