Underdamped Response Research Articles

Unique influences of reboiler inventory control on the operation of totally reboiled reactive distillation columns

In this work, the dynamics and operation of the totally reboiled reactive distillation columns are visualized in terms of transfer function based process models. This kind of processes is found to be characterized by under-damped step responses due to the special topological configuration and the intricate interplay between the reaction operation and the separation operation involved. The under-dampness can be substantially alleviated through the tight inventory control of bottom reboiler and this presents beneficial effects to process dynamics and operation. Two totally reboiled reactive distillation columns, separating, respectively, a hypothetical synthesis reaction from reactants A and B to product C, and a real decomposition reaction from 1, 4-butanediol to tetrahydrofuran and water, are employed to demonstrate these uncommon behaviors. The results obtained give full support to the above qualitative interpretation. Despite the strong influences of reaction kinetics and thermodynamic properties of the reacting mixtures, the totally reboiled reactive distillation columns are generally considered to present such unique behaviors and require tight inventory control of bottom reboiler to facilitate their control system development.

A Multivariate Sensor for Intelligent Polymer Processing

A multivariate sensor is described for intelligent polymer processing that incorporates a piezoelectric ring to acquire melt pressure as well as a thermopile to acquire melt temperature and mold temperature. The mechatronic system analyzes the process states according to mechanistic relations to estimate the melt velocity and melt viscosity. Validation experiments are implemented to characterize the sensor's performance against an array of commercial sensors. Models of product quality with the described sensor far outperform those based on data from commercial sensors. While system identification of the transient thermopile voltage indicates an underdamped response that limited the model fidelity, the existing capability suggests a new standard for mold design that incorporates multivariate sensors into the runner system to provide a consistent set of physical states for process tuning irrespective of molding machine manufacturer and model.

The degenerative state of the intervertebral disk independently predicts the failure of human lumbar spine to high rate loading: An experimental study

BackgroundIn the elderly, 30%–50% of patients report a fall event to precede the onset of vertebral fractures. The dynamic characteristics of the spine determine the peak forces on the vertebrae in a fall. However, we know little about the effect of intervertebral disk degeneration on the failure of human spines under the high loading rates associated with such falls. We hypothesized that MR estimates of disk hydration and viscoelastic properties will provide better estimates of failure strength than bone density alone. MethodsSeventeen L1–L3 human spine segments were imaged (magnetic resonance imaging, dual-energy X-ray absorptiometry), their dynamic responses quantified using pendulum based impact, and the spines tested to failure under high rate loading simulating a fall event. The spines' stiffness and damping constants were computed (Kelvin–Voigt model) with disk hydration and geometry assessed from T2 and proton density images. FindingsUnder impact, the spines exhibited a second-order underdamped response with stiffness and damping ranging (17.9–754.5) kN/m and (133.6–905.3) Ns/m respectively. Damping, but not stiffness, was negatively correlated with higher ultimate strength (P<0.05). Higher bone mineral density and MR-estimated disk hydration correlated with higher ultimate strength (P<0.01 for both). No such correlations were observed for the T2 values. Adding disk hydration yielded a 20% increase in the model's association with failure load compared to bone density alone (MANOVA, P<0.001). InterpretationThe strong correlation between disk viscoelastic properties and MR-estimated hydration with the spine segments' ultimate strength clearly demonstrates the need to include disk degeneration as part of fracture risk assessment in the elderly spine.

Dynamic Stability of the Trunk During Unstable Sitting in People With Low Back Pain

Cross-sectional study. To evaluate the dynamic stability and kinematics of the trunk during unstable sitting, and to determine the differences in these biomechanical parameters between healthy participants and participants with low back pain (LBP). Patients with LBP exhibited alterations in trunk kinematics while performing different dynamic tasks and in static posture as a result of pain. It is not clear if changing in trunk motion may reduce postural control and the ability to perform a balancing task. Twenty-three participants with LBP and 31 healthy participants were requested to sit on a custom-made swinging chair and to regain the balance after tilting the chair backward for 10° and 20°. Lumbar spine, pelvis, and chair motions were recorded using FASTRAK sensors. The thoracolumbar curvature of all participants was also evaluated in the standing position. The angular displacement of the chair was fitted in an equation describing the underdamped second-order response to a step input. Kinematic analysis showed that the hip range of motion increased whereas spine range of motion angle decreased in participants with LBP for both tilt angles (P < 0.05). There were no significant differences between the 2 subject groups in the time required to regain balance, and the natural frequency and damping ratio of the kinematic equation. Lumbar lordosis significantly decreased in LBP group. Participants with LBP showed trunk postural and movement adaptations that seems to be compensatory strategies to decrease the risk of further injuries and aggravation of the symptoms, but their ability to regain the balance was not affected by LBP. Clinicians should encourage patients with LBP to remain active while they are experiencing pain.

