Model Order Reduction of Linear Sampled-Data Control Systems

Virtually all industrial control systems are implemented digitally by a sample-and-hold device. The design and performance analysis of sampled-data control systems for large-scale systems, represented by a set of high-dimensional differential equations, is challenging. Therefore, commonly, the complex high-dimensional system (plant) model is reduced to 1) support computationally efficient performance analysis for a given digital controller or 2) support (sampled-data) controller synthesis. This paper proposes a novel approach for reduction of such systems taking the sampled-data effects into account in the reduction process. In addition, we propose a condition under which stability of the closed-loop sampled-data control system is preserved in the reduction. This easy-to-check condition depends on 1) reduction error on the continuous-time plant model, 2) the sampling interval, 3) the controller gain. Finally, under this condition also an error bound for the reduced-order system is provided. The proposed methodology is illustrated by numerical examples of a controlled structural dynamical system.