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The trend today is to use many inexpensive sensors instead of a few expensive ones, since the same accuracy can generally be obtained by fusing several dependent measurements. It also follows that the robustness against failing sensors is improved. As a result, the need for high-dimensional regression techniques is increasing. As measurements are dependent, the regressors will be constrained to some manifold. There is then a representation of the regressors, of the same dimension as the manifold, containing all predictive information. Since the manifold is commonly unknown, this representation has to be estimated using data. For this, manifold learning can be utilized. Having found a representation of the manifold constrained regressors, this low-dimensional representation can be used in an ordinary regression algorithm to find a prediction of the output. This has further been developed in the Weight Determination by Manifold Regularization (WDMR) approach. In most regression problems, prior information can improve prediction results. This is also true for high-dimensional regression problems. Research to include physical prior knowledge in high-dimensional regression i.e., gray-box high-dimensional regression, has been rather limited, however. We explore the possibilities to include prior knowledge in high-dimensional manifold constrained regression by the means of regularization. The result will be called gray-box WDMR. In gray-box WDMR we have the possibility to restrict ourselves to predictions which are physically plausible. This is done by incorporating dynamical models for how the regressors evolve on the manifold. / MOVIII

Continuous-time system identification deals with the problem of building continuous-time models of dynamical systems from sampled input and output data. In this field, there are two main approaches: indirect and direct. In the indirect approach, a suitable discrete-time model is first determined, and then it is transformed into continuous-time. On the other hand, the direct approach obtains a continuous-time model directly from the sampled data. In both approaches there exists a dichotomy between discrete-time data and continuous-time models, which can induce robustness issues and complications in the theoretical analysis of identification algorithms. These difficulties are addressed in this thesis. First, we consider the indirect approach to continuous-time system identification. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree one, independent of the relative degree of the strictly proper true system. Inspired by the indirect prediction error method, we propose an indirect-approach estimator that enforces the desired number of poles and zeros in the continuous-time transfer function estimate, and show that the estimator is consistent and asymptotically efficient. A robustification of this method is also developed, by which the estimates are also guaranteed to deliver stable models. In the second part of the thesis, we analyze asymptotic properties of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC), which is one of the most popular direct identification methods. This algorithm applies an adaptive prefiltering to the sampled input and output that requires assumptions on the intersample behavior of the signals. We present a comprehensive analysis on the consistency and asymptotic efficiency of the SRIVC estimator while taking into account the intersample behavior of the input signal. Our results show that the SRIVC estimator is generically consistent when the intersample behavior of the input is known exactly and subsequently used in the implementation of the algorithm, and we give conditions under which consistency is not achieved. In terms of statistical efficiency, we compute the asymptotic Cramér-Rao lower bound for an output error model structure with Gaussian noise, and derive the asymptotic covariance of the SRIVC estimates. We conclude that the SRIVC estimator is asymptotically efficient under mild conditions, and that this property can be lost if the intersample behavior of the input is not carefully accounted for in the SRIVC procedure. Moreover, we propose and analyze the statistical properties of an extension of SRIVC that is able to deal with input signals that cannot be interpolated exactly via hold reconstructions. The proposed estimator is generically consistent for any input reconstructed using zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. Comparisons with the Maximum Likelihood technique and an analysis of the iterations of the method are provided, in order to reveal the influence of the intersample behavior of the output and to propose new robustifications to the SRIVC algorithm. / <p>QC 20200511</p>

This thesis presents the design, modeling, and control of a fully-actuated multi-rotor unmanned aerial vehicle (UAV). Unlike conventional multi-rotors, which suffer from two degrees of underactuation in their propeller plane, the choice of an unconventional propeller configuration in the new drone leads to an even distribution of actuation across the entire force-torque space. This allows the vehicle to produce any arbitrary combination of forces and torques within a bounded magnitude and hence execute motion trajectories unattainable with conventional multi-rotor designs. This system, referred to as the \omninospace, decouples the position and attitude controllers, simplifying the motion control problem. Position control is achieved using a PID feedback loop with gravity compensation, while attitude control uses a cascade architecture where the inner loop follows an angular rate command set by the outer attitude control loop. A novel model is developed to capture the disturbance effects among interacting actuator airflows of the \omninospace. Given a desired actuator thrust, the model computes the required motor command using the current battery voltage and thrusts of disturbing actuators. A system identification is performed to justify the use of a linear approximation for parameters in the model to reduce its computational footprint in real-time implementation. The \omni benefits from two degrees of actuation redundancy resulting in a control allocation problem where feasible force-torques may be produced through an infinite number of actuator thrust combinations. A novel control allocation approach is formulated as a convex optimization to minimize the \omnis energy consumption subject to the propeller thrust limits. In addition to energy savings, this optimization provides fault tolerance in the scenario of a failed actuator. A functioning prototype of the \omni is built and instrumented. Experiments carried out with this prototype demonstrate the capabilities of the new drone and its control system in following various translational and rotational trajectories, some of which would not be possible with conventional multi-rotors. The proposed optimization-based control allocation helps reduce power consumption by as much as 6\%, while being able to operate the drone in the event of a propeller failure. / Thesis / Master of Applied Science (MASc)

In this Dissertation, we develop, and provide proof of principle for, parameter identification techniques for structural systems that can be described in terms of one or two nonlinear normal modes. We model the dynamics of these modes by second-order ordinary-differential equations based on the principles of mechanics, past experience, and engineering judgment. We perform a number of separate experiments on a two-mass structure using several different types of excitation. For the linear tests, the theoretical system response is known in closed-form. For the nonlinear test, we use the method of multiple scales to determine second-order uniform expansions of the model equations and hence determine the approximations to responses of the structure. Then, we estimate the linear and nonlinear parameters by regressive fits between the theoretically and experimentally obtained response relations. We report deviations and agreements between model and experiment. / Ph. D.

