# Rapid and Precise Zoom Lens Design Based on Voice Coil Motors with Tunnel Magnetoresistance Sensors
## 1 Introduction
[9] proposed a new design concept for a VCM in digital video camera focusing systems, meeting the strict requirements of low power consumption, high efficiency, and fast zoom. By varying the diameter of the winding coil, the thickness of the magnet, and the winding space in the VCM in order to reduce the battery loss caused by VCM focusing, the performance of the digital camera achieves lower battery consumption, higher efficiency, and a shorter focusing time. [PERSON] et al. [14] proposed a thin optical zoom system using Alvarez freeform lenses, developing a 3\(\times\) optical zoom system with two pairs of Alvarez lenses, where the movable components are driven by VCMs. Two voice coil actuators control the lateral movement of the Alvarez lenses, while the rear focusing lens group can be moved along the optical axis by another VCM, achieving autofocus. [PERSON] et al. [15] proposed a conceptual design for a small actuator for camera lens zoom or focusing systems in camera phones using traditional VCMs due to their small size, simplicity, and reliability. They applied a topology optimization method to design the structure, maximizing the driving force without changing the input power and coil. Although commercial VCM products are widely used in industry, their resolution is typically limited to the micron level. Furthermore, research on positioning platforms with higher accuracy and a greater travel range is currently being carried out. [PERSON] et al. [16] designed a VCM for high-precision applications with accuracy of less than 5 \(\upmu\)m at a low speed and an amplitude of 500 \(\upmu\)m. The error increased with the increasing amplitude and operating frequency. [PERSON] et al. [17] designed a control system based on VCMs for talbot lithography. A double closed-loop control strategy including a position loop and a current loop was utilized, in which the current loop was attained through a driver in order to achieve the fast following of the system current; the position loop was attained using a digital signal processor (DSP) and the position feedback was realized through a high-precision linear scale. Feedforward control and position feedback proportional-integral-derivative (PID) control were used to compensate for the dynamic hysteresis and improve the response speed of the system. [PERSON] [18] proposed a VCM design that used a PID controller to control a high-precision positioning stage with a resolution of 200 nm and a travel range of 11 mm. [PERSON] et al. [19] introduced fuzzy predictive compensation following the digital control of PID. Compared with the traditional method, the experimental results show that fuzzy predictive compensation is an effective and promising method. [PERSON] et al. [20] configured a VCM positioning system with a proportional-integrator observer and a discrete sliding mode controller to achieve a position error of 0.25 percent. The result for the implemented control system was superior to the 0.57% position error obtained with the PID controller. [PERSON] et al. [21] proposed an improved active disturbance rejection double closed-loop controller, which had a good suppression effect on the internal and external disturbances of the rotating VCM system and satisfied the requirements of the moving mirror control system regarding the uniformity of the scanning speed and the positional accuracy control of the optical path. Although VCMs have been widely used in the field of zoom lenses, their applications are mainly limited to smartphones, tablets, and other portable mobile devices. In these application scenarios, the VCM's travel range is usually short, which is sufficient for basic zoom and focus demands. Typical VCMs only have a travel range of less than 300 \(\upmu\)m, and, although previous studies have proposed VCMs with larger travel ranges for zoom lenses, this is insufficient for certain types, especially security lenses. In this work, we propose a long-travel zoom drive technology based on VCMs.