Design and Real-Time Application of Explicit Model-Following Techniques for Nonlinear Systems in Reciprocal State Space

This paper presents an efficient algorithm for Explicit Model-Following (EMF) control using an Output-derivative Feedback Control (OFC) scheme within the Reciprocal State Space (RSS) framework, aimed at overcoming the performance limitations associated with state-derivative dependence. For Lipschitz Nonlinear Systems (LNS), two approaches are proposed: a linear EMF (LEMF) strategy, which transforms the system into a Linear Parameter-Varying (LPV) representation via the Differential Mean Value Theorem (DMVT) to facilitate controller design, and a nonlinear EMF (NEMF) scheme, which enables the direct tracking of a nonlinear reference model. The stability of the closed-loop system is ensured by deriving control gains through Linear Quadratic Regulator (LQR) optimization. The proposed algorithms are validated through Real-Time Implementation (RTI) on an Arduino DUE platform, demonstrating their effectiveness and practical feasibility.