The successful operation of the laser-based synchronization system of the European X-Ray Free Electron Laser relies on the precise functionality of numerous dynamic systems operating within closed loops with controllers. In this paper, we present how data-based machine learning methods can detect and classify disturbances to such dynamic systems based on the controller output signal. We present 4 feature extraction methods based on statistics in the time domain, statistics in the frequency domain, characteristics of spectral peaks, and the autoencoder latent space representation of the frequency domain. These feature extraction methods require no system knowledge and can easily be transferred to other dynamic systems. We combine feature extraction, fault detection, and fault classification into a comprehensive and fully automated condition monitoring pipeline. For that, we systematically compare the performance of 19 state-of-the-art fault detection and 4 classification algorithms to decide which combination of feature extraction and fault detection or classification algorithm is most appropriate to model the condition of an actively controlled phase-locked laser oscillator. Our experimental evaluation shows the effectiveness of clustering algorithms, showcasing their strong suitability in detecting perturbed system conditions. Furthermore, in our evaluation, the support vector machine proves to be the most suitable for classifying the various disturbances.