Microgyroscopes find popular applications in modern life, such as, vehicle navigation, inertial positioning, human body motion monitoring, etc. In this study, three unique MEMS gyroscopic sensors were investigated using experimental methods and finite element analysis (FEA) modelling, particularly their modal behaviour. The analytical, simulated and experimental results were compared and the discrepancy between resonant frequencies of the significant mode shapes was discussed. Three microfabricated gyroscopes were investigated: a thermally-actuated in-plane gyroscope, an electrostatically-actuated in-plane gyroscope and an electrostatically-actuated out-of-plane gyroscope. Numerical finite element modal analysis for these three gyroscopes was conducted using COMSOL Multiphysics. The experimental testing was conducted using a microsystem analyzer (MSA-400 PolyTec) with an integrated laser vibrometer. The simulation models predicted that the frequencies for driving and sensing modes were 4.948kHz and 5.459kHz for a thermally-actuated gyroscope, which agreed well with experimentally determined results of 5.98kHz and 6.0kHz respectively. The power requirements of a thermally-actuated gyroscope were 363.39mW to elicit a maximum peak-to-peak displacement of 4.2μm during dynamic operation. Similarly, the simulated frequencies for the driving and sensing modes were 1.170kHz and 1.644kHz for an electrostatically-actuated in-plane gyroscope, which corresponded to experimentally determined resonant frequencies 1.6kHz and 1.9kHz. Simulation for the electrostatically-actuated out-of-plane gyroscope was conducted and the frequencies for the driving and sensing modes were found to be 2.159kHz and 3.298kHz. Due to some fabrication defects, the experimental testing for this microgyroscope was not successful. Some recommendations to improve the design were provided for the future work. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2010-06-02 22:00:52.994

Studies aimed at the development of indigenous low cost star tracker and gyroless attitude and angular rate estimation is presented in the thesis. This study is required for the realization of low cost micro satellites. A target specification of determining the attitude with accuracy (3σ) of 0.05 degrees and attitude rate with accuracy (3σ) in the range of 50rad/sec at a rate of 10 samples/second in all the axes is set as a goal for the study. Different sensor arrays available in the market are evaluated on the basis of their noise characteristics, resolution of the analog-to-digital converter (ADC) present and ability to work in low light conditions, for possible use in the hardware realization of star tracker. STAR1000 APS CMOS array, manufactured by Cypress Semiconductors, qualified these performance criteria, is used for the simulation study. An algorithm is presented for scanning the sensor array, detection of star image and retrieving the information concerning the photoelectron counts corresponding to a star image. The exact designation of the center of the star image becomes crucial as it has direct implications on the accuracy of the estimated attitude. Various algorithms concerning the centroid estimation of a defocused star image on the sensor array to subpixel accuracy are studied and Gaussian Weighed Center of Gravity algorithm is adapted with some modifications and an accuracy of 0.039 pixels is obtained in both horizontal and vertical direction of the array. A one-to-one relationship is established between the stars obtained in the field-of-view (FOV) of the star tracker with the stars present in the star catalog resident in the star tracker through star identification algorithm. A star identification algorithm which relies on the interstar angles and brightness of the stars is developed in this thesis. The interstar angles of the stars visible in the FOV of the star sensor is recorded, compared with the inter-star angles made by the stars selected in the catalog, based on initial brightness match with stars formed on image plane. After identification at the initial epoch, consequent instants can drive information from the previous matches so as to decrease the computational complexity and storage requirement for the subsequent instants. The memory constraints and computational overhead on the processor and the dynamic range of the image detector used in the star tracker are the limiting factors. The stars thus identified with the stars in the catalog are used for the estimation of attitude. A point