## 3 Measured Parameters and Signal
### Direct and Indirect Measurements  
Part of the signals described in the previous section can be measured directly. All of the temperatures and pressures are measured directly, as well as air flow, weight of the material and grinding media, frequency, and active power of the inverter. Measurement of the rest signals is either impossible or too expensive to be applied. In such a case indirect way is used. From the control point of view the most important is fulfilment level of the working chamber (LI). This signal determines average grinding time and feeds fulfilment controller which stabilize the entire circuit. Extremely harsh and destructive environment in the working chamber does not allow for direct measurement. Several ideas of indirect measurement were tested as e.g., active power measurement with grinding media compensation or air pressure. The final solution bases on acoustic signal measurement [10]. A measurement microphone (Bayerdynamic, Heilbronn, Germany) is installed at the bottom of the preliminary classifier i.e., on the top of working chamber. Measured signal is preliminary tuned during empty mill runoff using information about the mill frequency and mass of the grinding media in the working chamber [21]. Figure 7 presents exemplary data of the acoustic measurement. Figure 7 presents changes of the signal amplitude (upper part) and frequency (bottom part) in the time period of 39 s. The mill operated in a steady frequency. Starting form 15 s, the working chamber was gradually filled with the material. One can notice in Figure 7 the decrease of the signal amplitude (upper part), as well as changes in the signal spectrogram in the frequency range of 6.2-6.6 kHz (marked on Figure 7 bottom part by dashed lines). The power of the measured signal in the given frequency range is presented on spectrogram in Figure 7 by colours: magenta-red-yellow reflecting low-moderate-high power values, respectively. Specific values are not important at this point, while normalization is introduced at later stages of signal processing. Amplitude characteristic is sensitive to disturbances, but the spectrogram characterizes significant robustness, thus the indirect measurement of the working chamber fulfilment bases on the spectrogram. Figure 7: Time series and spectrogram of exemplary working chamber acoustic signal measurement. The working chamber can be understood as a tank with inflow and outflow. In order to keep constant level of the tank, inflow and outflow need to be equal. As air flow can be easily measured in a direct way, flow of the solid particles is very difficult to be measured. Although market offers robust sensors but they need long enough path to form measured stream uniformly (this is the case of air stream measurement in the electromagnetic mill system). Recycle path of the material form the main classifier to put back into the working chamber servers as an example of where such conditions are not provided. In this case, the vibration signal is measured as indirect flow measurement [11]. This method is contactless; the sensors (accelerometers) are small, not expensive, easy to use, and non-invasive to existing installation. Accelerometers (PCB, Depew, NY, USA) were mounted on the transporting pipes. Figure 8 presents an example of waveforms acquired for fine and coarse grains transported with two flows (fast and slow). After extraction, noise reduction, and smoothing, it becomes possible to recognize flow and granulation of the load. Figure 9 presents example of power spectral densities (PSD) that were obtained for exemplary flow and different grain size, which was measured in one (Z) three axis of the accelerometer. These characteristics can be recalculated into specially defined energy index [12], which recognizes flow. Figure 9 presents energy index for different grain sizes. Several trails have been tested for two flows: fast (red lines) and slow (blue lines). Averaged result (solid line) is located between two dotted lines which represent lowest and highest result of the tests.