This thesis presents the development of a six degree of freedom nonlinear dynamic model for a single-mast fully submerged hydrofoil vehicle. The aim of the model is to aid in evaluating various model-based controllers for autonomous operation by simulating their performance before implementation in the field. Initially, first principles approach is employed to develop an approximate dynamic model of the vehicle. Prediction of the vehicle motion using the first principles model is then compared with the data from the tow tank experiments to assess the accuracy of the assumptions made in estimating the hydrofoil performance. Additionally, the dynamic model is adjusted to reflect the measured hydrodynamic forces in the tow tank tests. Utilizing the modified dynamic model to simulate the vehicle motion, an initial height controller is designed and tuned in field trials until stable foiling state was achieved. We evaluate the field results and discuss the limitation of employing steady-state tow tank data in establishing the vehicle dynamic model. / Master of Science / This thesis presents the development of a model describing the motion of a hydrofoil vehicle. The craft uses hydrofoils which act like conventional airplane wings that work in water instead of air to lift the hull fully out of the water. In order to maintain a set height above the water and direction of travel, the vehicle needs some form of a controller for autonomous operation. The purpose of the vehicle model is to aid in development of these controllers by simulating and evaluating their performance before implementation in the field. Initially, forces acting on the vehicle are approximated using fundamental hydrodynamic theory. The theoretical model is then compared with experimental data to assist in characterization of the hydrofoils. Building upon the measured test data, we create a preliminary height controller in simulation and conduct field trials to achieve stable foiling state.

The aim of this work is to develop a two-port black-box dc-dc converter modeling methodology for system level simulation and analysis. The models do not require any information about the components, structure, or control parameters of the converter. Instead, all the information needed to build the models is collected from unterminated experimental frequency response function (FRF) measurements performed at the converter power terminals. These transfer funtions are known as audiosuceptibility, back current gain, output impedance, and input admittance. The measurements are called unterminated because they do not contain any information about the source and/or the load dynamics. This work provides insights into how the source and the load affect FRF measurements and how to decouple those effects from the measurements. The actual linear time invariant model is obtained from the experimental FRFs via system identification. Because the the two-port model obtained from a set of FRFs is linear, it will be valid in a specific operating region defined by the converter operating conditions. Therefore, to satisfy the need for models valid in a wide operating region, a model structure that combines a family of linear two-port models is proposed. One structure, known as the Wiener structure, is especially useful when the converter nonlinearities are reflected mainly in the steady state currents and voltage values. The other structure is known as a polytopic structure, and it is able to capture nonlinearities that affect the transient and steady state converter behavior. The models are used for prediction of steady state and transient behavior of voltages and currents at the converter terminals. In addition, the models are useful for subsystem interaction and small signal stability assesment of interconnected dc distribution systems comprising commericially available converters. This work presents for first time simulation and stability analysis results of a system that combines dc-dc converters from two different manufucturers. All simulation results are compared against experimental results to verify the usefulness of the approach. / Ph. D.

Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed. / Ph. D.

Successful race teams rely heavily on track testing to search for the ideal suspension setup. As more restrictions are placed on the amount of on-track testing by major racing sanctioning bodies, such as NASCAR, teams have increased their attention to alternate testing methods to augment their track data and better understand the dynamics of their racecars. One popular alternate to track testing is 8-post dynamic shaker rig testing. Eight-post rig testing gives the team a better understanding of the vehicle's dynamics before they arrive at the race track, allowing them to use their limited track testing time more efficiently. While 8-post rig testing certainly is an attractive option, an extensive test matrix is often required to find the best suspension setups. To take full advantage of 8-post rig tests, more efficient experimental methods are needed. Since investigating shock absorber selection is often the most time-consuming task, this study focuses on developing more efficient methods to select the best shock absorber setups. This study develops a novel method that applies dynamic substructuring and system identification to generate a mathematical model that predicts the results of future tests as both command inputs and components are changed. This method is used to predict the results of 8-post rig tests as actuator commands and shock absorber forces are varied. The resulting model can then be coupled with shock absorber models to simulate how the vehicle response changes with shock absorber selection. This model can then be applied to experimental design. First, a physically-motivated nonlinear dynamic shock absorber model is developed, suitable for quickly fitting experimental data and implementing in simulation studies. Next, a system identification method to identify a vehicle model using experimental data is developed. The vehicle model is then used to predict response trends as shock absorber selection is varied. Comparison of simulation and experimental results show that this model can be used to predict the response levels for 8-post rig tests and aid in streamlining 8-post rig testing experimental designs. / Ph. D.