Pneumatic Permeameter for Transient Tests on Coarse Gravel

A new permeameter is proposed for performing laboratory hydraulic conductivity tests on gravels with hydraulic conductivity values ranging from 0.1 to 1 m/s. A small diameter riser is connected to a large diameter cylinder, which holds the coarse-grained specimen saturated in a water bath. The release of pneumatic pressure, applied to the free surface in the riser, induces an underdamped oscillatory response of the water level in the riser, similar to an underdamped in situ slug test response in monitoring wells. A closed-form model is used to analyze the measured oscillatory hydraulic head data to calibrate the minor losses in the permeameter and the hydraulic conductivity of the specimen by performing tests without and with a specimen. The average model error of calibrated pressure head values in the riser for the tests considered are about 5% of the initial displacement of about 2 cm. The hydraulic conductivity values are calibrated considering the replicate tests, the tests of different specimen lengths, and the different time periods within a test to verify that the results reflect the hydraulic conductivity of the specimen alone. The Kozeny-Carman equation, which considers the specific surface area of the tested material, gave a hydraulic conductivity value within 5% of the measured value for the marbles, which is a good comparison because the uniform marbles have a known specific surface area. For all the various tests performed on each specimen, most of the hydraulic conductivity values were within 10% of the average, while the specimens with hydraulic conductivity greater than 1 m/s were within 10 to 20% of the average.

Effect of the Degenerative State of the Intervertebral Disk on the Impact Characteristics of Human Spine Segments.

Models of the dynamic response of the lumbar spine have been used to examine vertebral fractures (VFx) during falls and whole body vibration transmission in the occupational setting. Although understanding the viscoelastic stiffness or damping characteristics of the lumbar spine are necessary for modeling the dynamics of the spine, little is known about the effect of intervertebral disk degeneration on these characteristics at high loading rates. We hypothesize that disk degeneration significantly affects the viscoelastic response of spinal segments to high loading rate. We additionally hypothesize the lumbar spine stiffness and damping characteristics are a function of the degree of preload. A custom, pendulum impact tester was used to impact 19 L1–L3 human spine segments with an end mass of 20.9 kg under increasing preloads with the resulting force response measured. A Kelvin–Voigt model, fitted to the frequency and decay response of the post-impact oscillations was used to compute stiffness and damping constants. The spine segments exhibited a second-order, under-damped response with stiffness and damping values of 17.9–754.5 kN/m and 133.6–905.3 Ns/m respectively. Regression models demonstrated that stiffness, but not damping, significantly correlated with preload (p < 0.001). Degenerative disk disease, reflected as reduction in magnetic resonance T2 relaxation time, was weakly correlated with change in stiffness at low preloads. This study highlights the need to incorporate the observed non-linear increase in stiffness of the spine under high loading rates in dynamic models of spine investigating the effects of a fall on VFx and those investigating the response of the spine to vibration.

The Impact of Parasitic Inductance on the Performance of Silicon–Carbide Schottky Barrier Diodes

1200V/300A silicon carbide Schottky barrier diode (SiC SBD) and Si pin diode modules have been tested as free-wheeling diodes under conditions of clamped inductive switching over a temperature range between -40 °C and 125 °C. Over the temperature range, the turn-OFF switching energy increases by 100% for the Si pin diode, whereas that of the SiC diode is temperature invariant and is 50% less than that of the Si pin diode at 125°C. However, the SiC SBD suffers from ringing/oscillations due to an underdamped response to an RLC circuit formed among the diode depletion capacitance, parasitic inductance, and diode resistance. These oscillations contribute to additional power losses that cause the SiC SBDs to be outperformed by the Si pin diodes at -40 °C and 0 °C. The higher depletion capacitance and lower series resistance of the SiC SBD contribute to a lower damping factor compared to the Si device. Furthermore, the positive temperature coefficient of the ON-state resistance in silicon contributes to better damping at high power levels, whereas the temperature invariance of the ON-state resistance in SiC means the oscillations persist at high temperatures. SPICE simulations and experimental measurements have been used to validate analytical expressions that have been developed for the circuit damping and oscillation frequency.

