Adaptive fuzzy PID cross coupled control for multi-axis motion system based on sliding mode disturbance observation

Abstract

Multi-axis motion system is widely applied in commercial industrial machines such as precision CNC machine tools, Robot manipulator and laser cutting machines, etc. Contour accuracy plays a major role for the multi-axis servo motion system. The contour machining accuracy is related to the synthesis of single-axis position accuracy and multi-axis linkage accuracy. Only improving the single-axis tracking performance cannot effectively guarantee the machining accuracy of multi-axis system. The primary objective of this study was to design a contour control method to improve single-axis tracking accuracy and multi-axis contour accuracy. A control strategy that combines a sliding mode tracking controller, a disturbance observer and an adaptive fuzzy PID cross coupled controller is proposed. Sliding mode control is simple and has strong robustness to parameter changes and disturbance, which is especially suitable for control of such as non-linear multi-axis motion system. Besides, disturbance is inevitable in practical application, which degrades the motion accuracy. In order to eliminate the influence of external disturbance and uncertainty, disturbance observer is adopted to accurately estimate external disturbance and reduce the chattering phenomenon of sliding mode control, then improve the single-axis tracking accuracy. In order to further consider the coordination between different motion axes and improve the contour accuracy, the PID cross coupled control is used. Owing to conventional PID control cannot satisfy the multi-axis servo motion system with nonlinearity and uncertainty, an adaptive fuzzy method with on-line real-time PID parameters adjustment is proposed. The three-axis motion platform driven by PMLSM is used as the control object, to analysis the influence of disturbance observer on sliding mode control signal and analysis adaptive fuzzy PID cross coupled control performance respectively. The disturbance observer is used to observe the disturbance signal and estimate the disturbance well. The chattering of the sliding mode control signal is obviously improved. Next, compared with the conventional PID-CCC control, adaptive fuzzy PID- CCC control can significantly reduce the tracking error, the contour accuracy is also obviously improved. The disturbance observer can effectively eliminate the influence of external disturbance, reduce the chattering of sliding mode control, and ensure the single-axis accurate tracking. The self-adaptive fuzzy PID cross coupled controller can eliminate the influence of the dynamic characteristics mismatching and parameter difference of each axis, and improve contour accuracy. The simulation results clearly demonstrate the effectiveness of the proposed control method.

Keywords: Multi-axis motion system; adaptive fuzzy control; contour error; cross coupled control; disturbance observation.

Figure 1.

Geometric relationship of three-axis motion system.

Figure 2.

The structure diagram of the control system.

Fig.3.

Membership function.

Figure 4.

Structural diagram of adaptive-fuzzy PID controller.

Figure 5.

Simulation effect of single axis SMC without disturbance observation: (a) SMC control signal of $x$ axis, (b) SMC control signal of $y$ axis, (c) SMC control signal of $z$ axis, and(d) Contour error.

Figure 6.

Simulation effect of single axis SMC with disturbance observation: (a) SMC control signal of $x$ axis, (b) SMC control signal of $y$ axis, (c) SMC control signal of $z$ axis, and (d) triaxial disturbance signal and its observation.

Figure 7.

(a) $x$ axis tracking error comparison, (b) $y$ axis tracking error comparison, and (c) $z$ axis tracking error comparison.

Figure 8.

(a) Tracking error of $x$ -axis, (b) tracking error of $y$ -axis, (c) tracking error of $z$ -axis, (d) contour error, and (e) contour tracking.