Nonlinear Dynamic Relative Gain Array for control configuration selection in nonlinear MIMO systems

This paper presents the Nonlinear Dynamic Relative Gain Array (NDRGA) as an input-output interaction measure for control configuration selection (CCS) in dynamic, nonlinear multi-input multi-output (MIMO) systems. The proposed method is derived by extending the primary definition of the DRGA to nonlinear systems, enabling the incorporation of higher-order nonlinear interaction effects. Unlike existing CCS approaches, the NDRGA is formulated in the frequency domain and allows simultaneous analysis of system dynamics and nonlinearities. Since the NDRGA depends on the generalized frequency response functions (GFRFs) of both the nominal forward system and its corresponding inverse, their estimation is carried out using a harmonic probing algorithm and Rönnow's recursive method. This framework provides a frequency-based CCS criterion for nonlinear systems, addressing a gap in the current state-of-the-art where no frequency-domain CCS techniques are available for nonlinear MIMO systems. The effectiveness of the proposed approach is demonstrated in two examples for two nonlinear systems. The closed-loop simulations under decentralized and based on the selected control configuration (CC) confirm the validity of the NDRGA and demonstrate its effectiveness for CCS in nonlinear dynamic systems.