Nonlinear Dynamic Surface Control for the Underactuated Translational Oscillator With Rotating Actuator System

Abstract

This paper is concerned with the issue of nonlinear dynamic surface control for an underactuated translational oscillator with a rotating actuator (TORA). The nonlinear feedback cascade model of the underactuated TORA is obtained through a collocated partial feedback linearization and a global change of coordinates. A nonlinear controller is designed to treat the state variables as virtual control inputs to design the virtual controller step by step. Dynamic surface control is used to avoid the ''explosion of complexity'' in the backstepping design process. Considering that there is no affine appearance of the variables to be used as virtual controls for the second state, the first step is designed for a one-input and two-state system. It is proved that the proposed design method can guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system with arbitrary small tracking error by appropriately choosing design constants. The simulation results demonstrate the effectiveness of the proposed approach.

Sliding Mode Observe and Control for the Underactuated Inertia Wheel Pendulum System

“…From (5), it can be seen that the system model of IWP is a nonlinear feedback cascade model. Unlike available results [10], the controllers to be studied in this paper are derived without using backstepping.…”

“…In the following, the output-feedback control design for (7) will be considered to stably control the system (5), and finally achieve the purpose to stably control system (1). The sliding mode observers will be introduced and a sliding mode controller will be proposed.…”

“…Remark 6: The proposed approach is designed for the nonlinear canonical system (7), so it can be used to control all the mechanical systems that can be described with the formation as (7), including the underactuated systems that can be transformed to the cascade system (5), such as the TORA [27] and the Acrobot [28].…”

“…However, their control inputs can only control part of the dynamics while the remaining part is adjusted through the system internal dynamics, and they exhibit a non-zero degree of underactuation and a highly nonlinear dynamic [3]. Therefore, none of the techniques proposed for fully actuated systems can be applied directly and the matured nonlinear control techniques such as feedback linearization [4] and backstepping [5] can also not be applied directly. The advantages and complexity of the underactuated systems have led many researchers devote themselves to the automatic control in underactuated systems field to propose some appropriate techniques to indirectly control the coordinates through the internal dynamics.…”

Adaptive Dynamic Surface Control for Aircraft With Multiple Disturbances Based on Radial Basis Network

“…Neural network tuning algorithm, backstepping method based on non-dynamic feedback compensation, a new finite time instruction filtering inversion method have been proposed one after another [5]- [7]. In the adaptive control, the feedback passivation can be used to carry out the backstepping design with tuning function more simply [8]. In recent years, the application of backstepping method has also been greatly developed.…”