Dynamics and control of totally refluxed reactive distillation columns

According to the mechanism of the reaction operation involved, reactive distillation columns are often designed to work in a totally refluxed operation mode. The totally refluxed operation mode makes the reflux drum interact solely with the reaction operation involved and retards considerably the dynamics of the latter. The resultant great difference in process dynamics between the reaction operation and the separation operation involved leads frequently to under-damped responses with the degree of under-dampness closely dependent on the inventory control of the reflux drum. With the tight inventory control of the reflux drum, the degree of under-dampness can be suppressed and this presents a favorable effect to process dynamics and controllability of the totally refluxed reactive distillation columns. Two hypothetical ideal reactive distillation columns with and without a side reaction, respectively, and a high-purity ethylene glycol reactive distillation column are employed to examine the unique dynamics and controllability of the totally refluxed reactive distillation columns. The results obtained are in good accordance with the above interpretation. The current work reveals the general behaviors of the totally refluxed reactive distillation columns and can be particularly useful in control system synthesis and design.

Radiation and near field in resistance-inductor circuit transients

A full wave solution to the classical problem of a transient response in an RL circuit is analyzed. We show that when radiation effects are rigorously taken into account, the response differs from a familiar exponential decay. The circuit behaves more like an RLC circuit and can exhibit an underdamped response. As a result of a two way energy transfer between the circuit and the near field in the underdamped regime, despite the radiation losses, current decay may be slower than predicted by the standard RL circuit model. During a transient, when retardation effects become important, inductance can no longer be defined as a coefficient of proportionality between the magnetic flux through the circuit and the current in the circuit. If rate of current decay is nearly constant, one can define a time-dependent generalized inductance which turns into conventional inductance after time D/c, where D is the diameter of the current loop. Connection of this generalized inductance with the radiation damping problem is discussed. The theory developed in this paper has been used to analyze ultra wide band radiation observed during a fast laser triggered superconducting to normal transition of a superconducting switch.

Nanoforce estimation based on Kalman filtering and applied to a force sensor using diamagnetic levitation

Nanoforce sensors based on passive diamagnetic levitation with a macroscopic seismic mass are a possible alternative to classical Atomic Force Microscopes when the force bandwidth to be measured is limited to a few Hertz. When an external unknown force is applied to the levitating seismic mass, this one acts as a transducer that converts this unknown input into a displacement that is the measured output signal. Because the under-damped and long transient response of this kind of macroscopic transducer cannot be neglected for time-varying force measurement, it is then necessary to deconvolve the output to correctly estimate the unknown input force. The deconvolution approach proposed in this paper is based on a Kalman filter that use an uncertain a priori model to represent the unknown nanoforce to be estimated. The main advantage of this approach is that the end-user can directly control the unavoidable trade-off that exists between the wished resolution on the estimated force and the response time of the estimation.

Discrete element modelling of a bucket elevator head pulley transition zone

This paper presents the results of discrete element simulations applied to a bucket elevator model with particular reference to the head pulley transition zone. This is the first stage in a larger study to better understand the mechanics of bucket elevator operation with reference to the discharge of particles at the head end. At the head end two issues arise; mechanically, the buckets are bolted to the conveying media (typically a fabric reinforced belt) and at the point of belt to headpulley tangency, the tip of the bucket undergoes a theoretical step change in velocity. This theoretical step change results in a classical under-damped response in the buckets tip velocity. In undergoing this motion, there are stresses that are passed to the carcass of the conveying media; understanding the magnitude of these stresses is one longer term goal of this research allowing a quantitative basis for the existing qualitative design guidelines such as (Handbook for conveyor and elevator belting, Apex Belting Pty Ltd). The discharge of the bulk material from the bucket has been addressed Beverly et al. (Bulk Solids Handling, 1983) but this analysis is dependent on simple, but common, bucket geometry and ignores the initial transition to the headpulley. Ignoring the transition with a low speed discharge elevator is not likely to impact on the predicted discharge pattern, however with high speed discharge elevators, the destabilising effect of the transition is expected to promote premature discharge of bulk material from the bucket. Depending on the design of the elevator casing this early discharge may or may not impact on the overall conveying efficiency.