solution to the attitude estimation problem is computed using a least square based algorithm called ESOQ-2. The algorithm for centroiding of star images and ESOQ-2 for finding the point solution satellite attitude is coded and tested on Da Vinci based emulator. This exercise shows that it is possible to implement above algorithm for real time operations. Estimation of attitude at a given epoch using algorithms like ESOQ-2 does not minimize the noise and error covariance as the attitude estimated at each instant of time depends only on the measurement taken at that particular instant. So a Kalman Filter (KF) based estimation using Integrated Rate Parameter (IRP) formulation called SIAVE algorithm, is adapted, with some modifications, for the estimation of incremental angle and attitude rates from vector observations of stars. From the point solution of attitude estimation problem of the satellite, the incremental angle and angular rate at successive time steps are predicted using a linear KF and refined with the measurements from the stand alone star tracker, taken at discrete time steps, using the SIAVE algorithm. The sensor noise is modeled from the characteristics of STAR1000 sensor array used in the algorithm in order to make the simulations more realistic in nature. The optimality of Kalman filter is based on the assumption that the state and measurement noises are white gaussian random processes and the state dynamics of the plant is completely known. However, for most real systems, modeling uncertainties are present. So a robust state estimator based on H∞ norm minimization is devised. The H∞ filter, based on game theory approach is used to minimize the worst case variance of noise signals with the only assumption on the noise signals that they are energy bounded. The aim is to find the feasibility of using H∞ filter for the estimation of incremental angle and attitude rate of the satellite. The studies shows that H∞ filter with proper tuning can serve as potential estimation scheme for the attitude and angular rate estimation of the satellite. It is found that both Kalman filter and H∞ are able to meet the specified accuracy desired from low cost accurate star sensor.

Design and analysis of polysilicon and single crystal silicon gyroscopes have been carried out. Variations in suspension design have been explored. Designs that utilize in-plane and out-of-plane sensing are studied. Damping plays an important role in determining the sense response. Reduction in damping directly affects sensor performance. The various damping mechanisms that are prevalent in gyroscopes are studied. Perforations on the proof mass are observed to significantly reduce the damping in the device when operated in air. The effects of perforation geometry and density have been analyzed. The analysis results show that there is a two orders of magnitude reduction in damping of thick gyroscope structures with optimized perforation design. Equivalent circuit lumped parameter models have been developed to analyze gyroscope performance. The simulation results of these models have been compared with results obtained from SABER, a MEMS specific system level design tool from Coventorware. The lumped parameter models are observed to produce faster simulation results with an accuracy comparable to that of Coventorware Three gyroscopes specific to the PolyMUMPS fabrication process have been designed and their performance analyzed. Two of the designs sense motion out-of-plane and the other senses motion in-plane. Results of the simulation show that for a given damping, the gyro design with in-plane modes gives a resolution of 4º/s. The out-of-plane gyroscopes have two variations in suspension. The hammock suspension resolves a rate of 25º/s in a 200 Hz bandwidth while the design with folded beam suspension resolves a rate of 2º/s in a 12 Hz bandwidth. A single crystal silicon in-plane gyroscope has been designed with vertical electrodes to sense Coriolis motion. This design gives an order of magnitude higher Capacitance change for a given rotation in comparison to conventional comb-finger design. The effects of process induced residual stress on the characteristic frequencies of the polysilicon gyroscopes are also studied. The in-plane gyroscope is found to be robust to stress variations. Analysis results indicate that the tuning fork gyroscope with the hammock suspension is the most susceptible to compressive residual stress, with a significant drop in sensitivity at high stress values.

