A comparative study of VRFT and set-membership data-driven controller design techniques: active suspension tuning case

In this chapter, we compare two approaches to the data-driven control (DDC) design problem. In this framework, the controllers are directly identified from data avoiding the plant identification step. The analyzed approaches are virtual reference feedback tuning (VRFT) and set-membership tuning (SMT) controller. They differ in the assumptions about the noise affecting the experimental data and the criteria to select an optimal controller. The former strategy assumes an stochastic description of the unknown signals, while the latter imposes an unknown but bounded (UBB) noise structure. Both methodologies are described and their main theoretical results are reported. The two approaches are evaluated on an experimental case study, consisting of the controller tuning for an active suspension (AS) system. Three Monte Carlo experiments are performed, where 100 controllers are derived from data affected by measurement noise using both methods, and their performance is evaluated on the experimental test-bench. Results show that both approaches offer a similar performance when the size of the dataset is much larger than the dimension of the controller parameters vector. However, for reduced datasets, the SMT approach gives consistent results while the VRFT method is not able to extract useful information. The same behavior is observed when the two approaches are applied to datasets affected by process disturbances. It is observed that the root mean squared error of the resulting loops can be up to 30 times lower using the set membership method for reduced datasets.