In industrial automation, there are numerous use cases for a model representing the equipment’s sequence of operations. Not only can such a model be used as a debugging aid, allowing users to observe the current state of the machinery at a glance, but it also can serve as a foundation for process improvements. Annotated process models can help pinpoint bottlenecks within the system, and a combination of models obtained from identical machines can be used to create a best-case baseline to which the devices can be optimised. Typically, the models used for such activities have been created during the equipment’s design phase, which means that many of the changes made during commissioning, start-up, and production are not reflected. The research domain of process mining suggests that an accurate model can be obtained from an activity log. Since most industrial processes are controlled by Programmable Logic Controllers (PLCs), which offer the capability of external access through Open Platform Communications (OPC), such a log can be created automatically. The theory is that process mining algorithms can then be used to discover the desired model from the data recorded. Unfortunately, it turns out that this whole procedure is a game of chance. The quality of the discovered models strongly depends on the logged data. Not only can the records be flawed, but also the information needed to discover a complete model might not have been observed at all. To better judge the quality of the discovered models, numerous quality metrics have been proposed, which in the authors’ opinion are a good guess at best. The industrial automation domain demands complete models, which cannot be guaranteed by any process mining algorithm unless it is known that the log contains all the data needed. This paper shows that for industrial equipment, it is possible to reason through the evaluation of a single recorded case, which case traces are required to guarantee that the discovered model will be complete. In the next step, the authors then introduced the concept of ‘trace induction’, which takes advantage of the fact that a PLC controls the observed processes. A minor change within the PLC’s logic is used to force the process to execute the desired traces on demand. The resulting, minimalistic log can then be analysed by the αLC-algorithm to create a guaranteed complete, model.