This thesis reports the development of high-performance symmetric and decoupled micromachined gyroscopes for tactical-grade inertial measurement applications. The symmetric structure allows easy matching of the resonance frequencies of the drive and sense modes of the gyroscopes for achieving high angular rate sensitivity / while the decoupled drive and sense modes minimizes mechanical cross-coupling for low-noise and stable operation. Three different and new symmetric and decoupled gyroscope structures with unique features are presented. These structures are fabricated in four different micromachining processes: nickel electroforming (NE), dissolved-wafer silicon micromachining (DWSM), silicon-on-insulator (SOI) micromachining, and silicon-on-glass (SOG) micromachining. The fabricated gyroscopes have capacitive gaps from 1.5&micro / m to 5.5&micro / m and structural layer thicknesses from 12&micro / m to 100&micro / m, yielding aspect ratios up to 20 depending on the fabrication process. The size of fabricated gyroscope chips varies from 1x1mm2 up to 4.2x4.6mm2. Fabricated gyroscopes are hybrid-connected to a designed capacitive interface circuit, fabricated in a standard 0.6&micro / m CMOS process. They have resonance frequencies as small as 2kHz and as large as 40kHz / sense-mode resonance frequencies can be electrostatically tuned to the drive-mode frequency by DC voltages less than 16V. The quality factors reach to 500 at atmospheric pressure and exceed 10,000 for the silicon gyroscopes at vacuum. The parasitic capacitance of the gyroscopes on glass substrates is measured to be as small as 120fF. The gyroscope and interface assemblies are then combined with electronic control and feedback circuits constructed with off-the-shelf IC components to perform angular rate measurements. Measured angular rate sensitivities are in the range from 12&micro / V/(deg/sec) to 180&micro / V/(deg/sec), at atmospheric pressure. The SOI gyroscope demonstrates the best performance at atmospheric pressure, with noise equivalent rate (NER) of 0.025(deg/sec)/Hz1/2, whereas the remaining gyroscopes has an NER better than 0.1(deg/sec)/Hz1/2, limited by either the small sensor size or by small quality factors. Gyroscopes have scale-factor nonlinearities better than 1.1% with the best value of 0.06%, and their bias drifts are dominated by the phase errors in the demodulation electronics and are over 1deg/sec. The characterization of the SOI and SOG gyroscopes at below 50mTorr vacuum ambient yield angular rate sensitivities as high as 1.6mV/(deg/sec) and 0.9mV/(deg/sec), respectively. The NER values of these gyroscopes at vacuum are smaller than 50(deg/hr)/Hz1/2 and 36(deg/hr)/Hz1/2, respectively, being close to the tactical-grade application limits. Gyroscope structures are expected to provide a performance better than 10 deg/hr in a practical measurement bandwidth such as 50Hz, provided that capacitive gaps are minimized while preserving the aspect ratio, and the demodulation electronics are improved.

Cette thèse étudie l’estimation de vitesse de rotation d’un corps rigide à partir de mesures de directions (par exemple champ magnétique, direction du soleil) embarquées. L’objectif est de remplacer les gyromètres qui sont chers comparés aux autres capteurs inertiels et sujets à des saturations et à des dysfonctionnements. Dans une première partie de la thèse, on traite les cas spécifiques d’une rotation à axe fixe ou légèrement variable. Dans une seconde partie, on traite le cas d’une rotation quelconque par un observateur asymptotique non-linéaire. On construit l’observateur à partir de mesures de deux vecteurs de référence non colinéaires, ou bien d’un seul vecteur. La connaissance des coordonnées inertielles des vecteurs de référence n’est pas nécessaire. On étend ensuite l’observateur pour estimer en plus le couple et les paramètres d’inertie. Les équations d’Euler jouent un rôle central dans les travaux présentés ici. Il apparaît que, du moins pour les illustrations considérées, les gyromètres peuvent être remplacés par un algorithme d’estimation basé sur des capteurs de direction qui sont bien moins chers et plus robustes. / This thesis addresses the general question of estimating the angular rate of a rigid body from on-board direction sensors (e.g. magnetometers, Sun sensors). The objective is to replace rate gyros which are very expensive compared to direction sensors, prone to saturation during high rate rotations and subject to failure. In a first part of the thesis, we address the specific cases of single-axis and slightly perturbed axis rotations.In a second part, we address the general case by an asymptotic non-linear observer. We build the observer from two non-collinear vector measurements or from a single vector measurements. The knowledge of the inertial coordinates of the reference vectors is not necessary. We then extend the observer to further estimate unknown torques and inertia parameters. The Euler’s equations play a central role in all the works developed in this thesis. It appears that, at least for the illustrative cases considered, rate gyros could be replaced with an estimation algorithm employing direction sensors which are much cheaper,more rugged and more resilient sensors.

