A Modification on Performance of MEMS Gyroscopes by Parametro-Harmonic Excitation

2010 ◽  
Author(s):  
Ali Pakniyat ◽  
Hassan Salarieh ◽  
Gholamreza Vossoughi ◽  
Aria Alasty
Keyword(s):  
Periodic Orbit ◽  
Parametric Excitation ◽  
External Rotation ◽  
Harmonic Excitation ◽  
Excitation Voltage ◽  
Mems Gyroscope ◽  
Mems Gyroscopes ◽  
Stable Periodic ◽  
Stiffness And Damping ◽  
Parameter Values

In this paper, parametric excitation for MEMS gyroscope proposed by Oropeza-Ramos, et al. [1–4] is examined and problems associated with this kind of excitation are shown. It is proved that origin has exponential stability for some sets of parameter values (including those considered in [1–4]). This stability is shown to be global for linearized system and local for the general nonlinear system. Hence, it is concluded that if there would be a periodic orbit, the system has difficulties reaching it. As a solution, a harmonic term to the parametric excitation is added and the new actuation is referred to as parametro-harmonic excitation. It is shown that there are some parameter values for which a stable periodic orbit exists. Finally, stability of periodic orbit of the linear parametro-harmonically excited MEMS gyroscope is analyzed based on Floquet Theory. Figures show that in the non-resonant driving frequencies, only stiffness and damping play important roles in the stability of periodic response and other terms like excitation voltage and imposed external rotation are of less influence on this stability. However, in the parametric resonant regions, not only stiffness and damping affect stability, but also excitation voltage is of great importance.

Open-loop stable running

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Katja D. Mombaur ◽  
Richard W. Longman ◽  
Hans Georg Bock ◽  
Johannes P. Schlöder
Keyword(s):  
Optimization Methods ◽  
Open Loop ◽  
Bipedal Robots ◽  
Model Parameter ◽  
Stable Periodic ◽  
Parameter Values ◽  
Difficult Issue ◽  
Loop Stability

We present simulated monopedal and bipedal robots that are capable of open-loop stable periodic running motions without any feedback even though they have no statically stable standing positions. Running as opposed to walking involves flight phases which makes stability a particularly difficult issue. The concept of open-loop stability implies that the actuators receive purely periodic torque or force inputs that are never altered by any feedback in order to prevent the robot from falling. The design of these robots and the choice of model parameter values leading to stable motions is a difficult task that has been accomplished using newly developed stability optimization methods.

Some Remarks on the Identification of Damping Parameters at the Boundary of Vibrating Systems

1995 ◽  
Vol 48 (11S) ◽  
pp. S107-S110
Author(s):  
Peter Hagedorn ◽  
Ulrich Pabst
Keyword(s):  
Mathematical Modeling ◽  
Modal Analysis ◽  
Mechanical Systems ◽  
Experimental Modal Analysis ◽  
Steel Beam ◽  
Modal Data ◽  
Stiffness And Damping ◽  
Parameter Values ◽  
Vibrating Systems

In many cases, vibrating mechanical systems permit a reliable mathematical modeling with parameter values which are reasonably well known beforehand, except for the joints between different subsystems and at the boundaries. The boundary stiffness, which is often assumed as infinite, and the damping at the boundary, which is frequently ignored, are typically not well known. In this note, we discuss the identification of the boundary stiffness and damping parameters from modal data. As an example, we treat an elastic steel beam, for which an experimental modal analysis had been carried out in our laboratory.

scholarly journals Modelling chronic hepatitis B using the Marchuk-Petrov model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012036
Author(s):  
M Yu Khristichenko ◽  
Yu M Nechepurenko ◽  
D S Grebennikov ◽  
G A Bocharov
Keyword(s):  
Time Delay ◽  
Hepatitis B ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stable Periodic ◽  
Delay Differential ◽  
Parameter Values

Abstract Systems of time-delay differential equations are widely used to study the dynamics of infectious diseases and immune responses. The Marchuk-Petrov model is one of them. Stable non-trivial steady states and stable periodic solutions to this model can be interpreted as chronic viral diseases. In this work we briefly describe our technology developed for computing steady and periodic solutions of time-delay systems and present and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values corresponding to the hepatitis B infection.

