Data-Driven Virtual Reference Set-Point Learning of PD Control and Applications to Permanent Magnet Linear Motors

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.