Systematic solution for multi-model control approaches in nonlinear dynamic systems based on the s-gap metric

• Published in: ISA transactions 2024-09, Vol.152, p.217-228
• Main Authors: Mafi, Maryam, Saki, Saman, Bolandi, Hossein
• Format: Article
• Language: English
• Subjects: And Multi-Model Control Systems; Generalized Stability Margin; Optimal Model Bank Distribution; Optimal Robustness; S-gap Metric
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2024.06.014

This paper proposes a systematic approach for optimizing the distribution of local models in multi-model control systems (MMCS) to enhance overall robustness. While existing literature discusses this method for linear parameter varying (LPV) and uncertain linear time-invariant (LTI) systems, significant limitations persist in addressing nonlinear dynamic systems. Robust control tools like the gap metric and generalized stability margin (GSM) have limited effectiveness in analyzing the robustness of nonlinear feedback systems. To address these challenges, novel concepts of the gap metric and GSM are introduced to determine central operating points (COPs) within local operating areas (LOAs) across the total operating area (TOA). These COPs guide the extraction of affine disturbance local models (ADLMs). Additionally, an optimization problem based on the s-gap metric and GSM is presented to optimize COPs placement and LOAs boundaries. Challenges such as non-monotonic behavior of the cost function and complexity arising from the s-gap metric formulation necessitate novel solution methods. To address these, constraints are applied to the cost function, and a novel discrete optimization approach is introduced. Finally, theoretical findings are applied to the Duffing system, pH neutralization process, and continuous stirred tank reactor (CSTR) plant to evaluate the proposed method's effectiveness. This comprehensive validation across different systems underscores the versatility and practical utility of the proposed approach. •We provide a systematic solution for addressing multi-model control systems (MMCS) for nonlinear dynamic systems.•Our approach stands out for its versatility, extending its applicability to a broad spectrum of nonlinear dynamical systems.•The solution is achieved through the utilization of s-gap metric concepts.•We tackle the optimization problem in a discrete form, introducing a novel clustering-based optimization approach.•The non-monotonic behavior of the s-gap metric is addressed by incorporating constraints into the problem formulation.