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At least 37 records · Page 2

Parameter identifiability of linear dynamical systems

It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.

Glover, K.↗

Dynamic linearity measurement technique

Measurement technique involves frequency modulated discriminator which produces an error signal as two signals, one of known and one of unknown frequency. The signals are electronically switched to a discriminator input, allowing independent measuring of dynamic linearity in a frequency modulated subcarrier oscillator.

Merz, K.↗

Application of non-linear dynamics to the characterization of cardiac electrical instability

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

NASA Discipline Cardiopulmonary↗

Non-linear dynamic analysis of geared systems, part 2

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Singh, Rajendra↗

Increasing Linear Dynamic Range of a CMOS Image Sensor

A generic design and a corresponding operating sequence have been developed for increasing the linear-response dynamic range of a complementary metal oxide/semiconductor (CMOS) image sensor. The design provides for linear calibrated dual-gain pixels that operate at high gain at a low signal level and at low gain at a signal level above a preset threshold. Unlike most prior designs for increasing dynamic range of an image sensor, this design does not entail any increase in noise (including fixed-pattern noise), decrease in responsivity or linearity, or degradation of photometric calibration. The figure is a simplified schematic diagram showing the circuit of one pixel and pertinent parts of its column readout circuitry. The conventional part of the pixel circuit includes a photodiode having a small capacitance, CD. The unconventional part includes an additional larger capacitance, CL, that can be connected to the photodiode via a transfer gate controlled in part by a latch. In the high-gain mode, the signal labeled TSR in the figure is held low through the latch, which also helps to adapt the gain on a pixel-by-pixel basis. Light must be coupled to the pixel through a microlens or by back illumination in order to obtain a high effective fill factor; this is necessary to ensure high quantum efficiency, a loss of which would minimize the efficacy of the dynamic- range-enhancement scheme. Once the level of illumination of the pixel exceeds the threshold, TSR is turned on, causing the transfer gate to conduct, thereby adding CL to the pixel capacitance. The added capacitance reduces the conversion gain, and increases the pixel electron-handling capacity, thereby providing an extension of the dynamic range. By use of an array of comparators also at the bottom of the column, photocharge voltages on sampling capacitors in each column are compared with a reference voltage to determine whether it is necessary to switch from the high-gain to the low-gain mode. Depending upon the built-in offset in each pixel and in each comparator, the point at which the gain change occurs will be different, adding gain-dependent fixed pattern noise in each pixel. The offset, and hence the fixed pattern noise, is eliminated by sampling the pixel readout charge four times by use of four capacitors (instead of two such capacitors as in conventional design) connected to the bottom of the column via electronic switches SHS1, SHR1, SHS2, and SHR2, respectively, corresponding to high and low values of the signals TSR and RST. The samples are combined in an appropriate fashion to cancel offset-induced errors, and provide spurious-free imaging with extended dynamic range.

Pain, Bedabrata↗

Modal interaction in linear dynamic systems near degenerate modes

In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other, eventually colliding, leading to eigenvalue degeneracy. Modal interaction is studied in linear systems with conservative and nonconservative coupling using singularity theory, sometimes known as catastrophe theory. The main result is this: eigenvalue degeneracy is a cause of instability; in systems with conservative coupling, it induces only geometric instability, whereas in systems with nonconservative coupling, eigenvalue degeneracy induces both geometric and elastic instability. Illustrative examples of mechanical systems are given.

Afolabi, D.↗

Non-linear dynamic analysis of geared systems

Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. A dynamic finite element model of the linear time invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.

Singh, Rajendra↗

Digital simulation of stiff linear dynamic systems.

A method is derived for digital computer simulation of linear time-invariant systems when the insignificant eigenvalues involved in such systems are eliminated by an ALSAP root removal technique. The method is applied to a thirteenth-order dynamic system representing a passive RLC network.

Holland, L. D.↗

On the identifiability of linear dynamical systems

Consider the situation in which the unknown parameters of a stationary linear system may be parametrized by a set of unknown parameters. The question thus arises of when such a set of parameters can be uniquely identified on the basis of observed data. This problem is considered here both in the case of input and output observations and in the case of output observations in the presence of a white noise input. Conditions for local identifiability are derived for both situations and a sufficient condition for global identifiability is given for the former situation, i.e., when simultaneous input and output observations are available.

Glover, K.↗

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗

Linear and non-linear dynamic models of a geared rotor-bearing system

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Kahraman, Ahmet↗

Linear dynamic analysis of the Space Station Freedom thermal/environmental control system

A methodology for dynamic analysis of the Space Station Freedom thermal/environmental control system is described which uses linear system analysis techniques to determine the ability of the system to accommodate thermal load transients. A nonlinear integrated model of the system as it exists at Stage 6, Man Tended Capability (MTC), is described which encompasses the cabin air cooling system, avionics air cooling system, internal and external thermal control systems. The nonlinear model is linearized at an assumed design operating point, and the linear model is evaluated by comparison with the nonlinear model. Transfer functions are derived to determine the response of the heat rejection system to time-varying thermal loads applied at various points in the heat acquisition system. The frequency response calculated from the transfer functions is used to determine allowable operating envelopes of thermal load magnitude and frequency for each point of application of thermal load. The dynamic operating envelopes provide a quantitative indication of the degree and duration of peak loads which the thermal/environmental system is able to transport and reject.

Tandler, John↗

Model-size reduction for the non-linear dynamic analysis of quasi-symmetric structures

A numerical technique is developed to reduce the size of models describing the nonlinear dynamic response of quasi-symmetric structures (i.e., structures with unsymmetric geometry). The response vectors of the structure are approximated by a linear combination of the symmetric and antisymmetric vectors at each time step. The mathematical formulation and numerical implementation of the method are described in detail, and results for a shallow laminated anisotropic panel of quadrilateral planform are presented in graphs and normalized contour plots.

Noor, Ahmed K.↗