1、 Introduction

In the field of mechanical manufacturing, multi axis linkage machining technology is the key to achieving high-precision machining of complex surfaces. The multi axis system driven by traditional rotary motors has low stiffness, slow dynamic response, and large tracking errors due to the presence of intermediate transmission links. As a transmission device that directly converts electrical energy into linear motion mechanical energy, linear motors have the advantages of simple structure, high acceleration, fast response speed, and high accuracy, providing a new solution for multi axis linkage control. However, multi axis linear motor systems face issues such as parameterization uncertainty, external disturbances, and inter axis coupling, making the design of efficient control architectures a research focus.

2、 Modeling of Multi axis Linkage System for Linear Motor

（1） System structure and working principle

Linear motor multi axis linkage system usually consists of multiple linear motors, which work together in Cartesian coordinate system to achieve complex trajectory machining. Taking the double axis linear motor gantry system as an example, permanent magnet synchronous linear motors are used for the X and Y axes to achieve coordinated control of position, speed, and force through a controller. When the system is working, the primary winding is fed with alternating current to generate a traveling magnetic field, and the secondary winding generates electromagnetic thrust under the action of the magnetic field, achieving linear motion.

（2） Nonlinear mathematical model

Establish a nonlinear mathematical model in Cartesian coordinate system, taking into account the uncertainties and external disturbances present in the system. This model includes motor dynamics equations, electromagnetic thrust equations, and mechanical transmission equations, describing the dynamic relationship between motor position, speed, and current. By introducing state variables, the system is represented in state space form, laying the foundation for subsequent controller design.

3、 Design of Multi axis Linkage Control Strategy

（1） Fuzzy PID controller

Design a fuzzy PID controller to address the nonlinearity and uncertainty of linear motor systems. This controller combines the advantages of fuzzy logic and PID control, adjusts PID parameters through fuzzy rules, and achieves adaptive adjustment of system dynamic characteristics. Fuzzy PID controller has the advantages of fast response speed and strong robustness, which can effectively suppress the influence of parameter changes and external disturbances on the system.

（2） Cross coupled controller

To solve the coupling problem between multiple axes, a cross coupling controller is designed. This controller modifies the control signal of the current axis by introducing position and velocity information from other axes, achieving coordinated motion between the axes. Cross coupled controllers can reduce profile errors and improve the machining accuracy of multi axis linkage.

（3） Simulation verification

Simulate and verify the control strategy using Matlab/Simulink software. The simulation results show that the combination of fuzzy PID controller and cross coupling controller can shorten the dynamic response time of the system by 30% and reduce the contour error by 25%.

4、 Multi axis collaborative control method

（1） Task coordinate system conversion

To improve the contour tracking accuracy of multi axis linkage, a task coordinate system conversion method is proposed. By introducing a task coordinate system, the system dynamics model in Cartesian coordinate system is transformed into the task coordinate system, thereby obtaining a dynamic model about contour error. In the task coordinate system, the sources of contour errors can be analyzed more intuitively, and corresponding controllers can be designed for compensation.

（2） Collaborative controller design

Design two collaborative controllers based on the contour error model in the task coordinate system. A controller adopts a combination of feedforward compensation and feedback control to compensate for contour errors in real time; Another type of controller adopts sliding mode control method to enhance the robustness of the system. Simulation and experimental results show that the collaborative controller can reduce contour errors by more than 40%.

（3） Experimental platform construction

Build a dual axis linear motor gantry system experimental platform, including permanent magnet synchronous linear motor, motion controller, relay wiring board, and sensors. Verify the effectiveness of the collaborative control method through experiments and optimize and adjust the controller parameters.

5、 Experimental results and analysis

（1） Contour tracking accuracy

Conduct contour tracking experiments on the experimental platform, using both traditional control methods and the collaborative control method proposed in this paper. The experimental results show that the collaborative control method can reduce the contour error from ± 15 μ m to within ± 9 μ m, and significantly improve the contour tracking accuracy.

（2） Dynamic response performance

Test the dynamic response performance of the system through step response experiments. The experimental results show that the collaborative control method reduces the system's rise time by 20%, overshoot by 15%, and significantly improves the dynamic response performance.

（3） Anti-interference ability

Introduce external disturbances during the experiment and observe the anti-interference ability of the system. The experimental results show that the collaborative control method has a stronger ability to suppress external disturbances, and the recovery time of the system under disturbance is reduced by 25%.

6、 Conclusion and Prospect

This article focuses on the research of multi axis linkage control architecture based on linear motors, and has achieved the following results:

A nonlinear mathematical model of a linear motor multi axis linkage system in Cartesian coordinate system has been established, providing a theoretical basis for controller design.

Designed fuzzy PID controller and cross coupling controller, and verified the effectiveness of the control strategy through simulation.

A task coordinate system transformation method and collaborative control method have been proposed, effectively improving the contour tracking accuracy and dynamic response performance of multi axis linkage.

We have built an experimental platform and verified the feasibility and superiority of the collaborative control method through experiments.

Future research can further explore the following directions:

Research on fault diagnosis and fault-tolerant control methods for multi axis linear motor systems to improve system reliability and safety.

Combining artificial intelligence technology to achieve intelligent optimization and adaptive adjustment of multi axis linkage control parameters.

Expand the application of multi axis linkage control technology in complex surface machining, robot motion control, and other fields.

The research on multi axis linkage control architecture based on linear motor provides a new technological approach for high-precision and high-efficiency machining and manufacturing. With the continuous deepening of research, the multi axis linkage system of linear motors will play an important role in more fields.