Model Order Reduction Method for Large-Scale $RC$ Interconnect and Implementation of Adaptive Digital PI Controller

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Model order reduction is a powerful tool widely used in complexity reduction of high-dimensional systems. It is used to optimize the storage memory size and to design the adaptive control strategies of complex large-scale linear and nonlinear systems. In this paper, we propose a novel model order reduction (MOR) method applied to linear electronic circuits. In addition, we implement an adaptive digital proportional–integral (PI) controller in a microcontroller to monitor the original system in real time. The controller’s initial parameters are determined from the reduced system. The proposed approach, which we call the Arnoldi-Lyapunov in the sequel, benefits from both the Krylov and Lyapunov techniques. It is in essence based on determining two projection matrices $V$ and $W$ and using them to project the original space onto a smaller one. The Krylov technique is used for its numerical efficiency. The use of the Lyapunov technique preserves the stability and passivity of reduced system, minimizes the $H_{2}$ - and $H_{\infty }$ -norm errors, and minimizes the error between the time response of the original system and the reduced one. Numerical examples are given to study the performance and the effectiveness of the proposed method. Furthermore, the experimental results of the resistor–capacitor $RC$ model are presented to demonstrate the effectiveness of the proposed method in generating the suitable controller parameters.