A Parametrically Amplified MEMS Gyroscope

2010 ◽  
Vol 2010 (DPC) ◽  
pp. 001322-001334
Author(s):  
Barry J. Gallacher ◽  
Z. X. Hu ◽  
J. S. Burdess ◽  
K. M. Harish
Keyword(s):  
Open Loop ◽  
Parametric Amplification ◽  
Vibration Modes ◽  
Q Factor ◽  
Amplitude Control ◽  
Mems Gyroscope ◽  
Primary Mode ◽  
Harmonic Forcing ◽  
Control Schemes ◽  
Order Of Magnitude

The applicability of parametric amplification of either the primary and secondary vibration modes of a MEMS gyroscope, shown in Fig.1 is investigated experimentally in this paper. All control schemes have been implemented digitally onto a SHARC DSP development board. Parametric gains in excess of 80, which correspond to multiplication of the Q-factor by a factor of 80, are demonstrated experimentally for open-loop operation of the primary mode and are shown in Fig. 2. For open-loop operation it is shown that amplitude limiting nonlinearities become important as the vibration amplitude increases (see Figs.3) and that parametric amplification in excess of 80 can be only be achieved by further reducing the harmonic forcing amplitude. In many applications it is desirable to have as high a Q-factor as possible. The rate gyroscope is one application were active control of the Q-factor is extremely pertinent. If applied to the primary mode then it permits reduced forcing levels and hence contamination from “feedthrough”. If applied to the sense mode then the Coriolis force is effectively amplified. Parametric amplification of the secondary mode of the gyroscope is a challenging problem but it has the potential to improve the performance of MEMS rate gyroscope but an order of magnitude. In operation as a rate gyroscope it is important to maintain the amplitude of the primary mode of vibration at a constant level. For the case of a parametrically amplified primary mode the amplitude control circuit automatically adjusts the parametric excitation parameters to ensure the required parametric gain is achieved whilst at the same time reducing the amplitude of the harmonic forcing. In closed loop parametric amplification of the primary mode by a factor 20 have been demonstrated. Experimental results obtained from the amplified primary mode are shown in Fig.4.

The Application of Parametric Excitation in MEMS Gyroscopes

2013 ◽  
Author(s):  
Barry J. Gallacher ◽  
Zhongxu Hu ◽  
Kiran Mysore Harish ◽  
Stephen Bowles ◽  
Harry Grigg
Keyword(s):  
Angular Velocity ◽  
Parametric Excitation ◽  
Signal To Noise Ratio ◽  
Parametric Amplification ◽  
Signal To Noise ◽  
Primary Mode ◽  
Harmonic Forcing ◽  
Mode Of Operation ◽  
Mems Gyroscopes ◽  
Secondary Mode

Parametric excitation, via electrostatic stiffness modulation, can be exploited in resonant MEMS gyroscopes. In the case of the Rate gyroscope, which is by far the most common type of MEMS gyro, parametric excitation may be used to amplify either the primary mode of the gyro or the response to the angular rate. Both approaches will be discussed. In the more complex mode of operation, known as “Rate Integrating” the output of the gyro is angle directly as opposed to angular velocity in the case of Rate gyro. In this rate integrating mode of operation parametric excitation does offer an effective energy control used to initiate, sustain the vibration and minimise damping perturbations. Parametric amplification of the primary mode of the rate gyroscope is presented and supported with experimental results. In this implementation parametric excitation is combined with external harmonic forcing of the primary mode in order to reduce electrical feedthrough of the driving signal to the sense electrodes. A practical parametric excitation scheme implemented using Digital Signal Processing has been developed to enable either amplification of the primary mode of the gyroscope or amplification of the response to the applied angular velocity. Parametric amplification of the primary mode of the gyroscope is achieved by frequency tracking and regulation of the amplitudes of the harmonic forcing and parametric excitation to maintain a desired parametric gain by closed loop PID control. Stable parametric amplification of the primary mode by a factor of 20 is demonstrated experimentally. This has important benefits regarding the minimisation of electrical feedthrough of the drive signal to the sense electrodes of the secondary mode. By taking advantage of the phase dependence of parametric amplification and the orthogonality of the Coriolis force and quadrature forcing, the response to the applied angular velocity may be parametrically amplified by applying excitation of a particular phase directly to the sensing mode. The major advantage of parametric amplification applied to MEMs gyroscopes is that it can mechanically amplify the Coriolis response before being picked off electrically. This is particularly advantageous for sensors where electronic noise is the major noise contributor. In this case parametric amplification can significantly improve the signal to noise ratio of the secondary mode by an amount approximately equal to the parametric amplification. Preliminary rate table tests performed in open loop demonstrate a magnification of the signal to noise ratio of the secondary mode by a factor of 9.5.

