On identification methods for direct data‐driven controller tuning

Abstract

SUMMARYIn non-iterative data-driven controller tuning, a set of measured input/output data of the plant is used directly to identify the optimal controller that minimizes some control criterion. This approach allows the design of fixed-order controllers, but leads to an identification problem where the input is affected by noise, and not the output as in standard identification problems. Several solutions that deal with the effect of measurement noise in this specific identification problem have been proposed in literature. The consistency and statistical efficiency of these methods are discussed in this paper and the performance of the different methods is compared. The conclusions offer a guideline on how to solve efficiently the data-driven controller tuning problem .

Virtual reference feedback tuning with Bayesian regularization

“…Since the method relies on IV techniques to cope with measurement noise, the variance of the parameter estimate is much larger than the Cramér-Rao lower bound [24]. However, since the final goal in practice is the minimization of (3) for a given N and not to find an unbiased controller, the bias and variance effects can be balanced via suitable trade-off tuning.…”

“…However, since the method is based on errors-in-variables estimation [21], it is not statistically efficient, i.e. the Cramér-Rao lower bound cannot be achieved [24].…”

Enhancing statistical performance of data-driven controller tuning via -regularization

“…However, it is known that in IV techniques the variance of the parameter estimate is larger than the Cramér-Rao lower bound [12]. Since the final goal in practice is the minimization of (1) for a given N and not to find an unbiased controller estimate, L 2 -regularization can be used, analogously to [13], to improve the quality of the estimates by introducing an additional tuning-knob to balance bias and variance effects.…”

“…However, these methods suffer from the drawback that, being based on errors-in-variables estimation [11], they are not statistically efficient, i.e. the Cramér-Rao lower bound cannot be achieved in all the cases [12]. The aim of this paper is then two-fold.…”

An Improvement on Data-Driven Pole Placement for State Feedback Control and Model Identification

“…In the data-driven control framework, where no explicit mathematical plant model is used, a feedback controller must be derived that satisfies the prescribed closed-loop performance and fits to known experimental data. In contrast with traditional model-based controller designs, techniques such as controller identification [14] or a combination of plant model and controller identification must be applied [15] [ 16].…”