Worst-case analysis and linear parameter-varying gain-scheduled control of aerospace systems

In this thesis, two main subjects are discussed. The first is a worst-case performance analysis, the second is a linear parameter varying (LPV) synthesis using a blending approach. On the first subject, a linear fractional transformation (LFT) model of the linearized X-38 Crew Return Vehicle (CRV) has been developed to facilitate the analysis of its flight control system. The LFT model represents uncertainty in nine aerodynamic stability derivatives at a given flight condition. The X-38 LFT model, combined with a controller at specific flight conditions, is used to determine the aerodynamic coefficients within a predefined set that result in the worst-case performance and worst-case gain/phase margins of the closed-loop system. LPV and μ controllers are synthesized for the X-38 CRV lateral-directional axes over the candidate flight envelope and compared with the baseline gain-scheduled classical control design. Worst-case analysis of the LPV and μ controllers are compared with the baseline gain-scheduled classical control design. Analysis and time simulations show that the LPV controller achieves significant performance and robustness improvements when compared to a linear μ controller and the baseline gain-scheduled controller.; On the second subject, a quasi-LPV model of the F-16 longitudinal axes was developed using three methods: Jacobian linearization, state transformation and function substitution. Time simulations of quasi-LPV models show that the quasi-LPV models developed using state transformation and function substitution accurately represent the nonlinear dynamics of the F-16 longitudinal axes. In designing an LPV controller for the F-16 longitudinal axes, the function substitution quasi-LPV models are used since these quasi-LPV models can represent the nonlinear dynamics at non-trim points. Two LPV controllers are synthesized for the F-16 longitudinal axes for two separated flight envelopes: low and high altitude regions. Blending these controllers over the overlapping regions results in a single controller for the full flight envelope. Time simulation results of the 12 state nonlinear model with the blended controller show that the controller achieves the desired performance requirements across altitude variations.