<p><h1>Abstract</h1></p> <p>As a compact, robust, and reliable power distribution method, hydraulic systems have been used for flight surface control for decades. Electro-hydrostatic Actuator (EHA) is increasingly replacing the conventional valve-controlled system for better performance, lighter weight and higher energy efficiency. The EHA is increasingly being used for flight control. As such its reliability is thereby critical important for flight safety. This research focuses on fault detection and diagnosis (FDD) for the EHA to enable predictive unscheduled maintenance when fault detected at its inception.</p> <p>An EHA prototype previously built at McMaster University is studied in this research and modified to physically simulate two faults conditions pertaining to leakage and friction. Nine different working conditions including normal running and eight fault conditions are simulated. Physical model has been derived mathematically capable of numerically simulating the fault conditions. Furthermore, for comparison, parametric model was obtained through system identification for each fault condition. This comparison revealed that parametric models are not suitable for fault detection and diagnosis due to the computation complexity.</p> <p>The FDD approach in this research uses model-based state estimation using filters. The filter based combined with the Interacting Multiple Model fault detection and diagnosis algorithm is introduced. Based on this algorithm, three FDD strategies are developed using a combination of the Extended Kalman Filter and IMM (IMM-EKF), the Smooth Variable Structure Filter with Varying Boundary and IMM (IMM-SVSF (VBL)), and the Smooth Variable Structure Filter with Fixed Boundary and IMM (IMM-SVSF (FBL)). All the three FDD strategies were implemented on the EHA prototype. Based on the results, the IMM-SVSF (VBL) provided the best performance. It detected and diagnosed faults correctly at high mode probabilities with excellent robustness to modeling uncertainties. It also was able to detect slow growing leakage fault, and predicted the changing trend of fault conditions.</p> / Master of Applied Science (MASc)

The clever designs of natural transducers are a great source of inspiration for man-made systems. At small length scales, there are many transducers in nature that we are now beginning to understand and learn from. Here, we present an example of such a transducer that is used by field crickets to produce their characteristic song. This transducer uses two distinct components—a file of discrete teeth and a plectrum that engages intermittently to produce a series of impulses forming the loading, and an approximately triangular membrane, called the harp, that acts as a resonator and vibrates in response to the impulse-train loading. The file-and-plectrum act as a frequency multiplier taking the low wing beat frequency as the input and converting it into an impulse-train of sufficiently high frequency close to the resonant frequency of the harp. The forced vibration response results in beats producing the characteristic sound of the cricket song. Based on various experimental observations reported in the literature, we model the sound production mechanism as consisting of three stages—actuator, frequency multiplier, and amplifier. We then examine how different features of the forewing govern the sound production. With careful experiments on the harp, we estimate the actual modulus of the harp cuticle and also measure the morphological features of the forewings of different field cricket species. Using this data, we construct a finite element model of the harp and carry out modal analysis to determine its natural frequency. We fine tune the model with appropriate elastic boundary conditions to match the natural frequency of the harp of a particular species—Gryllus bimaculatus. We model impulsive loading based on a loading scheme reported in the literature and predict the transient response of the harp. We show that the harp indeed produces beats and its frequency content matches closely that of the recorded song. Subsequently, we use our FEM model to show that the natural design is quite robust to structural perturbations in the file. The characteristic song frequency produced is unaffected by small variations in the spacing of file-teeth and even by larger gaps. We then attempt to predict a scaling law that crickets must use for spectrum allocation. We use our FEM model, with measurements and computations, to arrive at a predictive model that relates call frequencies of field crickets to the harp dimensions. We verify the validity of this model by using the measured dimensions of harps of nine field cricket species. We then use our model to provide possible explanations as to why the song frequency of various field crickets in our study is bounded between 3.1 kHz and 6.8 kHz. We also show that we are faced with similar challenges as crickets when designing miniature MEMS (Micro-Electro-Mechanical Systems) speakers. We present a design of MEMS speakers that is inspired by how the crickets actuate. We have been able to realize our first prototypes using simple fabrication processes. By electrostatically actuating the MEMS devices, we obtain a sound pressure of 70 dB SPL at a distance of 10 cm. We believe that with a few design and fabrication iterations, we will be able to achieve a much higher sound pressure output from the MEMS speakers.

