Abstract
Based on a nonlinear disturbance observer, a backstepping sliding mode robust control is proposed for a wire-driven parallel robot (WDPR) system used in the wind tunnel test to dominate the motion of the end effector. The control method combines both the merits of backstepping control and sliding mode robust control. The WDPR is subject to different types of disturbances, and these disturbances will affect the motion precision of the end effector. To overcome these problems, a nonlinear disturbance observer (NDO) is designed to reject such disturbances. In this study, the design method of the nonlinear disturbance observer does not require the reliable dynamic model of the WDPR. Moreover, the design method can be used not only in the WDPR but also in other parallel robots. Then, a backstepping design method is adopted and a sliding mode term is introduced to construct a desired controller, and the disturbances are compensated in the controller to reduce the switching gain and guarantee the robustness. For the sake of verifying the stabilization of the closed-loop system, the Lyapunov function is constructed to analyze the stabilization of the system. Finally, the feasibility and validity of the proposed control scheme are proved through both simulation and experimental results.
Highlights
E rest of this study is organized as follows
To control the pose of the end-effector during the operation, this study proposes a backstepping sliding mode robust control based on a nonlinear disturbance observer, improving the robustness and accuracy of the control method. e main contribution of this study is that the backstepping sliding mode robust control method is applied to a 6-DOF 8-wiredriven parallel robot which has been developed by us and used in the wind tunnel test
The dynamic model for wire-driven parallel robot (WDPR) used in the wind tunnel test is constructed
Summary
We will give the composition, working principle, dynamic equations, properties on the WDPR, and an initial disturbance observer, which play a central effect in designing the nonlinear disturbance observer and the controller. The WDPR is designed for the low-speed wind tunnel test. It is a nonlinear parallel system with multiinput and multioutput (MIMO). Where M0 is the inertia matrix equivalent to the driver, C0 is the viscous friction coefficient matrix equivalent to the driver, μ is the transmission coefficient of the ball screw, θm ∈ R8×1 is the motor angle vector, T ∈ R8×1 is the wire tension vector, τ ∈ R8×1 is the output torque vector of the driver, τ1 ∈ R8×1 is the vector of external disturbances, M(X) ∈ R6×6 is the inertial matrix of the end-effector, X (Xp, Yp, Zp, φ, θ, ψ)T is the pose of the end-effector, (XP, YP, ZP)T is the coordinate of point P relative to the static platform, (φ, θ, ψ)T is the attitude angle of the endeffector, and φ, θ, and ψ are the roll angle, pitch angle, and yaw angle, respectively; X_ ∈ R6×1 is the pose velocity of the end-effector, J ∈ R8×6 is a Jacobi matrix, N(X, X_ ) ∈ R6×1 is a nonlinear coriolis centrifugal matrix, wg ∈ R6×1 is a gravitational vector of the end-effector, wg (0, 0, mg, 0, 0, 0)T, and we ∈ R6×1 is subject to external dynamic loads at the end-effector, and we [fe; τe]. If the dynamic analysis is carried out under the condition of 0 wind speed, we 0:
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