1. Introduction
For a three-axis parallel motion platform, precision motion control can be achieved through the coordinated operation of joint motors. This type of platform features lower motion inertia and higher control precision, flexibility, and dynamic performance, enabling the realization of complex three-degrees-of-freedom motion trajectories [
1,
2]. Therefore, it finds wide applications in high-end equipment fields such as microelectronics manufacturing, high-speed machine tools, new energy equipment, and robotic operations [
3,
4,
5,
6].
Despite the parallel platform offering numerous advantages, it presents certain challenges concerning the mutual pulling and control difficulties among joint motors during motion [
7,
8]. To overcome these issues, advanced modeling theories and control strategies need to be researched and developed continuously to enhance the system’s motion performance. Currently, many scholars focus on controller design for platform motion control, primarily in both task space [
9] and joint space [
10]. Considering that the planned motion trajectory is established in task space, the motion error of the platform in task space more accurately reflects the processing accuracy of the workpiece compared to the tracking error in joint space [
11]. Therefore, designing a controller in task space can facilitate the development process to be more convenient and flexible. For this reason, Khalilpour et al. [
12] analyzed and implemented a cascade control method in task space. This approach employed a force sensor-based sliding mode control for inner-loop regulation and achieved precise measurement of the motion platform position through outer-loop control based on visual sensors. Zi et al. [
13] proposed a fuzzy control strategy integrating end-effector pose information to achieve rapid and adaptable trajectory tracking for parallel mechanisms. The proposed method achieved real-time measurement of the end-effector pose by using three automatic target rangefinders. Zhu et al. [
14] introduced a disturbance-resistant control method combining a sliding mode control and a disturbance observer. This method measured the angular velocity of the spatial robot base using a gyroscope, improving the robot’s motion accuracy while ensuring positioning overshoot and stability time. Fonseca et al. [
15] presented a dual-loop controller considering position and attitude impedance coupling. This method utilized a force sensor to measure the torque information of the motion platform, adjusting the mechanism’s motion trajectory through inner-loop position control and outer-loop admittance control to ensure accuracy and stability in the machining process. Altan et al. [
16] proposed a model predictive control method that utilized visual sensor measurements of input–output data to establish linear and nonlinear dynamic models, and employed these models for closed-loop control to achieve precise target tracking. However, the implementation of the aforementioned task space control methods often requires the use of external measuring instruments, such as force sensors [
17], gyroscopes [
18], and visual sensors [
19], to obtain essential motion information for each drive axis. Employing external sensors for measurement will increase the system’s complexity and cost. Additionally, if the data bandwidth of external sensors does not match the system’s control bandwidth, it may lead to data processing delays, subsequently affecting the system’s tracking performance [
20,
21]. Therefore, despite the issue of motion coupling among the drive chains of parallel platforms, designing control strategies in joint space still presents significant challenges [
22,
23,
24]. Fang et al. [
25] thus suggested intensified research to design decoupling controllers suitable for parallel platforms in joint space, aiming to meet the demands of high-speed and high-precision control for such systems.
