Abstract
Gain-scheduled control is widely applied in the aerospace domain, yet the selection of design points for gain-scheduling controllers to ensure stability and robustness throughout the range of scheduling variables remains theoretically unguided, requiring laborious trial-and-error to ensure control performance. Therefore, this paper proposes a theoretical method for design point selection through analysis and optimization processes to meet system stability and robustness requirements. First, the method characterizes the gain-scheduled control system as a polytopic linear parameter varying (LPV) system, wherein the design points of the gain-scheduled control system correspond to the vertices of the polytopic LPV system. Second, the method utilizes linear matrix inequality (LMI) techniques to demonstrate the stability of a polytopic LPV system with a corresponding number of vertices, and by assessing the approximation degree between the polytopic LPV system and the gain-scheduled control system with an identical number of design points, it evaluates and ensures the stability of the latter, thereby establishing the minimal requirements for the number of design points. Finally, the method further refines the number of design points within the gain-scheduled control system to meet additional robustness and performance considerations. A case study on turbofan engine controls validates the proposed method. New design points, selected via stability and robustness analysis, enhance the system's steady-state phase margin and robustness against model uncertainties. Moreover, compared to a v-gap metric-based method, the proposed method exhibits similar performance in terms of stability, robustness, and tracking control; however, it requires fewer design points, resulting in less conservatism.
