# Optimization of the Control Algorithm for an Active Bearing Support
## 4 Active Adjustment of Bearing Preload
With this assumption, the focus was on ensuring that overshoot did not occur, i.e., the amplitude value was not higher, even for a moment, than at the moment preceding the control. Efforts were made to reduce the control error by following the principle of manual tuning, which can use commonly known regularities (Table 1). Ultimately, the following operating parameters were adopted for the PID controller. The value of individual elements: \(p\) = 1.5, I = 0.04 D = 0, Output parameters 0-6, dt(s) = 1, time loop 500 ms. The control application used a while loop, in which three areas were distinguished (loading the displacement amplitude value, classification into the appropriate group and determining the control value for the active support). \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameter** & **Stability** & **Overshoot** & **Response Time** \\ \hline Increasing K\({}_{\text{P}}\) & Deterioration & Increase & A slight change \\ \hline Increasing T\({}_{\text{i}}\) & Improvement & Reduction & Reduction \\ \hline Increasing T\({}_{\text{d}}\) & Improvement & Reduction & Slight reduction \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Expected effects of manual tuning of the PID regulator. Figure 6: Front Panel view of the LabView application. Figure 7 shows the block diagram for the control application. It was modeled on the basis of a while loop, in which three areas were distinguished. The first one was area (1), where the spindle tip displacement value was loaded and then, based on conditional instructions, it was classified into one of six ranges (2). The ranges were selected to take advantage of the full range of piezoactuator displacement. After the appropriate classification of the spindle tip displacement value, the control value was determined and loaded into the PI controller (3), which was responsible for controlling the active bearing support. Figure 7 shows a block diagram for the active support control system. It was modeled using a while loop with a clock time of 500 ms. It had three areas: 1--loading the displacement value of the front spindle tip (signal from a non-contact displacement sensor); 2--classification of the displacement amplitude value into one of six ranges, <0-5), <5-10), <10-15), <15-20), <20-25) and above 25 um, 3--classifying the displacement value, the control value was read and entered into the PID controller. This controller then gave the output value controlling the advancement of the piezo actuators. The piezoactuators, pressing on the outer bearing ring, increased the preload value of the bearing system and at the same time reduced the amplitude of the displacement of the front spindle tip. The principle of operation of the entire control system can be observed by analyzing the control algorithm in Figure 8 and the measurement circuit diagram in Figure 9.  
Figure 8: Control algorithm for active change of bearing preload. 1—input value of the spindle tip displacement amplitude, 2—regulation error, 3—designated control value for the controller, 4—control value sent from the controller to the NI measurement card (see Figure 9), 5—output signal (amplitude after applying the regulation), 6—element classifying the need to apply regulation (see Figure 7), 7—PID controller, 8—object (tested spindle). Figure 7: Block Diagram view of the LabView application. To make it easier to understand the operation of the active support and determine the measuring and actuating elements, Figure 10 shows a diagram of the spindle system with the active support. Shown is the piezoelectric element (1), the displacement sensor of the front spindle tip (2), the equivalent mass (3), the exciter (4) and the displacement sensor of the outer bearing race (5). Figure 10: Diagram of the measuring system showing the measuring and actuating elements: 1—piezoactuator PSt 150/10/40 VS15, 2—non-contact displacement sensor (IPPT PAN Warszawa [25] design), 3—substitute mass, 4—GW-V20 type exciter from the company Data Physics, 5—displacement sensors type MDKa F1 from VIS.