Drones, like many other mechanical systems, operate under closed-loop control to ensure safety and economic efficiency. Real-time feedback is crucial for a drone to follow its predefined missions and to deal with hazardous conditions. Achieving optimal performance in such systems often requires a mathematical model, typically obtained using system identification techniques. Furthermore, monitoring changes in the system is essential, before an unexpected change leads to a fault and eventually a failure, causing costly disruptions of the system.

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.

This paper addresses the problem of change detection for a quadcopter in the presence ofwind disturbances. Different aspects of the quadcopter dynamics and various flight conditions have beeninvestigated. First, the wind is modeled using the Dryden wind model as a sum of a low-frequent and aturbulent part. Since the closed-loop control can compensate for system changes and disturbances andthe effect of the wind disturbance is significant, the residuals obtained from a standard simulation modelcan be misleading. Instead, a sensor-to-sensor submodel of the quadcopter is selected to detect a changein the payload using the Instrumental Variables (IV) cost function. It is shown that the mass variationcan be detected using the IV cost function in different flight scenarios.

This paper concerns the estimation of a dynamic model from two measured signals when it is not clear which signal should be used as input to the model. In this case, both a forward and an inverse model can be estimated. Here, a basic instrumental variable approach is used and it is shown that the forward and inverse model estimators give identical parameter estimates provided that corresponding model structures have been used. Furthermore, it is shown that this scenario occurs when properties of a quadcopter are estimated from accelerometer and gyro signals and, hence, that it does not matter which signal is used as input.

In recent years, the quadcopter has become a popular platform both in research activities and in industrial development. Its success is due to its increased performance and capabilities, where modeling and control synthesis play essential roles. These techniques have been used for stabilizing the quadcopter in different flight conditions such as hovering and climbing. The performance of the control system depends on parameters of the quadcopter which are often unknown and need to be estimated. The common approach to determine such parameters is to rely on accurate measurements from external sources, i.e., a motion capture system. In this work, only measurements from low-cost onboard sensors are used. This approach and the fact that the measurements are collected in closed-loop present additional challenges.

First, a general overview of the quadcopter is given and a detailed dynamic model is presented, taking into account intricate aerodynamic phenomena. By projecting this model onto the vertical axis, a nonlinear vertical submodel of the quadcopter is obtained. The Instrumental Variable (IV) method is used to estimate the parameters of the submodel using real data. The result shows that adding an extra term in the thrust equation is essential.

In a second contribution, a sensor-to-sensor estimation problem is studied, where only measurements from an onboard Inertial Measurement Unit (IMU) are used. The roll submodel is derived by linearizing the general model of the quadcopter along its main frame. A comparison is carried out based on simulated and experimental data. It shows that the IV method provides accurate estimates of the parameters of the roll submodel whereas some other common approaches are not able to do this.

In a sensor-to-sensor modeling approach, it is sometimes not obvious which signals to select as input and output. In this case, several common methods give different results when estimating the forward and inverse models. However, it is shown that the IV method will give identical results when estimating the forward and inverse models of a single-input single-output (SISO) system using finite data. Furthermore, this result is illustrated experimentally when the goal is to determine the center of gravity of a quadcopter.