Active Control of Combustion Instability Using Symmetric and Asymmetric Premix Fuel Modulation

2007 ◽  
Author(s):  
Daniel Guyot ◽  
Christian Oliver Paschereit
Keyword(s):  
Heat Release ◽  
Closed Loop ◽  
Modulation Frequency ◽  
Combustion Instability ◽  
Open Loop ◽  
Closed Loop Control ◽  
Nox Emissions ◽  
Loop Control ◽  
Asymmetric Modulation ◽  
Control Schemes

Active instability control was applied to an atmospheric swirl-stabilized premixed combustor using open loop and closed loop control schemes. Actuation was realised by two on-off valves allowing for symmetric and asymmetric modulation of the premix fuel flow while maintaining constant time averaged overall fuel mass flow. Pressure and heat release fluctuations in the combustor as well as NOx, CO and CO2 emissions in the exhaust were recorded. In the open loop circuit the heat release response of the flame was first investigated during stable combustion. For symmetric fuel modulation the dominant frequency in the heat release response was the modulation frequency, while for asymmetric modulation it was its first harmonic. In stable open loop control a reduction of NOx emissions due to fuel modulation of up to 19% was recorded. In the closed loop mode phase-shift control was applied while triggering the valves at the dominant oscillation frequency as well as at its second subharmonic. Both, open and closed loop control schemes were able to successfully control a low-frequency combustion instability, while showing only a small increase in NOx emissions compared to, for example, secondary fuel modulation. Using premixed open loop fuel modulation, attenuation was best when modulating the fuel at frequencies different from the dominant instability frequency and its subharmonic. The performance of asymmetric fuel modulation was generally slightly better than for symmetric modulation in terms of suppression levels as well as emissions. Suppression of the instability’s pressure rms level of up to 15.7 dB was recorded.

scholarly journals Automatic locking of a parametrically resonating, base-excited, nonlinear beam

2021 ◽  
Author(s):  
Nir Ben Shaya ◽  
Izhak Bucher ◽  
Amit Dolev
Keyword(s):  
Relative Phase ◽  
Closed Loop ◽  
Dynamical Behavior ◽  
Open Loop ◽  
Vibration Modes ◽  
Nonlinear Structure ◽  
Nonlinear Beam ◽  
Loop Control ◽  
Control Scheme ◽  
Slender Beams

AbstractDescribed is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between the spatially filtered response and the excitation, the open-loop unstable solution branches are stabilized under a 2:1 parametric excitation of a chosen mode of vibration. For a given phase, the closed-loop automatically locks on a limit cycle, through an Autoresonance scheme, at any desired point on the solution branches. Axially driven slender beams and nanowires develop large transverse vibration under suitable amplitudes and frequency base-excitation that are sensitive to small potential coupled field. To utilize such a structure as a sensor, stable and robust operation are made possible by the control scheme. In addition, an optimal operating point with large sensitivity to the sensed potential field can be set using phase as a tunable parameter. Detailed analysis of the dynamical behavior, experimental verifications, and demonstrations sheds light on some features of the system dynamics.

scholarly journals Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

2014 ◽  
Vol 762 ◽  
pp. 361-392 ◽  
Author(s):  
E. Boujo ◽  
F. Gallaire
Keyword(s):  
Passive Control ◽  
Expansion Ratio ◽  
Open Loop ◽  
Backward Facing Step ◽  
Amplitude Control ◽  
Loop Control ◽  
Realistic Representation ◽  
Noise Amplifier ◽  
Noise Amplification ◽  
Sensitivity Maps

