## 7 Real-Time Experiment
### Control System for Charge-Amplifier Drift Compensation  
The proposed tuning method was applied to a control system for charge-amplifier drift compensation [129]. As stated in Reference [129], \"A charge amplifier is an electronic current integrator that is frequently employed for converting electrical charges or electrical currents into voltage signals. The charge amplifier is very sensitive to DC drift, since the DC component in the input signal leads to a steady accumulation of charge in the feedback capacitor until the output voltage saturates\". As explained in Reference [129], the DC drift is compensated by an additional DC component with an opposite value for the charge-amplifier input. Since a charge-amplifier is an electronic integrator, the control process (charge amplifier) has an integrating character and the process input and output are DC voltages. Note that the charge amplifier is intended for low-level electric charge measurements. Therefore, it is a very precise low-noise instrument with stable characteristics. The studied drift compensation control system was part of a custom-made measuring system for the low-frequency and high-temperature polarisation measurements of dielectric materials (Figure 39). This system consists of a lock-in amplifier Stanford Research Systems SR830, a commercial charge-amplifier Kistler 5018A, and a temperature-regulated furnace (for measuring heated samples). More information about this dielectric-material characterisation concept can be found in References [130,131]. Figure 39: Custom-made measurement system for low-frequency and high-temperature polarisation measurements of dielectric materials with a charge-amplifier drift compensation control system. The PIDb, PIDI2, and PIDfh controllers were realised in the software package LabVIEW, and data acquisition was realised with an NI USB-6001 card. The process output and input signals were limited to \(-10\)-\(10\) V. The sampling time of the closed-loop control was \(5\) ms.  
First, a step change (input voltage signal \(0\) to \(-1\) V) was applied to the process input. Figure 40 shows the process response. Then, the following characteristic areas (with and without the added PID controller filter time constant, \(T_{F}\)) were calculated using Expressions (9)-(11):  
\[A_{0}=-8.5309,\ A_{1}=-1.0748,\ A_{2}=-0.0880,\ A_{3}=-5.7974\times 10^{-3},A_{ 4}=-3.1956\times 10^{-4}. \tag{62}\]  
\[T_{F}=0.02, \tag{63}\]  
\[A_{0\text{F}}=-8.5309,\ A_{1\text{F}}=-1.2454,\ A_{2\text{F}}=-0.11291,\ A_{3 \text{F}}=-8.0556\times 10^{-3},A_{4\text{F}}=-4.8067\times 10^{-4}. \tag{64}\]  
Based on the calculated characteristic Areas (62), by using Expression (34), the following second-order model of the process was calculated [126]:  
\[G_{M}(s)=\frac{-8.5309e^{-0.0179s}}{s(1+0.1081s+0.0035s^{2})}. \tag{65}\]  
The comparison of the model (\(G_{M}\)) and the actual process time responses are given in Figure 40.  
The next PIDb controller parameters for \(b\) = 0 and \(b\) = 0.5 were calculated via Equations (21) and (24) using the calculated characteristic Areas (63):  
\[b=0,\ K_{P}=-1.1655,\ K_{I}=-3.7512,\ K_{D}=-0.063854, \tag{66}\]  
\[b=0.5,\ K_{P}-1.0688,\ K_{I}=-2.8916,\ K_{D}=-0.061832. \tag{67}\]  
Figure 40: Open-loop response of the control system for charge-amplifier drift compensation and its second-order model. Next, using Expressions (25) and (32)-(43), the reference filter parameters for the PID\({}_{\text{fh}}\) controller  
\[ \begin{array}{l}b_{\text{F5}}=3.8442\times 10^{-6},\ b_{F4}=2.1293\times 10^{-4},\ b _{F3}=4.1389\times 10^{-3},\ b_{F2}=4.5521\times 10^{-2},\\ b_{F1}=0.30178,T_{dm}=1.7874\times 10^{-2},K_{CL}=1.2,T_{CL}=0.1244,\ n=2,\end{array}  \tag{67}\]  
and for the PID\({}_{\text{f2}}\) controller  
\[b_{F2}=1.3029\times 10^{-2},\ b_{F1}=0.16143, \tag{68}\]  
were calculated. Note that for the PID\({}_{\text{f2}}\) and PID\({}_{\text{fh}}\) controllers, the proportional, integral, and derivative gains for PID\({}_{\text{b}}\) with \(b=0\) (65) were used.