This dissertation addresses rigid body attitude control with piecewise sinusoidal signals. We consider rigid-body attitude kinematics on SO(3) with a class of sinusoidal inputs. We present a new closed-form solution of the rotation matrix kinematics. The solution is analyzed and used to prove controllability. We then present kinematic-level orientation-feedback controllers for setpoint tracking and command following. Next, we extend the sinusoidal kinematic-level control to the dynamic level. As a representative dynamic system, we consider a CubeSat with vibrating momentum actuators that are driven by small $\epsilon$-amplitude piecewise sinusoidal internal torques. The CubeSat kinetics are derived using Newton-Euler's equations of motion. We assume there is no external forcing and the system conserves zero angular momentum. A second-order approximation of the CubeSat rotational motion on SO(3) is derived and used to derive a setpoint tracking controller that yields order O(ε2) closed-loop error. Numerical simulations are presented to demonstrate the performance of the controls. We also examine the effect of the external damping on the CubeSat kinetics. In addition, we investigate the feasibility of the piecewise sinusoidal control techniques using an experimental CubeSat system. We present the design of the CubeSat mechanical system, the control system hardware, and the attitude control software. Then, we present and discuss the experiment results of yaw motion control. Furthermore, we experimentally validate the analysis of the external damping effect on the CubeSat kinetics.

The work presented herein explores the ability of Ultra High Frequency Radio Frequency (UHF RF) devices, specifically (Radio Frequency Identification) RFID passive tags and Bluetooth Low Energy (BLE) to be used as tools to locate items of interest inside a building. Localization Systems based on these technologies are commercially available, but have failed to be widely adopted due to significant drawbacks in the accuracy and reliability of state of the art systems. It is the goal of this work to address that issue by identifying and potentially improving upon localization algorithms. The work presented here breaks the process of localization into distance estimations and trilateration algorithms to use those estimations to determine a 2D location. Distance estimations are the largest error source in trilateration. Several methods are proposed to improve speed and accuracy of measurements using additional information from frequency variations and phase angle information. Adding information from the characteristic signature of multipath signals allowed for a significant reduction in distance estimation error for both BLE and RFID which was quantified using neural network optimization techniques. The resulting error reduction algorithm was generalizable to completely new environments with very different multipath behavior and was a significant contribution of this work. Another significant contribution of this work is the experimental comparison of trilateration algorithms, which tested new and existing methods of trilateration for accuracy in a controlled environment using the same data sets. Several new or improved methods of triangulation are presented as well as traditional methods from the literature in the analysis. The Antenna Pattern Method represents a new way of compensating for the antenna radiation pattern and its potential impact on signal strength, which is also an important contribution of this effort. The performance of each algorithm for multiple types of inputs are compared and the resulting error matrix allows a potential system designer to select the best option given the particular system constraints.

A series of tests were performed on nickel-titanium alloy wire, also known as nitinol, to determine the plausibility of designing an actuator using this wire as the method of actuation. These tests have been designed to fully characterize how the wire behaves under steady state and transient conditions allowing for a specific wire selection to be made given known actuator specifications which will result in an efficient design. The wire transient data can be used to design a controller which reduces the actuation time. The research done for the overall project covers a wide scope including wire hysteresis, nitinol transition temperature, variable wire resistance, wire actuation as a function of current and pull force, cable fabrication, and wire actuation control to optimize performance. Using these test results, a prototype actuator has been designed using nitinol wire. It has been determined that an actuator can be efficiently designed using this material.