scholarly journals Grazing-Sliding Bifurcations Creating Infinitely Many Attractors

2017 ◽  
Vol 27 (12) ◽  
pp. 1730042 ◽  
Author(s):  
David J. W. Simpson
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Simple Type ◽  
Asymptotically Stable ◽  
Sliding Bifurcation ◽  
Continuous Maps ◽  
Stable Periodic ◽  
Smooth System ◽  
Structurally Stable

As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation. Near grazing-sliding bifurcations, structurally stable dynamics are captured by piecewise-linear continuous maps. Recently it was shown that maps of this class can have infinitely many asymptotically stable periodic solutions of a simple type. Here this result is used to show that at a grazing-sliding bifurcation an asymptotically stable periodic orbit can bifurcate into infinitely many asymptotically stable periodic orbits. For an abstract ODE system the periodic orbits are continued numerically revealing subsequent bifurcations at which they are destroyed.

Vibration Isolation From Harmonic Disturbances Through Use of Internally Rotating Masses

2015 ◽  
Author(s):  
Eric Smith ◽  
Al Ferri
Keyword(s):  
Kinetic Energy ◽  
Vibration Isolation ◽  
Harmonic Excitation ◽  
Impulsive Loading ◽  
Qualitative Behavior ◽  
Single Degree Of Freedom ◽  
Transmitted Force ◽  
A Chain ◽  
Isolation Systems ◽  
Parameter Values

This paper considers the use of a chain of translating carts or housings having internally rotating eccentric masses in order to accomplish vibration isolation. First a single degree-of-freedom system is harmonically excited to uncover the qualitative behavior of each rotating mass. The simple model is then expanded into a chain of housings, containing rotating eccentric masses, which are interconnected with springs. The internal rotating eccentric masses are damped along their circular pathway by means of linear viscous damping. Due to the lack of elastic or gravitational constraint on the rotating eccentric masses, they provide a nonlinear inertial coupling to their housings. Previous research has shown that such systems are capable of reducing shock or impulsive loading by converting some of the translational kinetic energy into rotational kinetic energy of the internal masses. This paper examines the potential for vibration isolation of a chain of such systems subjected to persistent, harmonic excitation. It is seen that the dynamics of these systems is very complicated, but that trends are observed which have implications for practical isolation systems. Using simulation studies, tradeoffs are examined between displacement and transmitted force for a range of physical parameter values.

STABILIZATION OF CHAOTIC DYNAMICS OF ONE-DIMENSIONAL MAPS BY A CYCLIC PARAMETRIC TRANSFORMATION

1996 ◽  
Vol 06 (04) ◽  
pp. 725-735 ◽  
Author(s):  
ALEXANDER Yu. LOSKUTOV ◽  
VALERY M. TERESHKO ◽  
KONSTANTIN A. VASILIEV
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Exponential Map ◽  
One Dimensional ◽  
Stable Periodic ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Parametric Transformation

We consider one-dimensional maps, the logistic map and an exponential map, in those sets of parameter values which correspond to their chaotic dynamics. It is proven that such dynamics may be stabilized by a certain cyclic parametric transformation operating strictly within the chaotic set. The stabilization is a result of the creation of stable periodic orbits in the initially chaotic maps. The period of these stable orbits is a multiple of the period of the cyclic transformation. It is shown that stabilized behavior cannot be destroyed by a weak noise smearing of the required parameter values. The regions where the behavior stabilization takes place are numerically estimated. Periods of the created stabile periodic orbits are calculated.

