Data-driven MIMO model-free reference tracking control with nonlinear state-feedback and fractional order controllers

Abstract

In this paper we suggest an extension of the Virtual Reference Feedback Tuning (VRFT) framework to nonlinear state-feedback and fractional order (FO) controllers. Theoretical analysis incentivizes the use of VRFT for tuning general nonlinear controllers to achieve model reference matching because it is expected that the more complex controller parameterization of the nonlinear-state-feedback and FO controllers leads to improved control performance. Key factors needed for successful controller tuning are discussed: good exploration of process dynamics depending on careful input excitation signal selection, the influence of the controller parameterization and the selection of the reference model. VRFT is next applied to a Multi Input-Multi Output (MIMO) nonlinear coupled vertical tank system as a case study, to tune MIMO proportional–integral (PI), fractional order-proportional–integral (FO-PI) and neural network state-feedback controllers. PI and FO-PI controllers are tuned in continuous time but implemented in discrete time to enable their real-world applications. Controllers’ complexity vs. control performance trade-off is revealed. For comparisons purposes, an original combination of VRFT and Batch Fitted Q-Learning is employed as a two-step model-free controller tuning procedure for dramatic performance improvement.