Prohibitive cost and large size of conventional angular rate sensors have limited their use to large scale aeronautical applications. However, the emergence of MEMS technology in the last two decades has enabled angular rate sensors to be fabricated that are orders of magnitude smaller in size and in cost. The reduction in size and cost has subsequently encouraged new applications to emerge, but the accuracy and resolution of MEMS angular rate sensors will have to be greatly improved before they can be successfully utilised for such high end applications as inertial navigation. MEMS angular rate sensors consist of a vibratory structure with two main resonant modes and high Q factors. By means of an external excitation, the device is driven into a constant amplitude sinusoidal vibration in the first mode, normally at resonance. When the device is subject to an angular rate input, Coriolis acceleration causes a transfer of energy between the two modes and results in a sinusoidal motion in the second mode, whose amplitude is a measure of the input angular rate. Ideally the only coupling between the two modes is the Coriolis acceleration, however fabrication imperfections always result in some cross stiffness and cross damping effects between the two modes. Much of the previous research work has focussed on improving the physical structure through advanced fabrication techniques and structural design; however attention has been directed in recent years to the use of control strategies to compensate for these structural imperfections. The performance of the MEMS angular rate sensors is also hindered by the effects of time varying parameter values as well as noise sources such as thermal-mechanical noise and sensing circuitry noise. In this thesis, MEMS angular rate sensing literature is first reviewed to show the evolu- tion of MEMS angular rate sensing from the basic principles of open-loop operation to the use of complex control strategies designed to compensate for any fabrication imperfections and time-varying effects. Building on existing knowledge, a novel adaptively controlled MEMS triaxial angular rate sensor that uses a single vibrating mass is then presented. Ability to sense all three components of the angular rate vector with a single vibrating mass has advantages such as less energy usage, smaller wafer footprint, avoidance of any mechanical interference between multiple resonating masses and removal of the need for precise alignment of three separate devices. The adaptive controller makes real-time estimates of the triaxial angular rates as well as the device cross stiffness and cross damping terms. These estimates are then used to com- pensate for their effects on the vibrating mass, resulting in the mass being controlled to follow a predefined reference model trajectory. The estimates are updated using the error between the reference model trajectory and the mass's real trajectory. The reference model trajectory is designed to provide excitation to the system that is sufficiently rich to enable all parameter estimates to converge to their true values. Avenues for controller simplification and optimisation are investigated through system simulations. The triaxial controller is analysed for stability, averaged convergence rate and resolution. The convergence rate analysis is further utilised to determine the ideal adaptation gains for the system that minimises the unwanted oscillatory behaviour of the parameter estimates. A physical structure for the triaxial device along with the sensing and actuation means is synthesised. The device is realisable using MEMS fabrication techniques due to its planar nature and the use of conventional MEMS sensing and actuation elements. Independent actuation and sensing is achieved using a novel checkerboard electrode arrangement. The physical structure is refined using a design automation process which utilises finite element analysis (FEA) and design optimisation tools that adjust the design variables until suitable design requirements are met. Finally, processing steps are outlined for the fabrication of the device using a modified, commercially available polysilicon MEMS process.

