Operator-Based Nonlinear Optimized Multi-Input Control Design and Its Application to a Vibrating Plate with Reduced-Sensor Implementation

In nonlinear mechatronic systems with multiple coupled actuators, the allocation of control inputs affects both the feedback-system structure and the required actuator effort. This paper develops an operator-based nonlinear multi-input control framework within the robust right coprime factorization (RRCF) structure for systems with more actuator inputs than controlled outputs. The original multi-input plant is represented through a reduced-output formulation, and the control allocation is described by a mapping that selects a right inverse of the input-coupling. Specifically, the actuator inputs are determined by minimizing the quadratic voltage-based control-effort objective subject to the prescribed coupling relation and actuator constraints. Under the ideal allocation condition, the nominal Bezout Identity is preserved, while robust stability in the presence of plant perturbations, coupling uncertainty, and allocation errors is guaranteed when the generalized Lipschitz condition derived for the optimized RRCF system is satisfied. The proposed framework is applied to a vibrating plate actuated by multiple piezoelectric elements. For this application, the constrained two-input allocation problem is reduced to a scalar piecewise optimization problem and solved by a finite-candidate selection procedure. Comparative experiments show that the proposed approach achieves stronger vibration suppression, a lower voltage-based control-effort metric, and a more balanced allocation among the actuators. These results demonstrate the effectiveness of integrating constrained multi-input allocation with the operator-based robust control framework.