Closed-loop Diagnosis Using Submodels: With Applications to Quadcopters

This thesis investigates ways of obtaining robust fault detection and accurate parameter estimation in a closed-loop system. In detail, we focus on subsystems of larger systems where the parameters or changes are observable. This approach, referred to as submodeling, is adopted since examining the entire system dynamics can be challenging due to the complexities and interconnections between components. Moreover, it involves selecting and measuring only a subset of signals, which reduces the number of sensors required. However, the resulting submodels use certain measurements as the outputs and others as the inputs, yielding closed-loop errors-in-variables (EIV) problems.

The first contribution addresses fault detection in closed-loop EIV systems. We apply a projection-based nonadditive fault detection method where the residual is projected to a subspace that is orthogonal to additive faults and disturbances. By doing so, we demonstrate that additive and nonadditive faults can be decoupled, making residuals sensitive only to the nonadditive ones. This allows the nonadditive fault to be detected accurately despite the occurrence of additive faults, closed-loop effects, and disturbances.

In the second contribution, we establish a specific equivalence concept related to the residuals of models concerning input-output repartitionings, which is useful for studying estimators. Moreover, we show that the basic instrumental Variable (IV) estimator can yield equivalent estimates which are independent of the input-output partitionings, unlike other standard system identification methods. The algebraic equivalence of the basic IV estimates holds regardless of the true system structure, noise properties, and data length.

The third contribution is to utilize the approach to derive submodels of a quadcopter. More specifically, we exploit the cancellation of shared dynamics between actual inputs and measured outputs, allowing for the elimination of some input signals. These submodels, addressing various aspects of the quadcopter’s dynamics, are simpler than a complete model but still sufficient for the intended applications.

The fourth contribution is to validate all methods developed in this thesis using simulated and experimental data from a quadcopter. To do so, we apply a standard motion-planning framework based on the simulation model of the drone to establish a detailed experimental procedure. This procedure allows us to define scenarios similar to real-world tasks of the drone in a testbed and to obtain excitation trajectories that produce informative data. Both the simulated and experimental data-based validations show promising results.