Abstract
For any multi-DOF parallel mechanism, its system model is difficult to accurately establish and high-performance control is hard to achieve because of its high nonlinearity and strong coupling characteristics. In view of this, for a 6-PTRT parallel mechanism, the coupling characteristics are first analysed and then a novel smooth sliding mode control algorithm based on synchronization error is designed and the system's stability is proven - in theory - according to the Lyapunov stability theorem. By introducing the defined synchronization error into the smooth sliding mode control, the proposed method can resist the coupling effect among the branches of the parallel mechanism and realize the coordinated, synchronous and more accurate movement of each branch of the parallel mechanism with no accurate system model, whereby the tracking error of each branch may converge on zero simultaneously. The simulation results show that the synchronous smooth sliding mode control method proposed here has a shorter response time and a higher control precision when compared with the smooth sliding mode control method. By considering the errors of the adjacent branches, the synchronous coordination among the branches of the parallel mechanism with the coupling effect is effectively improved.
Highlights
A parallel mechanism with the advantages of high rigidity, strong structure vibration resistance, heavy payload, small moving inertia, a fast response speed and so on [1], [2], [3], [4], when compared with a serial mechanism, can allow for parallel robots in various applications, such as machine tools [5], manufacturing lines [6], climbing robots [7], aperture spherical radio telescopes [8], haptic devices [9] and so on
According to sliding mode control design theory, we introduce the synchronization error and determine the sliding surface of the synchronous smooth sliding mode control as:
In order to solve the coupling problem of the parallel mechanism and enhance its motion control performances, for a 6‐PTRT parallel mechanism, a novel smooth sliding mode control based on a synchronization error is proposed and the system stability is proven ‐ in theory ‐ according to Lyapunov stability theorem
Summary
A parallel mechanism with the advantages of high rigidity, strong structure vibration resistance, heavy payload, small moving inertia, a fast response speed and so on [1], [2], [3], [4], when compared with a serial mechanism, can allow for parallel robots in various applications, such as machine tools [5], manufacturing lines [6], climbing robots [7], aperture spherical radio telescopes [8], haptic devices [9] and so on. Koren [17] initially proposed the synchronized control concept and applied it to the tracking control of machine tools; for a parallel robot, a decoupling controller for adopting cross‐coupling pre‐compensation is proposed to weaken the system dynamic coupling effect in [18]; a synchronization controller based on contour errors for a parallel robot is designed to improve the position precision of the trajectory tracking control and improve the coordination among the joints of the parallel robot system in [15]; for a 4‐SPS type parallel manipulator, a synchronized control algorithm for synchronizing all of the actuators’ tracking by selecting a tracking error as a standardized tracking error is proposed in [19]; an adaptive synchronized control is proposed in [20] for improving the tracking accuracy of a PRR type planar parallel manipulator; a control approach based on adaptive control with the use of defined synchronization error is proposed in [21] to improve the motion coordination of a plane parallel robot, but it is very difficult for a multi‐DOF parallel mechanism to obtain the synchronous error as defined in the literature These explicit‐dynamic‐model‐based control design methods may improve the synchronized control performance of a parallel mechanism, but due to the complexity of the dynamic model of a multi‐DOF parallel mechanism, it takes a long time to solve the inverse dynamics, and it is difficult for the control system to meet real‐time requirements [22], [23]. The control method proposed can improve the motion control precision of the parallel mechanism and the synchronization coordination among the branches of the parallel mechanism
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