This thesis describes the design, fabrication, and testing process for a microfluidic phosphate colorimeter utilized for water quality analysis. The device can be powered by, and interfaced for data collection with, a common cell phone or laptop to dramatically reduce costs. Unlike commercially available colorimeters, this device does not require the user to measure or mix sample and reagent. A disposable poly(dimethylsiloxane) (PDMS) microfluid chip, powered by an absorption pumping mechanism, was used to draw water samples, mix the sample at a specific ratio with a molybdovanadate reagent, and load both fluids into an onboard cuvette for colorimetric analysis. A series of capillary retention valves, channels, and diffusion pumping surfaces passively controls the microfluidic chip so that no user input is required. The microfluidic chip was fabricated using a modified SU-8 soft lithography process to produce a 1.67mm light absorbance pathlength for optimal Beer Lambert Law color absorbance. Preliminary calibration curves for the device produced from standard phosphate solutions indicate a range of detection between 5 to 30mg/L for reactive orthophosphate with a linearity of R²=91.3% and precision of 2.6ppm. The performance of the PDMS absorption driven pumping process was investigated using flow image analysis and indicates an effective pumping rate up to approximately 7µL/min to load a 36µL sample.

Spacecraft pointing accuracy and structural longevity requirements often necessitate auxiliary vibration dissipation mechanisms. However, temperature sensitivity and material degradation limit the effectiveness of traditional damping techniques in space. Robust particle damping technology offers a potential solution, driving the need for microgravity characterization. A 1U cubesat satellite presents a low cost, low risk platform for the acquisition of data needed for this evaluation, but severely restricts available mass, volume, power and bandwidth resources. This paper details the development of an instrument subject to these constraints that is capable of capturing high resolution frequency response measurements of highly nonlinear particle damper dynamics.

<p>In the field of robotics there is a great interest in developing strategies and algorithms to reproduce human-like behavior. One can think of human-like machines that may replace humans in hazardous working areas, perform enduring assembly tasks, serve the elderly and handicapped, etc. The main challenges in the development of such robots are, first, to construct sophisticated electro-mechanical humanoids and, second, to plan and control human-like motor patterns.</p><p>A promising idea for motion planning and control is to reparameterize any somewhat coordinated motion in terms of virtual holonomic constraints, i.e. trajectories of all degrees of freedom of the mechanical system are described by geometric relations among the generalized coordinates. Imposing such virtual holonomic constraints on the system dynamics allows to generate synchronized motor patterns by feedback control. In fact, there exist consistent geometric relations in ordinary human movements that can be used advantageously. In this thesis the virtual constraints approach is extended to a wider and rigorous use for analyzing, planning and reproducing human-like motions based on mathematical tools previously utilized for very particular control problems.</p><p>It is often the case that some desired motions cannot be achieved by the robot due to limitations in available actuation power. This constraint rises the question of how to modify the mechanical design in order to achieve better performance. An underactuated planar two-link robot is used to demonstrate that springs can complement the actuation in parallel to an ordinary motor. Motion planning is carried out for the original robot dynamics while the springs are treated as part of the control action with a torque profile suited to the preplanned trajectory.</p><p>Another issue discussed in this thesis is to find stable and unstable (hybrid) limit cycles for passive dynamic walking robots without integrating the full set of differential equations. Such procedure is demonstrated for the compass-gait biped by means of optimization with a reduced number of initial conditions and parameters to search. The properties of virtual constraints and reduced dynamics are exploited to solve this problem.</p>

