1. Introduction Sensors are core components of instruments and measurement systems, and a primary link in process control systems. Their design objectives form the basis for user selection. Based on whether the measured quantity changes over time, sensor performance indicators are divided into two main categories: static and dynamic. Currently, research on the static characteristics of sensors is relatively in-depth and comprehensive both domestically and internationally, while research on dynamic characteristics is less common. However, with the development of technology, there is an increasing demand for measuring dynamic non-electrical quantities or non-electrical quantities during motion. For example, the measurement of transient temperature, speed, and pressure of certain components in aircraft and aerospace vehicles must be able to rapidly reflect changes in the controlled parameters; otherwise, the entire control system cannot function properly. The dynamic quality of sensors will attract more attention. Improving the speed of sensor dynamic response can be approached from two aspects: first, changing its structure, parameters, and design; second, implementing dynamic compensation. This paper focuses on the broad application prospects of magnetoelectric sensors in relative measurement. However, the calculation of hardware selection and the study of dynamic characteristics are quite complex. A software package for selecting magnetoelectric sensor materials was designed. Magnetoelectric sensors utilize the law of electromagnetic induction (e = -k) to convert input quantities into induced electromotive force outputs. This is based on the unified theory of bidirectional sensors. Such sensors do not require an auxiliary power supply, making them active sensors, also known as inductive or electrodynamic sensors. 2. Design and Calculation of Main Components of Magnetoelectric Sensors The design of the hardware materials for magnetoelectric sensors includes the design of magnetic circuit components, coil design, and determination of the operating point. The following section discusses the methods for hardware material design in relation to magnetic circuit design. Magnetic circuit design involves complex calculations: working air gap permeability [img=497,128]http://www.e-works.net.cn/images/128271458117343750.gif[/img], total permeability, and leakage coefficient calculation (A=A1+A2+A3+A4+A5+A6). During design, the magnetic circuit system is generally preliminarily determined based on the structure's size. Based on the magnetic circuit, the magnetic induction intensity can be calculated. Thus, the total length of the coil conductor can be obtained from the given sensitivity value and the determined magnetic induction intensity value. If the air gap size is fixed, the average circumference of the coil is also determined, and therefore the number of turns can be determined. However, performing such complex calculations manually is time-consuming and inaccurate, and may even affect actual production and scientific experiments. Therefore, this paper designs a software package program to calculate the materials of all components of a magnetoelectric sensor, and the parameters can be transferred between each other. For example, the software interface for calculating the leakage permeability A6 is shown in Figure 1. [align=center][img=253,146]http://www.e-works.net.cn/images/128271454455937500.GIF[/img] Figure 1 Calculation of leakage permeability A6[/align][align=left] 3. Research on the dynamic characteristics of magnetoelectric sensors The research on the dynamic characteristics of magnetoelectric sensors includes the derivation of the mathematical model of relative measurement, the calculation of dynamic parameters, and the output of dynamic characteristics. 3.1 Mathematical model of relative measurement Let the mass of the permanent magnet (also called the mass block) be m, the spring stiffness be K, the damping coefficient of the damper be c, the sensor housing is rigidly fixed to the measured body, and the coil is rigidly fixed to the housing. Therefore, when the measured body moves, the sensor housing and the coil produce the same motion. Let x0 be the absolute displacement of the measured body (vibrating body), xm be the absolute displacement of the mass block (magnet), and xt = xm - x0 be the relative displacement between the mass block and the housing (measured body). [/align] Taking the permanent magnet as the isolator, when the measured body produces a displacement x0, it is subjected to three forces. When the forces are balanced, we have [img=28,29]http://www.e-works.net.cn/images/128271457198437500.gif[/img]=0, then we have: [img=287,149]http://www.e-works.net.cn/images/128271458380468750.gif[/img] From equations (1~2), we know that when ωω01, xt＝x0. This means that when the vibration frequency ω of the measured object is much larger than the natural frequency ω0 of the sensor (usually ω≥3ω0), the relative displacement xt between the mass block (magnet) and the measured object (coil) is close to the absolute displacement x0 of the measured object. At this time, the mass block can be regarded as stationary with respect to a stationary coordinate, so the relative motion of the measuring coil with respect to the mass block can be used to replace the absolute displacement x0 of the measured object (coil). This is the basic principle of relative measurement. 