Robust LQ control with adaptive law for MIMO descriptor system

Abstract

This paper presents a robust LQ control system with Model Reference Adaptive Control(MRAC) law for MIMO system which is described as descriptor form. Generally, the performance degradation is expected to happen in case that uncertainty excess the upper and lower bound which are considered in the robust control synthesis process. For this problems, adaptive control algorithms have potential to improve performance and reliability in control system. In this study, we focus on this characteristics of adaptive control algorithms and add adaptive law into usual robust control system. The proposed system is synthesized by two-step approach. First of all robust LQ controller is synthesized through solving some LMI conditions. This robust LQ controller can be handle with limited uncertainty parameters. Second, adaptive law is designed and consolidated closed loop stability of adaptive loop and the robust LQ control loop is analyzed though solving quadratic stability conditions. The feature of this study are as follows: 1. Quadratic stability is analyzed in case of MIMO system described as descriptor form with adaptive law. 2. Convergence speed is considered at the design process of adaptive law with σ-modification. 3. The effectiveness of the proposed method is verified by some experiments using a test-scale 2 Degree-of-Freedom (2DOF) helicopter.