Data‐driven tuning of linear parameter‐varying precompensators

Abstract

SUMMARYMethods for direct data-driven tuning of the parameters of precompensators for LPV systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed precompensator parameterisation, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterised precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimise the mean squared tracking error. The theoretical results are demonstrated in simulation.

Nonlinear Model Predictive Controller Design for Identified Nonlinear Parameter Varying Model

“…Hence, parameter varying process identification has attracted many attentions from both academia and industry [11]. Some results have been proposed in literature to discuss the input-output linear parameter varying (IO-LPV) methods, most of which are based on parameter interpolation techniques [11], [13], [14]. Another feasible approach is provided by interpolating the linear models [5].…”

Virtual Reference Feedback Tuning for linear parameter-varying systems

“…, where y ζ (t) is the output of a second open-loop experiment performed by employing the same input and parameter sequences of the first dataset and p ζ (t) is the parameter sequence with a different realization of noise. It is already known in the literature (see Butcher et al [2008] and Butcher and Karimi [2010]) that for the IV estimate to be consistent it is required that the dataset {u(t), p(t)} t=1,...,N is persistently exciting and that ζ and φ are ergodic in correlation. The first condition is verified for polynomial-type coefficient dependence if u(t) is rich enough and the trajectory of p(t) visits n p + 1 points infinitely many times persistency of excitation condition when the noise model can be approximated with an ARX structure.…”

“…identification, system-transformation and gain-scheduled controller design are all included in one identification step, where a fixed-structure controller is directly identified from data. It should be mentioned that a linear parametervarying data-driven solution has been recently presented for precompensator tuning in Butcher and Karimi [2010].…”

Direct learning of LPV controllers from data

“…Specifically, in [30], the system is given in state-space form with measurable state vector, the optimal controller is assumed to be Lipschitz continuous and the whole method is developed in a deterministic set-membership setting. A direct data-driven LPV solution has been presented in a stochastic framework for feed-forward precompensator tuning in [4]. However, also in this case, no dynamic dependance is accounted for and the final objective is constrained to be LTI.…”