This dissertation addresses novel techniques in determining gyroless micro-satellite attitude and attitude rate. The main objective of this thesis is to explore the possibility of using commercially available low cost micro-light star sensor as a stand-alone sensor for micro-satellite attitude as well as attitude rate determination. The objective is achieved by developing accurate and computationally efficient algorithms for the realization of onboard operation of a low fidelity star sensor. All the algorithms developed here are tested with the measurement noise presented in the catalog of the sensor array STAR-1000. A novel accurate second order sliding mode observer (SOSMO) is designed for discrete time uncertain linear multi-output system. Our design procedure is effective for both matched and unmatched bounded uncertain ties and/or disturbances. The bound on uncertainties and/or disturbances is assumed to be unknown. This problem is addressed in this work using the second order multiple sliding modes approach. Second order sliding manifold and corresponding sliding condition for discrete time system is defined similar on the lines of continuous counterpart. Our design is not restricted to a particular class of uncertain (matched) discrete time system. Moreover, it can handle multiple outputs unlike single out-put systems. The observer design is achieved by driving the state observation error and its first order finite difference to the vicinity of the equilibrium point (0,0) in a finite steps and maintaining them in the neighborhood thereafter. The estimation synthesis is based on Quasi Sliding Mode (QSM) design. The problem of designing sliding mode observer for a linear system subjected to unknown inputs requires observer matching condition. This condition is needed to ensure that the state estimation error is a asymptotically stable and is independent of the unknown input during the sliding motion. In the absence of a matching condition, asymptotic stability of the reduced order error dynamics on the sliding surface is not guaranteed. However, unknown bounded inputs guarantee bounded error on state estimation. The QSM design guarantees an ultimate error bound by incorporating Boundary Layer (BL) in its design procedure. The observer achieves one order of magnitude improvement in estimation accuracy than the conventional sliding mode observer (SMO) design for an unknown input. The observer estimation errors, satisfying the given stability conditions, converge to an ultimate finite bound (with in the specified BL) of O(T2), where T Is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The robustness of the proposed observer with respect to measurement noise is also analyzed. The design algorithm is very simple to apply and is implemented for two examples with different classes of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results show the robustness with respect to the measurement noise for SOSMO. Second order sliding mode observer gain can be calculated off-line and the same gain can work for large band of disturbance as long as the disturbance acting on the continuous time system is bounded and smooth. The SOSMO is simpler to implement on board compared to the other traditional nonlinear filters like Pseudo-Linear-Kalman-filter(PLKF); Extended Kalman Filter(EKF). Moreover, SMO possesses an automatic adaptation property same as optimal state estimator(like Kalman filter) with respect to the intensity of the measurement noise. The SMO rejects the noisy measurements automatically, in response to the increased noise intensity. The dynamic performance of the observer on the sliding surface can be altered and no knowledge of noise statistics is required. It is shown that the SOSMO performs more accurately than the PLKF in application to micro-satellite angular rate estimation since PLKF is not an optimal filter. A new method for estimation of satellite angular rates through derivative approach is proposed. The method is based on optic flow of star image patterns formed on a star sensor. The satellite angular rates are derived directly from the 2D-coordinates of star images. Our algorithm is computationally efficient and requires less memory allocation compared to the existing vector derivative approaches, where there is also no need for star identification. The angular rates are computed using least square solution method, based on the measurement equation obtained by optic flow of star images. These estimates are then fed into discrete time second order sliding mode observer (SOSMO). The performance of angular rate estimation by SOSMO is compared with the discrete time First order SMO and PLKF. The SOSMO gives the best estimates as compared to the other two schemes in estimating micro-satellite angular rates in all three axes. The improvement in accuracy is one order of magnitude (around1.7984 x 10−5 rad/ sec,8.9987 x 10−6 rad/ sec and1.4222 x 10−5 rad/ sec in three body axes respectively) in terms of standard deviation in steady state estimation error. A new method and algorithm is presented to determine star camera parameters along with satellite attitude with high precision even if these parameters change during long on-orbit operation. Star camera parameters and attitude need to be determined independent of each other as they both can change. An efficient, closed form solution method is developed to estimate star camera parameters (like focal length, principal point offset), lens distortions (like radial distortion) and attitude. The method is based on a two step procedure. In the first step, all parameters (except lens distortion) are estimated using a distortion free camera model. In the second step, lens distortion coefficient is estimated by linear least squares (LS) method. Here the derived camera parameters in first step are used in the camera model that incorporates distortion. However, this method requires identification of observed stars with the catalogue stars. But, on-orbit star identification is difficult as it utilizes the values of camera calibrating parameters that can change in orbit(detector and optical element alignment get change in orbit due to solar pressure or sudden temperature change) from the ground calibrated value. This difficulty is overcome by employing a camera self-calibration technique which only requires four observed stars in three consecutive image frames. Star camera parameters along with lens (radial and decentering) distortion coefficients are determined by camera self calibration technique. Finally Kalman filter is used to refine the estimated data obtained from the LS based method to improve the level of accuracy. We consider the true values of camera parameters as (u0,v0) = (512.75,511.25) pixel, f = 50.5mm; The ground calibrated values of those parameters are (u0,v0) =( 512,512) pixel, f = 50mm; Worst case radial distortion coefficient affecting the star camera lens is considered to be k1 =5 x 10−3 .Our proposed method of attitude determination achieves accuracy of the order of magnitude around 6.2288 x 10−5 rad,3.3712 x 10−5 radand5.8205 x 10−5 rad in attitude angles φ,θ and ψ. Attitude estimation by existing methods in the literature diverges from the true value since they utilize the ground calibrated values of camera parameters instead of true values. To summarize, we developed a formal theory of discrete time Second Order Sliding Mode Observer for uncertain multi-output system. Our methods achieve the desired accuracy while estimating satellite attitude and attitude rate using low fidelity star sensor data. Our methods require lower on-board processing requirement and less memory allocation; thus are suitable for micro-satellite applications. Thus, the objective of using low fidelity star sensor as stand-alone sensor in micro-satellite application is achieved.

