Decoupled Sliding Mode Control for a Novel 3-DOF Parallel Manipulator with Actuation Redundancy

Abstract

This paper presents a decoupled nonsingular terminal sliding mode controller (DNTSMC) for a novel 3-DOF parallel manipulator with actuation redundancy. According to kinematic analysis, the inverse dynamic model for a novel 3-DOF redundantly actuated parallel manipulator is formulated in the task space using Lagrangian formalism and decoupled into three entirely independent subsystems under generalized coordinates to significantly reduce system complexity. Based on the dynamic model, a decoupled sliding mode control strategy is proposed for the parallel manipulator; the idea behind this strategy is to design a nonsingular terminal sliding mode controller for each subsystem, which can drive states of three subsystems to the original equilibrium points simultaneously by two intermediate variables. Additionally, a RBF neural network is used to compensate the cross-coupling force and gravity to enhance the control precision. Simulation and experimental results show that the proposed DNTSMC can achieve better control performances compared with the conventional sliding mode controller (SMC) and the DNTSMC without compensator.

A new fuzzy decoupled sliding mode control of flexible joint robotic manipulators based on the finite‐time observer in the presence of chaos with experimental validation

“…In [22], a non-singular decoupled terminal SMC method for a class of fourth-order is proposed. Another decoupled non-singular terminal SMC, based on a neural network for a novel 3-DOF parallel manipulator, is proposed in [23]. In [24], a robust self-tuning DSMC is presented for inverted pendulum and cart systems and optimized using a multi-objective genetic algorithm.…”

“…1. Based on the used coupling variable in the conventional DSMC, it can be seen this method can only guarantee the bounded uniform stability of the closed-loop system because the control input can only make the first sliding surface and its time derivative converge to zero and does not affect the performance of the second sliding surface, whereas all these papers stress the closed-loop system asymptotic stability [21][22][23][24][25][26][27]. Also, the papers have not provided any mathematical proof in this regard.…”

“…2. Some of these works don't address the proof of finite-time stability, and the DSMC error convergence time is infinite due to using a linear sliding surface [23,24]. 3.…”

“…5. The use of the sign function in the DSMC structure causes undesirable chattering, which can reduce the drive's lifetime and overall system efficiency [21][22][23][24][25]. 6.…”

“…6. Most of the papers have used this method for regulation objectives in nonlinear systems, while the performance of this method in high-change desired trajectory tracking is problematic [21][22][23][24][25][26][27].…”