AbstractThe two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of non-normal effects. This amplification potential is best captured by optimal transient growth analysis, optimal harmonic forcing, or the response to sustained noise. With a view to reducing disturbance amplification in these globally stable open flows, a variational technique is proposed to evaluate the sensitivity of stochastic amplification to steady control. Existing sensitivity methods are extended in two ways to achieve a realistic representation of incoming noise: (i) perturbations are time-stochastic rather than time-harmonic, (ii) perturbations are localised at the inlet rather than distributed in space. This allows the identification of regions where small-amplitude control is the most effective, without actually computing any controlled flows. In particular, passive control by means of a small cylinder and active control by means of wall blowing/suction are analysed for Reynolds number $\mathit{Re}=500$ and step-to-outlet expansion ratio ${\it\Gamma}=0.5$. Sensitivity maps for noise amplification appear largely similar to sensitivity maps for optimal harmonic amplification at the most amplified frequency. This is observed at other values of $\mathit{Re}$ and ${\it\Gamma}$ too, and suggests that the design of steady control in this noise amplifier flow can be simplified by focusing on the most dangerous perturbation at the most dangerous frequency.

Complete Bandgap in Three-Dimensional Holey Phononic Crystals With Resonators

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Yan-Feng Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Three Dimensional ◽  
Phononic Crystals ◽  
Vibration Modes ◽  
The Finite Element Method ◽  
Local Resonance ◽  
The Matrix ◽  
Order Of Magnitude ◽  
Complete Bandgap ◽  
Careful Design ◽  
Shape And Size

In this paper, the bandgap properties of three-dimensional holey phononic crystals with resonators are investigated by using the finite element method. The resonators are periodically arranged cubic lumps in the cubic holes connected to the matrix by narrow connectors. The influence of the geometry parameters of the resonators on the bandgap is discussed. In contrast to a system with cubic or spherical holes, which has no bandgaps, systems with resonators can exhibit complete bandgaps. The bandgaps are significantly dependent upon the geometry of the resonators. By the careful design of the shape and size of the resonator, a bandgap that is lower by an order of magnitude than the Bragg bandgap can be obtained. The vibration modes at the band edges of the lowest bandgaps are analyzed in order to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonance of the resonators. Spring-mass models or spring-pendulum models are developed in order to evaluate the frequencies of the bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

Simulation and Control of a Commercial Double Effect Evaporator: Tomato Juice

2010 ◽  
Vol 5 (1) ◽  
Author(s):  
Praveen Yadav ◽  
Amiya K Jana
Keyword(s):  
Double Effect ◽  
Open Loop ◽  
Simulation Experiments ◽  
Loop Control ◽  
Process Dynamics ◽  
Point Tracking ◽  
Tomato Paste ◽  
Control Schemes ◽  
And Control ◽  
Gain Scheduled

This work aims to present a detailed study on a commercial double-effect tomato paste evaporation system. The modeling equations formulated for process simulation belong to backward feeding arrangement. Open-loop process dynamics has been studied by rigorous simulation of the model structure. In the next, three multi-loop control schemes, namely conventional proportional integral (PI), gain-scheduled PI (GSPI) and nonlinear PI (NLPI), have been synthesized for the sample process. Finally, several simulation experiments have been conducted to investigate the comparative closed-loop performance based on set point tracking and disturbance rejection.

Lyapunov-Based Stabilization of MEMS Relays

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Y. Bastani ◽  
M. S. de Queiroz
Keyword(s):  
State Feedback ◽  
Parametric Uncertainty ◽  
Open Loop ◽  
Velocity Measurements ◽  
Electrical Parameters ◽  
Nonlinear Dynamic Model ◽  
Microelectromechanical System ◽  
Lyapunov Approach ◽  
Control Schemes ◽  
Opening And Closing

In this paper, nonlinear stabilizers are introduced for voltage-controlled microelectromechanical system (MEMS) relays. The control constructions follow a Lyapunov approach and are based on a nonlinear dynamic model applicable to the two types of MEMS relays—electrostatic and electromagnetic. Two control schemes are presented with the objectives of avoiding pull-in during the microrelay closing and improving the transient response during the microrelay opening. First, an adaptive state feedback stabilizer is proposed to compensate for parametric uncertainty in all mechanical parameters and selected electrical parameters while ensuring asymptotic regulation of the electrode opening and closing. Next, a model-based observer/stabilizer is proposed to account for the lack of velocity measurements. Simulations demonstrate the performance of the two control schemes in comparison to the typical open-loop operation of the MEMS relay.

