Nonlinear flight control with reduced model dependency - Byoung-Ju, Jeon (Cranfield University, 2020)
This thesis aims to innovate knowledge on nonlinear flight control algorithms with reduced model dependency by resolving the research gaps for practical applications. Two control schemes with different principles on reducing model dependency are considered in this thesis; incremental control scheme and adaptive control scheme. In incremental control scheme, state derivative and control surface deflection angle measurements are additionally utilized to substitute required model information except control effectiveness. In adaptive control scheme, uncertain model parameters are estimated online via adaptation law and these estimates are utilized in control input command calculation. Discussions in this thesis are based on incremental backstepping control (IBKS) and composite adaptive backstepping control (C-ABKS) which are obtained by applying those control schemes to backstepping control (BKS). Contributions of this thesis with each algorithm are detailed as follows. This thesis provides critical understandings on IBKS in a systematic way via theoretical analysis under various defects. As a starting point, closed-loop analyses under the model uncertainties are conducted with IBKS and BKS for theoretical interpretations on reduced model dependency in IBKS. Stability and performance of the closed-loop system with IBKS are shown to be not affected by the model uncertainties, while they significantly influence the closed-loop characteristics with BKS. One interesting observation is that the uncertainty on control effectiveness information, which is still required to implement IBKS, does not have any impact on the closed-loop system with IBKS if a control input is calculated, transmitted and reflected fast enough to an actual control surface. The next two analyses are conducted to identify how the defects on the additional measurements together with the model uncertainties affect stability and performance of the closed-loop system with IBKS. First, the closed-loop characteristics with IBKS is analyzed under biases on the additional measurements and the model uncertainties. The measurement biases result in a steady state error while not affecting the closed-loop system stability with IBKS. Unlike the analysis results only with the model uncertainties, the uncertainty in control effectiveness information has an impact on the steady-state error of the closed-loop system. Second, the closed-loop system with IBKS under delays on the additional measurements and the model uncertainties is examined with the analysis framework proposed in this thesis. New analysis framework with optimization concept is proposed to systematically and efficiently test the closed-loop system stability under measurement delays. The key finding is that the delays on the additional measurements should satisfy a specific relationship for the closed-loop stability with IBKS. Besides, it is identified that this stability condition is affected by the uncertainty on control effectiveness information. A new C-ABKS is designed by resolving research gaps of the composite adaptive control for a practical application as follows. First, parameter convergence under finite excitation (FE) is guaranteed with a new paradigm for the information matrix design which is suggested by developing a modulation-based approach. It is proven that the new information matrix is positive definite for all the time from the beginning under FE, while the accumulation-based approach in previous studies requires uncertain amount of time to populate the information matrix to be full rank. The closed-loop system with the C-ABKS utilizing the new information matrix is guaranteed to be globally exponentially stable for all the time under FE. Comparing to the accumulation-based approach, the new modulation-based approach provides advantages in adaptation speed and system robustness since the information matrix is designed to have all eigenvalues with moderate level of magnitudes. Second, the adaptation speed is improved without excessive increase of the adaptation gains in the new logarithmic regression-based composite adaptive control system. The parameter convergence speed is enhanced by slowing down the adaptation speed degeneration at the later stage where the estimation error is small; a concave and monotonically increasing characteristics of a logarithmic function is utilized for the regression term design in this research. The closed-loop system with the proposed logarithmic regression-based C-ABKS is shown to be asymptotically stable under FE by applying Lyapunov theory. Within the system boundary, the new logarithmic regression-based algorithm is proven to be always faster than the well-known linear regression-based algorithm under the same adaptation gain if its design parameters satisfy the suggested condition. In order to make the linear regression-based approach to become faster than the logarithmic regression-based approach with the design parameters satisfying this condition, the adaptation gain of the linear regression term should be increased and this can result in reduced robustness. Important findings for IBKS and C-ABKS are suggested and verified with simulations throughout the thesis. A comparative study is additionally conducted to show different properties of IBKS and C-ABKS under model uncertainties and measurement delays via numerical simulations.