# A Fast Calibration Method for Sensors of Atmospheric Detection System
## 3 System Control Method
### VPSSD Method  
In judging the adjustment time \(t_{p}\), the stable range of the acceptable steady-state error \(e_{\text{ss}}\) needs to be given. However, due to the resistance temperature characteristics of Negative Temperature Coefficient (NTC) thermistor and the accuracy of the detection circuit, the \(e_{\text{ss}}\) steady-state error range will change in the larger temperature range. By calibrating different temperature ranges and combining with the precision of the detection circuit, the steady-state error range of the response is given, and the calibration speed is further improved. A typical NTC thermistor detection circuit is shown in Figure 4, where \(R_{NTC}\) is the thermistor, \(R_{1}\) and \(R_{2}\) are voltage divider resistors, \(C\) is the filter capacitor, \(\mathit{AIN}\) is the analog signal input of the Analog-to-Digital Converter (ADC), and \(\mathit{REF}\) is the reference voltage input. \(R_{NTC}\) changes with temperature during operation, resulting in a change in its input voltage to \(\mathit{AIN}\). The ADC compares the input voltage with the reference voltage \(\mathit{REF}\) to obtain the quantized resistance value, and the temperature at this point can be obtained through subsequent computer processing. The resistance value in NTC thermistor changes with the change in external temperature, and the relationship between its resistance and temperature change can be described as  
\[R_{NTC}=R_{0}\exp\biggl{\{}B\biggl{(}\frac{1}{T}-\frac{1}{T_{0}}\biggr{)} \biggr{\}}, \tag{14}\]  
where \(R_{0}\) is the resistance of the thermistor at 25 \({}^{\circ}\)C, \(T\) is the ambient temperature, \(T_{0}=298.15\) K, and \(B\) is the constant associated with the thermistor. ```
1:Temperature setting signal \(T^{*}(t)\), system temperature response \(T^{*}(t)\), controller output \(c^{*}(t)\), initial parameters of the PID controller, adjustment time limit \(t_{s}\), overshoot \(\sigma\%\), temperature setting limit \(T_{s}\), switching time limit \(t_{s}\), steady-state error resistance \(e_{s}\), calibration points \(q\). 2:Proportional coefficient \(P\), integral coefficient \(I\), differential coefficient \(D\), and filter order \(N\) after adjustment of MCA PID parameters. 3:for all\(i=q,q+1,\ldots,t/\Delta t\)do
4:\(band=\left\{T\left(i-q+1\right),T\left(i-q+2\right),\ldots,T^{*}(i)\right\}\)
5:if\(100\times\left\lfloor T^{*}(t)-T^{*}\left(t\right)\right\rfloor T^{*}\left(t \right)>\sigma\)
6:Change PID controller parameters. 7:break
8:elseif\(\left\{\left\lfloor\frac{1}{q}\sum\limits_{i=1}^{q}band\left(k\right)-T^{*} \left(t\right)\right\rfloor<e_{s}\right\}\bigcap\left\{\left\lfloor\max\left( band\right)-\min\left(band\right)\right\rfloor\right\}=False\)
9:Change PID controller parameters. 10:break
11:else
12:Change PID controller parameters. 13:endif
14:endfor
```  
**Algorithm 1** MAC PID Controller Design Method  
Ideally, the resolution accuracy of the ADC voltage measurement can be expressed as \(\Delta V=V_{cc}/2^{p}\) (\(p\) is the number of ADC bits). Combined with the NTC resistor temperature  
Figure 4: Thermistor temperature measurement principle. variation law and the structure of the detection circuit, the temperature error range related to the ADC bit number \(p\) is derived as  
\[\Delta T_{ADC}=\Bigg{|}-\frac{\Big{\{}\exp\Big{[}B\Big{(}\frac{1}{T}-\frac{1}{T_{0 }}\Big{)}\Big{]}R_{0}+R_{1}+R_{2}\Big{\}}^{2}T^{2}}{2^{p}\exp\Big{[}B\Big{(} \frac{1}{T}-\frac{1}{T_{0}}\Big{)}\Big{]}R_{0}(R_{1}+R_{2})}\Bigg{|}. \tag{15}\]  
During the temperature calibration of NTC thermistors, when it is determined that the temperature is stable at a certain temperature point, a certain number \(q\) of the resistance value of the thermoresistor at that temperature needs to be recorded.