"Health monitoring of structures by experimental modal analysis is typically performed with piezoelectric based transducers. These transducers are usually heavy, large in size, and require high power to operate, all of which reduce their versatility and applicability to small components and structures. The advanced developments of microfabrication and microelectromechanical systems (MEMS) have lead to progressive designs of small footprint, low dynamic mass and actuation power, and high-resolution inertial sensors. Because of their small dimensions and masses, MEMS inertial sensors could potentially replace the piezoelectric transducers for experimental modal analysis of small components and structures. To transfer data from MEMS inertial sensors to signal analyzers, traditional wiring methods may be utilized. Such methods provide reliable data transfer and are simple to integrate. However, in order to study complex structures, multiple inertial sensors, attached to different locations on a structure, are required. In such cases, using wires increases complexity and eliminates possibility of achieving long distance monitoring. Therefore, there is a need to implement wireless communications capabilities to MEMS sensors. In this thesis, two different wireless communication systems have been developed to achieve wireless health monitoring of structures using MEMS inertial sensors. One of the systems is designed to transmit analog signals, while the other transmits digital signals. The analog wireless system is characterized by a linear frequency response function in the range of 400 Hz to 16 kHz, which covers the frequency bandwidth of the MEMS inertial sensors. This system is used to perform modal analysis of a test structure by applying multiple sensors to the structure. To verify the results obtained with MEMS inertial sensors, noninvasive, laser optoelectronic holography (OEH) methodology is utilized to determine modal characteristics of the structure. The structure is also modeled with analytical and computational methods for correlation of and verification with the experimental measurements. Results indicate that attachment of MEMS inertial sensors, in spite of their small mass, has measurable effects on the modal characteristics of the structure being considered, verifying their applicability in health monitoring of structures. The digital wireless system is used to perform high resolution tilt and rotation measurements of an object subjected to angular and linear accelerations. Since the system has been developed based on a microcontroller, programs have been developed to interface the output signals of the sensors to the microcontroller and RF components. The system is calibrated using the actual driving electronics of the MEMS sensors, and it has achieved an angular resolution of 1.8 mrad. The results show viability of the wireless MEMS inertial sensors in applications requiring accurate tilt and rotation measurements. Additional results presented included application of a MEMS gyroscope and microcontroller to perform angular rate measurements. Since the MEMS gyroscope only generates analog output signals, an analog to digital conversion circuit was developed. Also, a program has been developed to perform analog to digital conversion with two decimal places of accuracy. The experimental results demonstrate feasibility of using the microcontroller and the gyroscope to perform wireless angular rate measurements."

