Optimal linear quadratic model following with an application to a flexible aircraft

Abstract

This paper develops general theoretical results about an input–output model-following methodology for linear systems, as an optimal control problem. A control law is obtained by minimizing a quadratic index that takes into account the matching errors and the control inputs. The control is obtained from the Lagrange multiplier method and can be interpreted as an extension of the linear quadratic regulator, with finite and infinite horizon formulations. The major contribution of the paper is the development of solutions involving plant output feedback. The method is illustrated with an application to a nonlinear flexible aircraft with nonstationary aerodynamics and nine flexible modes. Simulations compare state and output feedback solutions. In the proposed example, when taking into account unmodeled flexible dynamics and parametric uncertainties, the best results are given by the proposed output feedback.

Design of adaptive optimal robust control for two-flexible-link manipulators in the presence of matched uncertainties

“…Because of the uncertainties and nonlinearities associated with two-flexible-link manipulators (TFLMs), it is essential to design a control scheme that can robustly and optimally control such robotic systems (Fareh et al, 2019). The challenging subject of designing a trajectory tracking controller for TFLMs has been investigated by various approaches, such as robust control methods (Fareh et al, 2019; Garcia-Perez et al, 2019; Hamzeh Nejad et al, 2020; Lochan and Roy, 2015; Yang and Tan, 2018), adaptive methods (Maouche and Attari, 2013; Shaheed and Tokhi, 2013), optimal control (Cao and Liu, 2018; Da Silva et al, 2014; Shafei and Korayem, 2017; Springer et al, 2013), and hybrid control methods (Chu et al, 2013; MoradiMaryamnegari and Khoshnood, 2019; Wang et al, 2014; Xing and Liu, 2019). A designed controller for an uncertain TFLM should enable the robot to follow a predefined path, while tackling the existing uncertainties and disturbances.…”

Mathematical model of one flexible transport category aircraft

“…This was done by Sousa (2013). Sousa acquired the model of one commercial transport aircraft developed by Da Silva (2012). Da Silva used the NFLS methodology and implemented the model of a commercial transport airplane.…”

“…The same was true for the mass distribution. Sousa (2013) distributed the mass along the wings, engines, fuselage and tails to obtain the same total mass and moments of inertia as defined in the model of Da Silva (2012). The values of structural rigidity had to be derived to follow the characteristics of the structural and geometry model presented by Da Silva (2012).…”