The development and fabrication of silicon-based phononic band gap crystals has been gaining interest since phononic band gap crystals have implications in fundamental science and display the potential for application in engineering by providing a relatively new platform for the realization of sensors and signal processing elements. The seminal study of phononic band gap phenomenon for classical elastic wave localization in structures with periodicity in two- or three-physical dimensions occurred in the early 1990’s. Micro-integration of silicon devices that leverage this phenomenon followed from the mid-2000’s until the present. The reported micro-integration relies on exotic piezoelectric transduction, phononic band gap crystals that are etched into semi-infinite or finite-thickness slabs which support surface or slab waves, phononic band gap crystals of numerous lattice constants in dimension and phononic band gap crystal truncation by homogeneous mediums or piezoelectric transducers. The thesis reports, to the best of the author's knowledge, for the first time, the theory, design methodology and experiment of an electrostatically actuated silicon-plate phononic band gap quasi-crystal architecture, which may serve as a platform for the development of a new generation of silicon-integrated sensors, signal processing elements and improved mechanical systems. Electrostatic actuation mitigates the utilization of piezoelectric transducers and provides action at a distance type forces so that the phononic band gap quasi-crystal edges may be free standing for potentially reduced anchor and substrate mode loss and improved energy confinement compared with traditional surface and slab wave phononic band gap crystals. The proposed phononic band gap quasi-crystal architecture is physically scaled for fabrication as MEMS in a silicon-on-insulator process. Reasonable experimental verification of the model of the electrostatically actuated phononic band gap quasi-crystal architecture is obtained through extensive dynamic harmonic analysis and mode shape topography measurements utilizing optical non-destructive laser-Doppler velocimetry. We have utilized our devices to obtain fundamental information regarding novel transduction mechanisms and behavioral characteristics of the phononic band gap quasi-crystal architecture. Applicability of the phononic band gap quasi-crystal architecture to physical temperature sensors is demonstrated experimentally. Vibration stabilized resonators are demonstrated numerically.

This thesis is concerned with the modeling and numerical study of nonsmooth dynamical systems (NSDS). The first part of the thesis deals with the modeling of some DC-DC power converters using the complementarity formalism. This mathematical theoretical framework allows us to ensure existence and uniqueness of solutions in a "natural" and synthetic way. Specifically, it works pretty well in power electronic converters because it incorporates generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM are stated and simulation results, showing a variety of behaviours, such as persistent or re-entering GDCM, are also presented. Furthermore, the analysis and simulation of a parallel resonant converter (PRC), which has four diodes, illustrate the convenience of the complementarity formalism to simulate electrical systems with a large number of ideal diodes. We also present the simulation of a boost converter with a sliding mode control, even though a general control theory for complementarity systems is not still developed.In the second part of the thesis we focus on the bifurcation analysis in NSDS, and in particular, we have studied different mechanical systems which involve impacts and dry-friction. It is known that nonsmooth or discontinuous dynamical systems can exhibit the bifurcations also exhibited by smooth systems. In addition to these, there are also some novel transitions so-called discontinuity-induced bifurcations (DIBs) which are unique to these systems. We have investigated the complex behaviour occurring in an impacting mechanical system. DIBs such as corner impact bifurcations and transitions from complete to uncomplete chattering motions have been analysed in detail. Another type of DIBs recently classified are the so-called sliding bifurcations. Such bifurcations are a characteristic feature of so-called Filippov systems. We present detailed examples of all the different sliding bifurcation scenarios in a dry friction oscillator using a measured friction characteristic firstly introduced by Popp. Furthermore, a codimension-two degenerate switching-sliding bifurcation is displayed. In this case of degenerate switching-sliding bifurcation two curves of codimension-one sliding bifurcations, crossing-sliding and adding-sliding, branch out from the codimension-two point. Also, a cusp smooth codimension-two bifurcation is shown and coexistence of periodic orbits in the region between both fold codimension-one curves is studied.We have also investigated the dynamic behaviour of the two-block Burridge model for earthquake simulations. Previous numerical studies investigated by Ruina verified that, with a friction force of Coulomb type, the system presents only periodic behaviour. We show that chaotic regions can be observed in a symmetric configuration even if a Coulomb friction is considered with the relaxation of one of the assumptions assumed in the seismological literature. Furthermore, we have studied the behaviour of the system with asymmetric configuration. Different periodic solutions and regions of chaos can be observed varying the asymmetry of the system. With respect to the bifurcation point of view, we have analysed several smooth bifurcations (smooth and DIBs) observed in this system.Chapter 6 of this thesis presents the SICONOS software platform dedicated to simulation of NSDS. We give an overview of the SICONOS software and the way NSDS are modeled and simulated within the platform. Routines for analysis (stability, bifurcations, invariant manifolds,.) of NSDS implemented in the platform are explained in detail. To conclude this part, several representative samples are shown in order to illustrate the SICONOS platform abilities.Conclusion and some open problems are presented in the last chapter.