Comparative analysis of model reduction strategies for circuit based periodic control problems

Abstract

This paper is a comparative analysis of two prominent iterative algorithms for model order reduction of linear time‐varying (LTV) periodic systems where the system's matrices are singular. Our proposed method is based on a reformulation of the LTV model to an equivalent linear time‐invariant (LTI) model using a suitable discretization procedure. The resulting LTI model is reduced in two ways, once by applying a balanced truncation method and once by applying a Krylov‐based method known as iterative rational Krylov algorithm (IRKA). During the application of balanced truncation, the low‐rank Cholesky factorized alternating directions implicit (LRCF‐ADI) method is used to estimate the solutions of the corresponding LTI form of Lyapunov equations. Since the system's matrices are singular, the concept of pseudo‐inverse is adopted to compute the shift parameters needed in the LRCF‐ADI iterations. For the Krylov‐based IRKA, our work is twofold. We solve the time‐invariant Lyapunov equation for the observability Gramian and apply a moment‐matching Krylov technique. The accuracy and effectiveness of the two proposed techniques are demonstrated with the help of frequency response graphs, bode plots, and eigenstructure of the main and reduced models.

Event-triggered robust tracking control for fractional-order uncertain systems

“…Next, to validate the advantages of the proposed ET errorfeedback controller, a time-triggered controller which was adopted in Hossain et al (2021), Villarreal-Cervantes et al (2020 is further applied to the considered uncertain FO system. Here, the time-triggered sampling period is chosen as 0:05s, then the corresponding tracking error trajectory is given in Figure 7.…”

Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

“…Therefore, it is time‐consuming and memory‐restricted to control, simulate, or optimize the large‐scale systems. To solve these problems, model order reduction (MOR) techniques [1,4–7] have been developed to produce a low‐dimension model that approximates the input‐output behavior of the original large‐scale system with high fidelity. However, there are many large‐scale parametric systems in engineering applications [8–10] because of significant modifications to the systems, such as geometric or material properties variations and alterations in boundary or initial conditions.…”