An infrared stealth spherical target simulation device and its surface temperature control algorithm

This paper presents a simulation device for infrared stealth spherical target and a feedforward temperature compensation algorithm for its surface temperature. A three-dimensional model and a mathematical model based on heat transfer equation are established. Experimental data from three different spherical targets is used to calculate feedforward compensation and obtain a detailed control law. Experiments verify the reliability of the mathematical model and the accuracy of the temperature control algorithm. The algorithm can control the surface temperature of the spherical target within ±2 °C and has good system dynamic characteristics.


Introduction
Temperature control systems are widely used in modern industries and have become an essential aspect of our lives.These systems are prevalent in engineering applications, and their use can be observed in numerous areas.Temperature control is crucial for various civil and military applications, such as controlling the temperature of factory water, hydraulic oil, and fighter engine cylinders.A well-designed temperature control algorithm is essential to ensure optimal performance of the temperature control system.
Currently, many scholars have made significant achievements in temperature control systems.For example, Zhou and Fessenden developed an adaptive system for large area superficial hyperthermia [1], while Chen and He discussed an algorithm for controlling DSW objective lens temperature [2].Tong and Xu presents the design of industrial temperature resistance furnace computer using PID algorithm [3]; Guo and Wang proposed a high accurate adaptive temperature control algorithm [4]; Wang designed an automatic decocting temperature control system of herbal cuisine based on ARM controller [5]; Other researchers have proposed models and algorithms for precise temperature control in various applications, including nanosatellites, surface temperature control in laboratories, steel slab reheating furnaces, cylindrical objects heated by induction, and solar tower power stations [6][7][8][9][10][11][12][13][14].Some researchers also used genetic algorithms and soft-measurement techniques for temperature compensation and minimization of temperature variation during abrasive honing process [15][16][17].
Despite the widespread use of temperature control systems, there has been little research on simulation devices and surface temperature control for infrared stealth spherical targets.This paper introduces a telescopic infrared stealth target ball device and establishes a three-dimensional model for it, as well as a surface temperature control system.The proposed system uses a feedforward temperature compensation algorithm based on classical PID.Three different target balls are utilized to test the stability and reliability of the algorithm.

Structure and principle of spherical target simulator
As shown in Figure 1, the spherical target simulator includes a half-sphere made of glass-reinforced plastic, a motor, fan, reducer, support flange, bearing, telescopic rod, retaining ring, and target ball mechanism.The inner surface of the target ball is heated by silicone heating films and the air generated by the fan enters the target ball to form air convection, achieving even heat distribution.The temperature closed-loop control system composed of silicone heating film, damper, and fan controls the temperature and achieves specific infrared radiation characteristics.The outer surface is coated with special optical materials, which shows stealth characteristics under laser detection.The motor powers the telescopic mechanism and moves the target ball in front of it to eliminate background interference.The principle of the spherical target simulation device is described as follows: the silicone heating film on the inner surface of the target ball is controlled by the temperature control algorithm.When the heating film generates heat, the air generated by the fan enters the target ball through the hollow telescopic mechanism, so that the heat is evenly distributed.The damper on the cover plate of the target ball is controlled by the preloaded spring, and the fan power is adjusted to control the gas inflow.In this way, a double closed-loop control system is formed to accurately control the temperature.When the temperature of the silicone heating film is transferred to the outer surface of the spherical shell, the spherical target has infrared radiation characteristics.The outer surface of the spherical shell is coated with optical materials with laser stealth characteristics, so as to form a target with infrared stealth characteristics.The target ball is installed in front of the telescopic rod, and when the telescopic rod is extended, it will have a spatial background state.

Principle and structure of target ball
The target ball in the spherical target simulator is hemispherical.Heating films are attached to the inner surface of the target ball and its main heat transfer mode is heat conduction.Its structure and schematic diagram are depicted in Figure 2. It includes a shell, temperature sensor, cover board, heating films, ventilation opening, and camouflage paint.The heating system of the target ball is composed of heating controller, controller and sensor.They form the closed-loop control system loop.The temperature control system adopts PID control.The temperature is the hysteresis control variable, so the need to constantly debug to find the appropriate PID parameters.

Thermodynamic calculation of infrared target simulation system
According to the heating principle of the target ball and the working environment, the power W1 required for the temperature rise of the target ball is the difference between the heating power W2 of the heating film and the cooling power W3, as shown in Equation (1).
(2) where c is the specific heat capacity of the target ball, m is the mass of target ball, t is the heating time.The heat dissipation power W3 of the target ball can be obtained from the convective heat transfer formula, as shown in Equation ( 3).