Hosseini et al. [
26] proposed a robust model-free decoupling control method. The proposed method employed time-delay estimation technology to estimate the dynamic inertia parameters of the mechanism, achieving high-speed decoupling and precise tracking of mechanism motion through robust nonlinear proportional-derivative controllers. Feng et al. [
27] designed a composite controller to ameliorate the tracking accuracy of motion joints. The controller used an adaptive fuzzy control scheme to suppress external disturbances during motion, achieving model-free decoupling control by calculating torque control to compensate for joint drive forces. Yang et al. [
28] developed an adaptive controller combining fuzzy neural networks and approximation functions. The controller utilized fuzzy neural networks to estimate the nonlinear dynamics, including friction models, and suppressed estimation errors occurring during the estimation of dynamic parameters by using a sliding mode-based approximation function. Ultimately, it achieved a stable operation of the mechanism under load variations. Escorcia-Hernandez et al. [
29] designed an adaptive robust integral control strategy. This method used B-spline functions to assist neural networks in feedforward compensation for nonlinear dynamics, combining robust integral feedback control considering the filtered tracking error for each joint to achieve high-speed positioning operation of parallel mechanisms with minimal tracking error. Zhang et al. [
30] and Yun et al. [
31] employed inverse dynamics for compensation to improve trajectory tracking accuracy while maintaining the high dynamic performance of robots. Xie et al. [
32] proposed a composite control method that combined dynamic feedforward compensation and input signal velocity planning for a five-degrees-of-freedom parallel mechanism to reduce the tracking errors of driving joints induced by multi-axis coupling and complex input signals. Makarem et al. [
33] introduced a dynamic tuning control method based on data-driven techniques. This strategy involved adjusting controller parameters using feedback data from grating encoders to address hysteresis and nonlinearities in ultrasonic motors, achieving precise positioning and model-free control of the system. For the control strategies in joint space, precise control can be achieved by fully utilizing real-time information provided by the encoder feedback. Consequently, decoupling control methods can be effectively employed in real-world scenarios to meet the high-speed motion control of the platform [
34,
35]. However, the drawbacks of the aforementioned controllers in joint space are apparent. Although the grating encoders of each joint possess high resolution and measurement accuracy, the pulling between the drive joints can significantly affect the control accuracy of each motor. This pulling arises from the interaction of the joint drive forces and the poor synchronous motion performance of each motor, and existing control methods in joint space often overlook the coordination of motion between motors [
36,
37].
Therefore, the implementation of decoupling controllers in joint space, as well as control strategies based on external sensors in task space, exhibit certain deficiencies, making it challenging for existing control methods to ensure the simultaneous fulfillment of tracking performance and synchronization performance for the three-axis parallel motion platform (TAPMP). Currently, synchronization control methods include parallel control, master–slave control, cross-coupling control, and control methods based on specific control theories. For instance, Zhong et al. [
38] proposed a fractional-order feedforward control method based on frequency characteristic adjustment theory to enhance the synchronization performance of a gantry platform. However, most of the existing synchronization control methods are primarily applicable to dual-motor platforms. Considering the three-motor co-axis structure of the TAPMP, this paper proposes a novel synchronization controller with dynamic compensation (SC–DC) in joint space to achieve motion synchronization between the three motors, ultimately enhancing the platform’s tracking accuracy in task space. The proposed controller primarily possesses two significant advantages. Firstly, it is established using information from the platform joint space, eliminating the need for external sensors to enhance the control performance of the TAPMP, thereby reducing cost and demonstrating high applicability. Secondly, compared to the traditional decoupling controllers, the proposed controller introduces a synchronization error of the common stator motors, which accurately represents the synchronization relationship between adjacent motors. Thus, the proposed method can achieve better tracking and synchronization accuracy. Finally, the effectiveness and advancement of the proposed controller are verified through simulation analysis and practical experiments.
To ensure the high accuracy and effective implementation of the proposed SC–DC method, a comprehensive dynamic model is developed, which encompasses the dynamics of the moving platform and auxiliary blocks. Subsequently, according to the motion characteristics of the common stator motors, a synchronization error of the common stator motors is introduced to represent the synchronized motion relationship between adjacent motors. Moreover, the coupling error is defined in an adjacent sequence based on the tracking error and the synchronization error. The proposed SC–DC is formulated to eliminate both coupling and synchronization errors, while compensating for the dynamics of the auxiliary blocks and the driving force of each motor. Utilizing Lyapunov theory, it is verified that the proposed controller can ensure convergence of both the tracking error and synchronization error. Trajectory tracking simulations and experimental studies are conducted on the TAPMP. The results show that, compared to the augmented proportional-derivative controllers with dynamic compensation, the proposed controller significantly reduces the synchronization error and tracking error for each motor, demonstrating its performance advantages in trajectory tracking and synchronization.
The remaining sections of this paper are organized as follows. The structure and kinematic model of the TAPMP are introduced in
Section 2. The dynamic modeling of the TAPMP is elaborated in
Section 3. The implementation process and stability analysis of the proposed SC–DC are described in
Section 4. Simulation results are discussed in
Section 5. Experimental validation is conducted in
Section 6. Finally, the main research of this paper is summarized in
Section 7.