Stability analysis for an ad-hoc model predictive control in DC/DC converters with a constant power load

• Published in: Results in engineering Vol. 22; p. 102262
• Main Authors: Garcés-Ruiz, Alejandro, Gil-González, Walter, Montoya, Oscar Danilo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2024; Elsevier
• Subjects: Asymptotic stability; Discrete bi-linear model; One-step model predictive control; Second-order DC/DC converters; Asymptotic stability; MPC; One-step model predictive control; FCS-MPC; Second-order DC/DC converters; CCS-MPC; OCP; Discrete bi-linear model; CPL
• ISSN: 2590-1230; 2590-1230
• DOI: 10.1016/j.rineng.2024.102262

This paper presents a stability analysis for a horizon-one continuous control set model predictive control (MPC) for DC/DC converters connected to a constant power loads (CPLs). Different MPC approaches have been previously presented, each tailored to a specific type of converter but without a formal stability proof, failing to ensure robust performance across various operating conditions. Unlike previous works in the scientific literature, our approach is general and applicable to any second-order DC/DC converter, including the Buck, Boost, Buck-Boost, and non-inverting Buck-Boost converters. A formal stability analysis was conducted using the proposed approach, initially for the open-loop system and subsequently for the closed-loop system. The trace-determinant or triangle criterion was employed for discrete-time systems in R2. Three analyses were conducted to evaluate the performance of the proposed MPC, showing the stability issues of DC/DC converters with CPLs in open loops. This work proposes solutions using the suggested technique. Numerical simulations utilizing the Boost and Buck-Boost converters demonstrate that, in open-loop operation, even minor perturbations in the CPL value can destabilize the behavior of electrical variables. In addition, simulations show that, for the Boost converter, the settling time was about 1.5ms. Meanwhile, in the Buck-Boost case, it was about 5ms. Standardized control indicators, such as the integral absolute error criterion (IAE), the integral of the time-multiplied absolute error criterion (ITAE), and the integral of the time-multiplied square error criterion (ITSE), confirm the effective performance of the proposed one-step MPC. The values range between 1.521×10−2 and 4.591×10−6 for the Boost converter, and between 6.607×10−3 and 3.366×10−6 for the Buck-Boost topology. •A one-step model predictive controller for stabilizing constant power loads in DC-DC converters is proposed.•The trace-determinant criterion allows demonstrating the closed-loop stability of the proposed one-step MPC.•A discrete-time analysis allows proposing an effective stable controller for DC-DC converters feeding constant power loads.