# Active Control Loop of the BOROWIEC SLR Space Debris Tracking System
## 2 Satellite Laser Ranging Process
### Tracking Process  
Taking into account the dynamics of the changes in the angular position (\(Az(t),El(t)\)) of the orbital object in relation to the ground station position in the time domain (mainly for the LEO region) and the required high accuracy of the tracking process (\(x*10\)\(arcsec\); due to laser beam divergence) with respect to the uncertain \(\sigma_{\kappa}\) of the theoretical position of the object, the task of the movement control should be carried out as continuously as possible (close to linear mapping). Therefore, the real object trajectory should be reflected by the iterative operation of the control algorithm, the result of which is projected onto the telescope follow-up movement. The iterative nature of the algorithm in predicting the successive points of the trajectory determines the computational time necessary to minimize the tracking error. In practice, it is assumed that the iteration interval should not be greater than 100 ms (mainly due to the high dynamics of position changes for objects from the LEO region). The tracking task is performed in two steps. In the first step, the time interval \(<\)\(pass_{start}-pass_{stop}>\) should be estimated, in which the position of the object \(\kappa\) (in relation to the station) will enable its observation. Specifying the beginning of the observation time (\(t_{0}\)), the position of the object (\(X_{t_{0}}\), \(Y_{t_{0}}\), \(Z_{t_{0}}\Rightarrow Az_{t_{0}}/El_{t_{0}}\)), and the telescope angles (\(Az_{T_{t_{0}}}/El_{T_{t_{0}}}\)), the telescope is positioned relative to the beginning of the observation. This part of the procedure is not sensitive to the tracking process flow. The second stage starts at the time \(t_{1}>t_{0}\), when the algorithm starts the tracking procedure. The procedure is based on the implementation of a software control loop, which consists of the following activities:  
* Importing the telescope's axes encoder values: \(Az_{t_{n}}^{\prime}/El_{t_{n}}^{\prime}\), in the \(t_{n}\) moment of time;
* Prediction of the theoretical position of the object based on the ephemeris: \(X_{t_{n}+1}\), \(Y_{t_{n}+1}\), \(Z_{t_{n}+1}\Rightarrow Az_{t_{n}+1}/El_{t_{n}+1}\), in the \(t_{n+1}\) moment of time;
* Determining the difference in the form of a correction (\(\Delta Az\), \(\Delta El\));
* Setting new motion parameters for the hardware layer (\(V_{AZ},V_{EL}\Rightarrow v_{a},v_{g}\)). In contrast to the control loop implemented directly at the hardware layer, this approach allows flexibility in changing the motion parameters, although it is costly with additional software calculations outside the servomotor driver. There are a few approaches that determine the control method. The management software may provide with some advance (\(t_{j:j<i}\)) the drive controller information only about the new positions \(X_{i}\), \(Y_{i}\), \(Z_{i}\) (\(Az_{j}/El_{i}\)) for a certain time \(t_{i}\) (the controller must be equipped with a local RT clock). Then, the hardware layer, in the form of the NC servo controller, makes appropriate calculations/corrections (e.g., position, velocity, acceleration) so that the controlled axis follows the determined setting of the controlled parameters (\(Az/El\)) and in the moment of time \(t_{i}\) reaches the position consistent with \(X_{i}\), \(Y_{i}\), \(Z_{i}\) (\(Az_{i}/El_{i}\)). In this way, the entire adjustment process is performed locally by the drive controller (the data transmission of the determined new parameters between the management software and the drive controller does not affect the quality of the control process due to the predictive nature of these parameters).