= W hA T ∆
(3) where h is the convective heat transfer coefficient between the surface of the target ball and the air, A is the surface area of the target ball, and ΔT is the temperature difference between the target ball and the environment.The convective heat transfer coefficient h can be obtained by the following formula.n = h Bv (4) where B is the empirical coefficient; n is the speed index; v is wind speed.When the wind is force 6, the wind speed v is 13.8 m/s.Therefore, according to Equations ( 1) - (4).
The maximum heating power of the heating film of the target ball is 10 kw, and the maximum temperature difference between the target ball and the environment is 70 °C.The target ball with a diameter of 1m has the largest mass, the most heat required, the largest heat dissipation area and the largest heat dissipation power.Therefore, taking the target ball as an example, the working condition of it under the gale force 6 is calculated.Then the maximum heating temperature time is The maximum heat dissipation power of the target ball is The maximum power of the target ball heating controller is 10 kw.The output power of the target ball heating controller is equal to the heat dissipation power by adjusting the output voltage.Therefore, the stable working temperature of the target ball can be maintained through the temperature control system.

Principle of temperature control system
The block diagram of the temperature control system is shown in Figure 3.The set temperature is fed into the PID controller.The PID controller will control the power regulator to heat the heating film and transfer heat to the target ball by means of heat conduction.And then the target ball produces a specific thermal radiation that mimics a specific infrared target.Temperature sensors are installed on the target ball, and the temperature is fed back to the PID controller and the disturbance is compensated.The specific PID signal is output through PID operation, and then the output temperature Y(t) is controlled.Finally, the temperature control transfer function of the heating module is shown in Equation (8).
The transfer function of temperature control is a typical hysteresis link, in which the transfer function of the heating device is shown in Equation ( 9). ( ) 1 where K1 is the heating coefficient of the system, λ1 is the time constant of the system.The simplified block diagram of the system is shown in Figure 4.

Mathematical expression of control algorithm
The temperature control system is interfered by external conditions, and the temperature of the target ball changes with the change of air humidity, wind speed and solar radiation intensity.In addition, different target balls have different diameters and different degrees of external influences.So, the design of its algorithm requires different parameters.The feedback value of the temperature sensor is different from the target temperature value, and the signal of the difference is amplified to drive the controller in the system, and then control the whole system.The expression of output signal u(t) of standard PID is shown in Equation (10).
where kp is the proportional gain coefficient, ki is the integral coefficient, and kd is the differential coefficient.
The system in this paper needs good dynamic response characteristics and can stabilize the temperature at the set value within 10 minutes.Therefore, as shown in Equation (11), the control algorithm of temperature feedforward compensation of target ball is designed.

T T u t e T T T T T T k e t k e T T
τ τ where T0 is the ambient temperature, Ts is the set target temperature; Ta is the current detection temperature.
The object controlled by the temperature control system in this paper is the average temperature of target ball.Temperature is a lagging variable, so the temperature change on the surface of the target ball is slow.The differential term in PID control is eliminated, and gain control and integral control are retained.The cooling system of the temperature control system can carry out convection heat dissipation to the target ball.When the set-temperature Ts is less than room temperature T0, the situation does not conform to the actual physical significance.So, u(t) is 0. When the temperature setvalue Ts is greater than room temperature T0 and greater than the current average temperature of the sphere surface, the control signal is set to emax, and the heater adopts full power heating.When the heating temperature (Ta) reaches the set-temperature Ts for the first time, the system performs proportional integration (PI) control and convection heat dissipation.And when the temperature drops to Ts+2 for the first time, the cooling system is shut down.Thereafter, the temperature control is under the control of PI (proportional-integral), and the cooling system will be turned back on when the temperature meets Ta > Ts +2.Under the control of the algorithm, the mean temperature of the target ball (Ta) becomes stable within 10 minutes, and the steady-state error is within ±2 °C.The surface temperature of the target ball needs to reach the specified temperature within a short period of time and stabilize within (-2,2) °C, so positive compensation for the set temperature value is adopted in the system.And directly control the input signal through the way of feedforward, so that it can quickly reach the specified temperature.When the target ball reaches the specified temperature, the target ball is cooled by a cooling treatment.The temperature of the target ball reaches a stable state after one or two shocks.
Before determining the amount of compensation, the heat required for the temperature of the target ball to achieve dynamic equilibrium should be measured.That is, the heat provided by the heater is equal to the heat required to maintain the temperature of the target ball plus the heat lost from the environment.We assume that the ambient temperature is 25 °C, there is no wind, and there is no solar radiation.And we use 10 °C as the increment interval.In this interval, the relationship between current and heat transfer is approximately linear.When the temperature is stable at a certain value within the interval, the relationship between heating power and temperature is measured.Change the heating power and stabilize the temperature of the target sphere at another value for a period of time.The relationship between heating power and temperature can be measured at this time.The linear relationship between heating power and temperature can be approximated, as shown in the following equation.1 1 where P is heating power, ΔT is the difference between the set temperature and the ambient temperature, α1 is the proportional coefficient measured by actual calculation, β1 is the constant value obtained by fitting.
The set temperature is given, and the target ball is heated and stabilized under the control law of PI.The above operations are repeated and the data is recorded for multiple measurements.Finally, the above data is fitted to a linear function.In addition, the feedforward compensation is carried out with the set temperature as the input quantity, and the feedforward compensation of temperature can be obtained as shown in Formula (13).(13) where Td is the temperature feedforward compensation amount, α is the proportional coefficient fitted according to the data, β is the constant value obtained by data fitting.