Performance and Reliability of MEMS Gyroscopes and Packaging at High Temperatures

2010 ◽  
Vol 2010 (HITEC) ◽  
pp. 000359-000366 ◽  
Author(s):  
Patrick McCluskey ◽  
Chandradip Patel ◽  
David Lemus
Keyword(s):  
High Temperature ◽  
Indoor Environment ◽  
Elevated Temperatures ◽  
High Sensitivity ◽  
Effect Of Temperature ◽  
Gps Tracking ◽  
Mems Gyroscope ◽  
Mems Gyroscopes ◽  
Gyroscope Sensor

Elevated temperatures can significantly affect the performance and reliability of MEMS gyroscope sensors. A MEMS vibrating resonant gyroscope measures angular velocity via a displacement measurement which can be on the order on nanometers. High sensitivity to small changes in displacement causes the MEMS Gyroscope sensor to be strongly affected by changes in temperature which can affect the displacement of the sensor due to thermal expansion and thermomechanical stresses. Analyzing the effect of temperature on MEMS gyroscope sensor measurements is essential in mission critical high temperature applications, such as inertial tracking of the movement of a fire fighter in a smoke filled indoor environment where GPS tracking is not possible. In this paper, we will discuss the development of the high temperature package for the tracking application, including the characterization of the temperature effects on the performance of a MEMS gyroscope. Both stationary and rotary tests were performed at room and at elevated temperatures on 10 individual single axis MEMS gyroscope sensors.

The Application of Parametric Excitation in Resonant MEMS Gyroscopes

2014 ◽  
pp. 473-492
Author(s):  
Barry J. Gallacher ◽  
Zhongxu Hu ◽  
Kiran M. Harish ◽  
Stephen Bowles ◽  
Harry Grigg
Keyword(s):  
Parametric Excitation ◽  
Mems Gyroscopes

scholarly journals High-sensitivity tunneling magneto-resistive micro-gyroscope with immunity to external magnetic interference

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Li Jin ◽  
Shi-Yang Qin ◽  
Rui Zhang ◽  
Meng-Wei Li
Keyword(s):  
Bridge Circuit ◽  
High Sensitivity ◽  
Micro Electro Mechanical System ◽  
Detection Sensitivity ◽  
Force Detection ◽  
Mems Gyroscope ◽  
Mems Gyroscopes ◽  
Potential Applications ◽  
Magneto Resistance ◽  
Total Sensitivity

Abstract Micro-electro-mechanical system (MEMS) gyroscopes have numerous potential applications including guidance, robotics, tactical-grade navigation, and automotive applications fields. The methods with ability of the weak Coriolis force detection are critical for MEMS gyroscopes. In this paper, we presented a design of MEMS gyroscope based on the tunneling magneto-resistance effect with higher detection sensitivity. Of all these designed parameters, the structural, magnetic field, and magneto-resistance sensitivity values reach to 21.6 nm/°/s, 0.0023 Oe/nm, and 29.5 mV/Oe, thus, with total sensitivity of 1.47 mV/°/s. Multi-bridge circuit method is employed to suppress external magnetic interference and avoid the integration error of the TMR devices effectively. The proposed tunneling magneto-resistive micro-gyroscope shows a possibility to make an inertial grade MEMS gyroscope in the future.

ANALYTICAL PREDICTION OF THE TWO FIRST PERIOD-DOUBLINGS IN A THREE-DIMENSIONAL SYSTEM

2000 ◽  
Vol 10 (06) ◽  
pp. 1497-1508 ◽  
Author(s):  
M. BELHAQ ◽  
M. HOUSSNI ◽  
E. FREIRE ◽  
A. J. RODRÍGUEZ-LUIS
Keyword(s):  
Periodic Orbit ◽  
Critical Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Period Doubling ◽  
Dimensional System ◽  
Analytical Prediction ◽  
Parameter Values ◽  
Three Dimensional System ◽  
Period Doubling Bifurcations

Analytical study of the two first period-doubling bifurcations in a three-dimensional system is reported. The multiple scales method is first applied to construct a higher-order approximation of the periodic orbit following Hopf bifurcation. The stability analysis of this periodic orbit is then performed in terms of Floquet theory to derive the critical parameter values corresponding to the first and second period-doubling bifurcations. By introducing suitable subharmonic components in the first order of the multiple scale analysis the two critical parameter values are obtained simultaneously solving analytically the resulting system of two algebraic equations. Comparisons of analytic predictions to numerical simulations are also provided.

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