This thesis reports the development of various high performance readout and control electronics for implementing angular rate sensing systems using MEMS gyroscopes developed at METU. First, three systems with open loop sensing mechanisms are implemented, where each system has a different drive-mode automatic gain controlled (AGC) self-oscillation loop approach, including (i) square wave driving signal with DC off-set named as OLS_SquD, (ii) sinusoidal driving signal with DC off-set named as OLS_SineD, and iii) off-resonance driving signal named as OLS_OffD. A forth system is also constructed with a closed loop sensing mechanism where the drive mode automatic gain controlled (AGC) self-oscillation loop approach with square wave driving signal with DC off-set named as CLS_SquD. Sense and drive mode electronics employ transimpedance and transresistance amplifiers as readout electronics, respectively. Each of the systems is implemented with commercial discrete components on a dedicated PCB. Then, the angular rate sensing systems are tested with SOG (Silicon-on-Glass) gyroscopes that are adjusted to have two different mechanical bandwidths, more specially 100 Hz and 30 Hz. Test results of all of these cases verify the high performance of the systems. For the 100 Hz bandwidth, the OLS_SquD system shows a bias instability of 4.67 &amp / #730 / /hr, an angle random walk (ARW) 0.080 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 22.6 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the OLS_SquD system shows a bias instability of 5.12 &amp / #730 / /hr, an ARW better than 0.017 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 49.8 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the OLS_SineD system shows a bias instability of 6.92 &amp / #730 / /hr, an ARW of 0.049 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 17.97 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the OLS_SineD system shows a bias instability of 4.51 &amp / #730 / /hr, an ARW of 0.030 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 43.24 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the OLS_OffD system shows a bias instability of 8.43 &amp / #730 / /hr, an ARW of 0.086 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 20.97 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the OLS_OffD system shows a bias instability of 5.72 &amp / #730 / /hr, an ARW of 0.046 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 47.26 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the CLS_SquD system shows a bias instability of 6.32 &amp / #730 / /hr, an ARW of 0.055 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 1.79 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the CLS_SquD system shows a bias instability of 5.42 &amp / #730 / /hr, an ARW of 0.057 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 1.98 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the R2 nonlinearities of the measured scale factors of all systems are between 0.0001% and 0.0003% in the &plusmn / 100 &amp / #730 / /sec measurement range, while for the 30 Hz bandwidth the R2 nonlinearities are between 0.0002% and 0.0062% in the &plusmn / 80&amp / #730 / /sec measurement range. These performance results are the best results obtained at METU, satisfying the tactical-grade performances, and the measured bias instabilities and ARWs are comparable to the best results in the literature for a silicon micromachined vibratory gyroscope.

Die vorliegende Arbeit befasst sich mit der Methode der modalen Superposition als Ordnungsreduktionsverfahren in der Mikrosystemtechnik. Typische Anwendungsgebiete sind Inertialsensoren und dabei im Besonderen Drehratensensoren, für die die Simulation von zeitabhängigen Phänomenen von entscheidender Bedeutung ist. Im Rahmen der Weiterentwicklung der Ordnungsreduktion nach der Methode der modalen Superposition ist es gelungen für typische lineare Kräfte eine auf analytischen Gleichungen basierende Beschreibung im reduzierten Raum zu finden. Für die Beschreibung von nichtlinearen Kräften ist im Rahmen dieser Arbeit ein Verfahren entwickelt worden, das es erlaubt, bestehende Modelle im Finite-Elemente-Raum in der modalen Beschreibung zu nutzen. In dieser Arbeit werden die theoretischen Grundlagen zur Berücksichtigung von Einflüssen der Aufbau- und Verbindungstechnik in ordnungsreduzierten Modellen dargestellt. Neben der Einkopplung äußerer Kräfte und der Veränderung der mechanischen Randbedingungen wird auch der Einfluss der Aufbau- und Verbindungstechnik auf die elektrostatischen Eigenschaften untersucht. Die Parametrisierung des Verfahrens der modalen Superposition über Fit- und Interpolationsverfahren erlaubt es, parametrisierte ordnungsreduzierte Modelle für die zeitabhängige Systemsimulation zu generieren. Damit wird die Durchführung von Designoptimierung und die Berücksichtigung von Fertigungs- und Prozessschwankungen in ordnungsreduzierten Modellen auf Systemebene möglich.