Experiment and verification of temperature control algorithm
The experimental diagram of the target simulation device is shown in Figure 5.The temperature control system is added to the above temperature compensation control algorithm.After PID calculation, the control signal is transferred to the heater to heat the target ball.When the target ball begins to be heated, the wind will transport air to the inside of the target ball, making sufficient heat contact the surface of the target ball.When the temperature is too high, the target ball will stop heating and open the damper on the cover plate.The hot air inside is expelled to reduce the temperature of the target ball.
The experiment was carried out with three different diameter target balls.The diameters of the three target balls are 1m,0.5mand 0.2m respectively.Their experimental data are shown in Tables 1, 2 and 3.The temperature sensor records the temperature change data over time for verification, and the experimental curves and simulation curves of the three target balls are shown in Figure 6.The temperature simulation curve and experimental curve of the large target ball are shown in Figure 6.As can be seen from the figure, when the temperature of the target ball drops to a reasonable temperature range for the first time, the curve experiences two oscillations and gradually stabilizes within the allowed error range.And the experimental curve is slightly behind the simulation curve.Considering the actual environmental error and system error, the experimental curve is within the allowable error range.So, the algorithm is feasible to control the surface temperature of large target ball.The temperature curves of medium and small target balls are shown in Figures 7 and 8 The temperature feedforward compensation of the three target balls can be obtained by fitting the data, as shown in Equation ( 14).where ΔT is the temperature difference between the set temperature of the large target ball and the ambient temperature, and Td is the compensation amount of the large target ball to the set temperature.

Conclusions
This paper proposes a novel infrared stealth spherical target simulator and studies its surface temperature control algorithm.Combined with the thermodynamic equation, the mathematical model of temperature control system of infrared stealth target simulator is established.A feedforward temperature compensation algorithm based on classical PID control theory is designed.The compensation amount is determined by parameter identification method, and the mathematical expression of the algorithm is obtained.The algorithm can well adjust the dynamic characteristics of the system, so that the temperature of the target ball can rise to the set temperature within 2min, and reach stability within 10min, and the steady-state error is within ±2 °C.Finally, the experiment was carried out with three different diameter target balls.The stability and reliability of the algorithm are verified by experimental data and simulation.

Figure 1 .
Figure 1.Structure diagram of spherical target simulator.

Figure 2 .
Figure 2. Structure diagram and schematic diagram of the target ball.
temperature raising power W1 of the target ball is shown in Equation (2).

Figure 3 .
Figure 3. Block diagram of temperature control system.

Figure 4 .
Figure 4. Block diagram of simplified system.

Figure 5 .
Figure 5. Physical picture of infrared stealth spherical target simulation device.

Figure 6 .
Figure 6.Temperature curve of large target sphere.

Figure 8 .
Figure 8. Temperature curve of small target ball.

Table 1 .
. The experimental curves of both are slightly behind the simulation curves, but both are within the allowable range, so the temperature control algorithm is stable and reliable.Large target ball compensation parameters.

Table 2 .
Medium target ball compensation parameters.

Table 3 .
Small target ball compensation parameters.