Air compression as a mechanism for the underdamped slug test response in fractured glacier ice

Artificial perturbations of borehole water levels, known as slug tests, are a useful means of characterizing the glacier hydrologic system. Slug tests were performed on Bench Glacier, Alaska, in 21 boreholes over three field seasons during the transition from a winter to a summer drainage mode. Fifty‐four slug tests were conducted, with water level monitoring in up to five boreholes adjacent to the slugged borehole. Seven of the slug tests were performed in conjunction with dye dispersion tests to identify water pathways within the slugged borehole following perturbation. Nearly 60% of monitored adjacent boreholes showed a hydraulic connection to the slugged borehole via the glacier bed. The nature and degree of connectivity was temporally variable, suggesting that the drainage network at the bed was highly dynamic on a daily timescale and spatial scale of tens of meters. The variability of slug test responses over time and space limit the feasibility of six alternative explanations for the oscillatory water level behavior characteristic of the underdamped response. We propose a seventh, that is, that coherent air packages are a reasonable means of producing the compliance needed to generate the underdamped slug test responses on Bench Glacier, and that these air packages may exist within the glacier at the tips of subglacially propagated fractures.

Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection

Limit cycle walkers are bipeds that exhibit a stable cyclic gait without requiring local controllability at all times during gait. A well-known example of limit cycle walking is McGeer's ldquopassive dynamic walking,rdquo but the concept expands to actuated bipeds as involved in this study. One of the stabilizing effects in limit cycle walkers is the dissipation of energy that occurs when the swing foot hits the ground. We hypothesize that this effect can be enhanced with a negative relation between the step length and step time. This relation is implemented through an open-loop strategy called swing-leg retraction; a predefined time trajectory for the swing leg makes the swing leg move backwards just prior to foot impact. In this paper, we study the effect of swing-leg retraction through three bipeds; a simple point mass simulation model, a realistic simulation model, and a physical prototype. Their stability is analyzed using Floquet multipliers, followed by an evaluation of how well disturbances are handled using the Gait Sensitivity Norm. We find that mild swing-leg retraction is optimal for the disturbance rejection of a limit cycle walker, as it results in a system response that is close to critically damped, rejecting the disturbance in the fewest steps. Slower retraction results in an overdamped response, characterized by a positive dominant Floquet multiplier. Likewise, faster retraction results in an underdamped response, characterized by a negative Floquet multiplier.

Application of physical science analysis to strategic management monitoring and control systems

This article illustrates the potential for using mathematical reasoning and analogy from physical sciences to conceptualise and explore the effect of dynamic external forces on the response of a company. An example of a generalised second-order linear differential model is applied to study the dynamic response of a company or industry to an exogenous shock. In most systems, significantly over-damped or under-damped response characteristics are expected. However, strategic management monitoring and control systems can scan for external shocks in order to apply dynamic adaptive controls to optimise the company's response. Mathematical tools are used to predict conditions under which an efficient response to external shocks is expected. It is shown that active strategic management can provide superior response characteristics. Additional complementary mathematical modelling approaches are outlined to show how the model may be expanded to address inter-firm linkages, supply chain dynamics, and the propagation of shocks through an industry.

Fast settling opamp with low power consumption

This paper presents a design strategy to minimize step response settling time of a two stage miller opamp with low power consumption. Appropriate spacing between poles and zero has been kept, so an underdamped transient response with minimum settling time is obtained. Analytical results show that for a specific load capacitor, if zero frequency is placed at appropriate distance from unity gain frequency, then minimum settling time can be obtained. Analysis using device modelling has been carried out to determine element values for optimum compensation followed by its simulations in triple metal layer n-well CMOS process using 0.5 µ technology. Best simulation results obtained on Tanner tool show 86.2 dB gain, 136.6 MHz unity gain frequency (ωμ ), 25 ns settling time (ts ) with 1pf load, 211 V/µs slew rate (SR) with 1pf load, and 2.56 mW of power dissipation. The approach reported has been found to be the best after carrying out extensive performance evaluation through simulation.

