Introduction

Voice Coil Motor (VCM) is a linear motor widely used in industrial automation, known for its simple structure, fast response, direct force output, and high positioning accuracy. The working principle of VCM is derived from speakers, which generates precise linear motion by controlling the current to excite a single coil winding. It is widely used in high-precision small-stroke scenarios such as semiconductor manufacturing equipment, digital camera autofocus modules, and hard disk head positioning servo systems.

However, in practical applications, VCM control systems face many challenges, such as parameter disturbances, load changes, hysteresis nonlinearity, viscous friction, and Coulomb friction in high-frequency applications, which will significantly reduce the performance of control algorithms. Therefore, improving the Self-Adaptation of control algorithms has become the key to achieving high-precision positioning.

This paper introduces a Self-Adaptation optimal positioning control algorithm based on a second-order discrete-time model . The algorithm can achieve optimal control by learning input and output data without the need for a VCM dynamic model. Based on the second-order discrete-time model, the algorithm is similar to the commonly used third-order model in frequency response characteristics, and introduces a control update mechanism to prevent overshoot when the reference signal changes. Compared with existing Self-Adaptation control methods, the design process of this algorithm is simpler and suitable for online implementation. Simulation results show that the method has positioning performance equivalent to the theoretical optimal feedback law and can self-adapt to a wide range of VCM parameters.

Technical Overview

The dynamic model of a voice coil motor is usually a third-order system, covering both electrical and mechanical parts. However, in most practical applications, the equivalent inductance of the VCM coil is very small, and its voltage drop can be ignored. Therefore, through reasonable approximation, the VCM model can be simplified into a second-order system. Studies have shown that the frequency response characteristics of the second-order model are basically consistent with those of the third-order model within the range of operating frequency ≤ 200 rad/s, and are suitable for most industrial scenarios. This model simplification not only reduces computational complexity, but also provides convenience for online Self-Adaptation control.

Bode diagram of third-order and second-order model of VCM

This white paper adopts a discrete-time model for controller design to adapt to the discrete sampling characteristics in actual control systems. By specifying a fixed sampling time T, the system updates control inputs within each time interval to ensure compatibility between control laws and hardware implementation.

Issue statement

In the practical application of VCM, system parameters such as resistance, inductance, quality, etc. will drift due to long-term use or environmental changes, resulting in a decrease in control performance. In addition, factors such as load changes and nonlinear friction further exacerbate the difficulty of control. Traditional control methods usually rely on accurate dynamic models, but obtaining and maintaining such models is time-consuming and expensive, especially in scenarios with frequent parameter changes, making it difficult to achieve real-time adjustment.

Therefore, there is an urgent need for a control method that can automatically adjust the control strategy to maintain high performance under unknown or changing system parameters.

Solution

This white paper proposes a Self-Adaptation optimal positioning control algorithm based on a second-order discrete-time model. The algorithm uses reinforcement learning technology to learn the optimal control law through historical input and output data, without the need for a prior system dynamic model. Specifically, the algorithm is implemented through the following steps:

1. State Reconstruction : Based on the controllability and observability of the system, the system state is reconstructed using historical input and output data to avoid noise problems caused by direct measurement of speed and current.
2. Bellman equation parameterization : The Bellman equation is expressed as a function of input and output data, and the kernel matrix of performance indicators is solved by the least squares method.
3. Control Law Update : Based on the solved kernel matrix, the control law is updated to minimize performance indicators, and a control update mechanism is introduced to prevent overshoot when the reference signal changes.
4. The design process of the algorithm is simple, suitable for online implementation, and can self-adapt to different VCM parameters and load conditions.

Implementation and results

In the simulation experiment, we first tested a nominal VCM model. The experimental results show that the proposed Self-Adaptation algorithm can make the positioning performance of VCM equivalent to the theoretical optimal feedback law. When the reference signal changes step by step, the overshoot phenomenon is effectively avoided by adjusting the control update mechanism, ensuring the stability of the system.

The graph shows that the kernel matrix estimation error gradually decreases and approaches zero during the learning process, proving the learning ability of the algorithm.

Estimation error of ?

The graph shows that the algorithm can still achieve accurate position tracking under different VCM parameters, proving its Self-Adaptation.

Subsequently, we applied the algorithm to another VCM model with different parameters. The experimental results show that the algorithm can adjust the control law with Self-Adaptation, maintain good positioning performance, and prove its universality under different system parameters.

Conclusions and future prospects

The Self-Adaptation optimal positioning control algorithm introduced in this white paper provides an innovative and practical solution for precise control of VCM. The algorithm achieves optimal control by learning input and output data without the need for precise dynamic models, greatly simplifying the design and implementation process. Simulation results verify the effectiveness and Self-Adaptation of the method, which is applicable to a wide range of VCM parameters.

Future research will focus on the following areas:

1. Hardware implementation : The Self-Adaptation algorithm is applied to the actual microcontroller platform to verify its performance in the real environment.
2. Time-varying reference signal tracking : Based on the principle of internal model, explore the application of this algorithm in tracking time-varying reference signals (such as sine signals), and further expand its application scenarios.
3. Algorithm lightweighting and computation acceleration: Optimizing algorithm structure for edge devices to improve real-time performance and resource utilization
4. Through continuous research and optimization, the Self-Adaptation optimal positioning control algorithm is expected to play a greater role in the fields of industrial automation and precision positioning. It is particularly suitable for the following equipment:

• Intelligent camera autofocus and image stabilization system
• Displacement control of semiconductor exposure platform
• High precision linear drive system in medical equipment
• High-end printing module and precision nozzle control

Immediately learn more

If you want to obtain the complete PDF white paper or solution of this algorithm, please contact the CJC technical team