Metamorphic testing for optimisation: A case study on PID controller tuning

Abstract

Context:

Tuning PID controller parameters is essential for achieving stable and efficient system behaviour. However, traditional methods often depend on expert heuristics or exhaustive simulations, which can be time-consuming and difficult to generalise across configurations.

Objective:

This paper explores Metamorphic Testing (MT) as a validation-driven approach for identifying optimal PID parameter set based on expected behavioural trends.

Method:

We define a set of domain-informed Metamorphic Relations (MRs) that capture control-theoretic expectations. These MRs are used to evaluate and compare simulated parameter sets, based on how many behavioural constraints they satisfy.

Results:

Our findings show that high MR satisfaction is a strong indicator of potentially optimal parameter sets, often yielding smooth, stable control responses. Although trade-offs between metrics—such as energy usage and error correction occasionally led to partial MR violations, expert-preferred parameter sets still closely matched those with the highest MR scores. These results support the use of MR-based evaluation as a practical approach to identifying high-quality tuning parameters.

Conclusion:

Metamorphic Testing offers an interpretable and structured way to guide controller tuning by formalising expected system behaviour. This approach helps identify near-optimal configurations and complements traditional tuning practices through systematic validation.