Extended State Observers (ESO) provide the appealing capability of estimating states and disturbances (like modeling errors) simultaneously. In this paper we present a modified fullstate linear ESO as an augmentation of a baseline attitude tracking controller for a hexacopter. The baseline controller is designed using Nonlinear Dynamic Inversion with relative degree 2. By feeding back the estimated modeling error from the ESO, the performance as well as the robustness of the overall control system is significantly improved. These capabilities are demonstrated in outdoor flight tests with a hexacopter, where controlled flight is achieved even under severe actuator degradation. Due to the linear structure of the presented ESO, this might be an alternative to adaptive controllers in view of certification issues.
A position tracking controller for a hexacopter is presented which is robust against disturbances like modeling errors or propulsion efficiency degradation. The presented controller stands out because of its simple design which does not resort to reconfiguration and avoids the necessity of a Failure Detection and Isolation (FDI) filter. The baseline controller has a cascaded structure with two loops. The outer loop corresponds to the position and velocity control and is designed using linear control. The inner loop corresponds to the attitude control which is a Nonlinear Dynamic Inversion (NDI). The baseline controller is augmented by an Extended State Observer (ESO) which provides an estimate of the disturbances and modeling errors which is then fed back to the control law. The performance as well as the robustness of the control system is significantly improved as demonstrated in simulation, where controlled flight is achieved even under severe actuator degradation.
In this paper, a novel Linear Matrix Inequality (LMI) condition for Uniform Ultimate Boundedness (UUB) of Model Reference Adaptive Control with σ -Modification in the presence of unmatched parametric uncertainties is presented. Due to the presence of unmatched uncertainties and due to the usage of the σ -Modification, the control objective of tracking a reference model may only be achieved approximately. A formulation of the UUB condition within the LMI framework provides less conservative bounds on the tracking error. This feature also enables the extension of the UUB condition towards a gain synthesis procedure, which allows the explicit specification of tracking error requirements. For a low-order system, it is demonstrated that the theoretically guaranteed bound on the tracking error of the synthesized adaptive controller is not overly conservative.
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