scholarly journals Simulation of closed-loop deep brain stimulation control schemes for suppression of pathological beta oscillations in Parkinson’s disease

2019 ◽  
Author(s):  
John E. Fleming ◽  
Eleanor Dunn ◽  
Madeleine M. Lowery
Keyword(s):  
Deep Brain Stimulation ◽  
Closed Loop ◽  
Pi Controller ◽  
Open Loop ◽  
Beta Band ◽  
Preclinical Testing ◽  
Control Schemes ◽  
The Mean ◽  
Band Activity ◽  
Deep Brain

AbstractThis study presents a computational model of closed-loop control of deep brain stimulation (DBS) for Parkinson’s disease (PD) to investigate clinically-viable control schemes for suppressing pathological beta-band activity. Closed-loop DBS for PD has shown promising results in preliminary clinical studies and offers the potential to achieve better control of patient symptoms and side effects with lower power consumption than conventional open-loop DBS. However, extensive testing of algorithms in patients is difficult. The model presented provides a means to explore a range of control algorithms in silico and optimize control parameters before preclinical testing. The model incorporates (i) the extracellular DBS electric field, (ii) antidromic and orthodromic activation of STN afferent fibers, (iii) the LFP detected at non-stimulating contacts on the DBS electrode and (iv) temporal variation of network beta-band activity within the thalamo-cortico-basal ganglia loop. The performance of on-off and dual-threshold controllers for suppressing beta-band activity by modulating the DBS amplitude were first verified, showing levels of beta suppression and reductions in power consumption comparable with previous clinical studies. Proportional (P) and proportional-integral (PI) closed-loop controllers for amplitude and frequency modulation were then investigated. A simple tuning rule was derived for selecting effective PI controller parameters to target long duration beta bursts while respecting clinical constraints that limit the rate of change of stimulation parameters. Of the controllers tested, PI controllers displayed superior performance for regulating network beta-band activity whilst accounting for clinical considerations. Proportional controllers resulted in undesirable rapid fluctuations of the DBS parameters which may exceed clinically tolerable rate limits. Overall, the PI controller for modulating DBS frequency performed best, reducing the mean error by 83% compared to DBS off and the mean power consumed to 25% of that utilized by open-loop DBS. The network model presented captures sufficient physiological detail to act as a surrogate for preclinical testing of closed-loop DBS algorithms using a clinically accessible biomarker, providing a first step for deriving and testing novel, clinically-suitable closed-loop DBS controllers.

Dissipative Energy Flow in Systems at Parametric Anti-Resonance

2012 ◽  
Author(s):  
F. Dohnal
Keyword(s):  
Energy Flow ◽  
Open Loop ◽  
Vibration Modes ◽  
Approximate Analytical Expression ◽  
Loop Control ◽  
System Parameters ◽  
Damped System ◽  
Constant Coefficients ◽  
Time Periodicity ◽  
Time Periodic

Recent investigations have shown theoretically and experimentally that the transient vibrations of a lightly damped system can be suppressed or even stabilized by a time-periodic open-loop control of one of its system parameters. Introducing time-periodicity in system parameters may lead, in general, to a dangerous and well-known parametric resonance. In contrast to such a resonance, a properly tuned time-periodicity is capable to extract vibration energy from the system and to increase the effective damping of transient vibrations. At this specific operation the system is tuned at parametric anti-resonance. The beneficial interaction of damping and time-periodicity was first formulated by A. Tondl in 1998. His pioneering work deals with stabilizing self-excited vibrations. It was proven by F. Dohnal in 2005 that the vibrations of a general lightly damped system (not necessarily unstable) can be reduced by parametric anti-resonance, too. A physical interpretation of the parametric anti-resonance is related to the coupling of vibration modes of the underlying system with constant coefficients. This interpretation leads intuitively to the calculation of the energy flow of each vibration mode and leads to clear physical insight of how parametric anti-resonances work. This interpretation of mode coupling is developed further resulting in an approximate analytical expression for the effective damping of a system driven at parametric anti-resonance. This expression allows the statement of the maximum effective damping achievable by this method. The discussion of the energy flow of a linear, lightly damped system possessing a time-periodic stiffness coefficient its physical and modal displacements highlights the coupling of vibration modes of the underlying system with constant coefficients.

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