Optimizing fuzzy neural networks for tuning PID controllers using an orthogonal simulated annealing algorithm OSA

In this paper, we formulate an optimization problem of establishing a fuzzy neural network model (FNNM) for efficiently tuning proportional-integral-derivative (PID) controllers of various test plants with under-damped responses using a large number P of training plants such that the mean tracking error J of the obtained P control systems is minimized. The FNNM consists of four fuzzy neural networks (FNNs) where each FNN models one of controller parameters (K, T/sub i/, T/sub d/, and b) of PID controllers. An existing indirect, two-stage approach used a dominant pole assignment method with P=198 to find the corresponding PID controllers. Consequently, an adaptive neuro-fuzzy inference system (ANFIS) is used to independently train the four individual FNNs using input the selected 176 of the 198 PID controllers that 22 controllers with parameters having large variation are abandoned. The innovation of the proposed approach is to directly and simultaneously optimize the four FNNs by using a novel orthogonal simulated annealing algorithm (OSA). High performance of the OSA-based approach arises from that OSA can effectively optimize lots of parameters of the FNNM to minimize J. It is shown that the OSA-based FNNM with P=176 can improve the ANFIS-based FNNM in averagely decreasing 13.08% error J and 88.07% tracking error of the 22 test plants by refining the solution of the ANFIS-based method. Furthermore, the OSA-based FNNMs using P=198 and 396 from an extensive tuning domain have similar good performance with that using P=176 in terms of J.

Gain and temporal response of AlGaN solar-blind avalanche photodiodes: An ensemble Monte Carlo analysis

Multiplication and temporal response characteristics of p+-n-n+ GaN and n-type Schottky Al0.4Ga0.6N avalanche photodiodes (APD) have been analyzed using the ensemble Monte Carlo method. Reasonable agreement is obtained with the published measurements for a GaN APD without any fitting parameters. In the case of AlGaN, the choice of a Schottky contact APD is seen to improve drastically the field confinement resulting in satisfactory gain characteristics. For the GaN APD, an underdamped step response is observed in the rising edge, and a Gaussian profile damping in the falling edge under an optical pulse with the switching speed degrading towards the gain region. In the AlGaN case, alloy scattering is seen to further slow down the temporal response while displacing the gain threshold to higher fields.

Design of PI and PID controllers with transient performance specification

Proportional-integral-derivative (PID) controllers are widely used in industrial control systems because of the reduced number of parameters to be tuned. The most popular design technique is the Ziegler-Nichols method, which relies solely on parameters obtained from the plant step response. However, besides being suitable only for systems with monotonic step response, the compensated systems whose controllers are tuned in accordance with the Ziegler-Nichols method have generally a step response with a high-percent overshoot. In this paper, tuning methods for proportional-integral (PI) and PID controllers are proposed that, like the Ziegler-Nichols method, need only parameters obtained from the plant step response. The methodology also encompasses the design of PID controllers for plants with underdamped step response and provides the means for a systematic adjustment of the controller gain in order to meet transient performance specifications. In addition, since all the development of the methodology relies solely on concepts introduced in a frequency-domain-based control course, the paper has also a didactic contribution.

DTT: direct truncation of the transfer function - an alternative to moment matching for tree structured interconnect

A method is introduced to evaluate time domain signals within RLC trees with arbitrary accuracy in response to any input signal. This method depends on finding a low frequency reduced-order transfer function by direct truncation of the exact transfer function at different nodes of an RLC tree. The method is numerically accurate for any order of approximation, which permits approximations to be determined with a large number of poles appropriate for approximating RLC trees with underdamped responses. The method is computationally efficient with a complexity linearly proportional to the number of branches in an RLC tree. A common set of poles is determined that characterizes the responses at all of the nodes of an RLC tree which further enhances the computational efficiency. Stability is guaranteed by the DTT method for low-order approximations with less than five poles. Such low-order approximations are useful for evaluating monotone responses exhibited by RC circuits.

Fuzzy neural networks for tuning PID controller for plants with underdamped responses

In this paper, the fuzzy neural network (FNN) for tuning proportional-integral-derivative (PID) controller for plants with underdamped step responses is proposed. The underdamped systems are modeled by second-order-plus-dead-time transfer functions. For deriving the FNN, the dominant pole assignment method is applied to design the PID controllers for a batch of test plant models that represent the plants with underdamped responses. Then, a fuzzy neural modeling method is utilized to identify the relationship between the parameters that characterize the plant dynamics and the controller parameters. We then utilize the obtained FNN to tune the PID controller for plants with underdamped responses. Several simulation examples are given to demonstrate the effectiveness and robustness of the FNN obtained.