3.2 Design calculation of dynamic parameters The design calculation of dynamic parameters includes the design calculation of parameters such as the mass of the movable part, the spring stiffness, and the damping coefficient. The design process is described below using the design calculation of the mass of the movable part as an example. (1) Design calculation of the mass of the movable part The movable part mainly includes: the push rod, the coil frame, the wire, and the mass of the coil. Wire: m1 = 0.0181 (g); Frame: ρ = 2.7 × 10³; v1 = лd (m³); m2 = ρv1 (g); Top rod diameter is D1, density is ρ1, top rod length is 2, S = JID21/4, m3 = ρ12S (g); Therefore, the total mass m = m1 + m2 + m3 (g), thus determining the sensor housing material. All calculations are completed by VB programming, and the specific analysis is shown in Figure 2. [align=center][img=254,154]http://www.e-works.net.cn/images/128271458851875000.GIF[/img] Figure 2 Calculation of the mass of the movable part[/align] 3.3 Description of dynamic characteristics From the physical model of the magnetoelectric sensor and its two-port network theory, the actual transfer matrix of the sensor is: [img=219,48]http://www.e-works.net.cn/images/128271460774375000.gif[/img] Thus, the parameters F and v of the mechanical part can be obtained from the voltage and current at the sensor output. Conversely, the voltage e and current i of the circuit part can be obtained from the F and v of the mechanical part. The phase-frequency characteristic output curves are shown in Figures 4 and 5 using VB programming. The parameters m, k, and c passed from Section 3.2 are used. A detailed analysis is shown in Figure 3. In addition to the transfer matrix of the parametric model, the amplitude-frequency characteristic analysis of the non-parametric model can also be used to describe the sensor. Therefore, the working mechanism of the magnetoelectric sensor can be described using the amplitude-frequency characteristic and the phase-frequency characteristic. The amplitude-frequency characteristic and phase-frequency characteristic output curves were compiled according to the mathematical models of equations (2) and (3) as shown in Figures 4 and 5. The specific amplitude-frequency characteristic and phase-frequency characteristic output curves can be obtained by using the parameters such as m, k, c and ξ value transferred from Section 3.2. [align=center][img=236,235]http://www.e-works.net.cn/images/128271459234062500.GIF[/img] Figure 3 Calculation diagram of mechanical part and circuit part[/align][align=center][img=224,175]http://www.e-works.net.cn/images/128271459508281250.GIF[/img] Figure 4 Phase-frequency characteristic curve [/align][align=center][img=222,179]http://www.e-works.net.cn/images/128271459710781250.GIF[/img] Figure 5 Phase-frequency characteristic curve [/align][align=left] 4. Error Analysis and Compensation of Magnetoelectric Sensors 4.1 Error Analysis of Magnetoelectric Sensors The main errors of magnetoelectric sensors are temperature error, instability error of permanent magnets, and nonlinearity error of magnetoelectric sensors. The causes of temperature error and compensation methods are explained below. Temperature error In magnetoelectric sensors, the error caused by temperature is an important issue and must be calculated. When the input resistance of the measuring circuit is Ri, the output current i0 of the magnetoelectric sensor is: [/align][align=left] [img=319,131]http://www.e-works.net.cn/images/128271461341562500.gif[/img] When the temperature changes, none of the three terms on the right side of the above formula are equal to zero. Based on this mathematical model, the parameters are modified using VB programming to maintain the sensor sensitivity as constant. [/align][align=left] 4.2 Error Compensation of Magnetoelectric Sensors Magnetoelectric sensors are affected by external temperature, pressure, electromagnetic fields and their own structural limitations during measurement, resulting in various errors in actual operation. Therefore, it is necessary to design a new sensor to replace the old one, or to change the structure or parameters of the sensor itself. Experiments have shown that the latter method is more feasible and economical to implement. The compensation method and compensation effect of the second-order sensor are described below. (1) Compensation Link of the Second-Order Model Let the second-order model of the sensor be: H(s) = (b1s + b2) / (s2 + a1s + a2) There are two methods to construct the compensation link: The first is to eliminate all the zero poles of the sensor and replace them with suitable poles. At this time, the compensation link is: [/align][align=left] [img=372,312]http://www.e-works.net.cn/images/128271463700156250.gif[/img] (2) Compensation Steps and Simulation Results The steps for dynamic compensation using the zero-pole cancellation method are as follows:[/align]

[＊] Model the system using the system identification method; [＊] Calculate the step response through simulation and determine whether the dynamic performance meets the requirements; [＊] If it does not meet the requirements, find the zeros and poles of the sensor model; [＊] Determine the parameters of the dynamic compensation digital filter; [＊] Connect it to the sensor to obtain a new equivalent system; [＊] Compare the equivalent system with the sensor step response to determine the compensation effect.

If the dynamic performance requirements are not met, the compensator parameters are redefined; if the requirements are met, the parameters are output and the curve is plotted, as shown in Figure 6. [align=center][img=237,196]http://www.e-works.net.cn/images/128271461982968750.GIF[/img] Figure 6 Simulation diagram of zero-order point cancellation method[/align] Simulation results show that the effects of the two methods are comparable. However, the compensation element obtained by the first method is a third-order non-homogeneous model; the second method is a second-order homogeneous model. The second method is easier to implement and more reliable. [b]5. Conclusion[/b] Computer-aided design of magnetoelectric sensors has strong practicality and economy. Based on the original model, slight changes to the parameters can improve the dynamic quality while maintaining the characteristics of the original system. The zero-pole placement method is used to design the compensation element, and the simulation results show that the compensation effect is very obvious.