The cost of model reference adaptive control - Analysis, experiments, and optimization

In this paper the performance of Model Reference Adaptive Control (MRAC) is studied in numerical simulations and verified experimentally with the objective of understanding how differences between the plant and the reference model affect the control effort. MRAC is applied analytically and experimentally to a single degree of freedom system and analytically to a MIMO system with controlled differences between the model and the plant. It is shown that the control effort is sensitive to differences between the plant and the reference model. The effects of increased damping in the reference model are considered, and it is shown that requiring the controller to provide increased damping actually decreases the required control effort when differences between the plant and reference model exist. This result is useful because one of the first attempts to counteract the increased control effort due to differences between the plant and reference model might be to require less damping, however, this would actually increase the control effort. Optimization of weighting matrices is shown to help reduce the increase in required control effort. However, it was found that eventually the optimization resulted in a design that required an extremely high sampling rate for successful realization.