Pure Time Delay Research Articles

Effects of Overlapping and Windowing on Frequency Response Function Estimates of Systems With Random Inputs

The use of block overlapping and time windowing in the estimation of the frequency response functions (FRFs) of linear systems is considered. The systems are subjected to stationary white random excitation, and there is no external noise. The sources of errors for the bias and variance of the frequency response are identified to be due to the Fourier transforms of the transient terms or end effects that arise due to nonperiodic signals. Using a pure time delay as an example for the system, it is shown that there is a limit to the improvement achievable in reducing the variance as the block overlap is increased.

Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach

In this paper, a stability test procedure is proposed for linear nonhomogeneous fractional order systems with a pure time delay. Some basic results from the area of finite time and practical stability are extended to linear, continuous, fractional order time-delay systems given in state-space form. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems. A numerical example is given to illustrate the validity of the proposed procedure.

Decoding rule from vasoconstrictor skin sympathetic nerve activity to nonglabrous skin blood flow in humans at normothermic rest

Although an importance of vasoconstrictor skin sympathetic nerve activity (SNA) in control of cutaneous circulation is widely recognized, the decoding rule that translate dynamic fluctuations of vasoconstrictor skin SNA into skin blood flow is not fully understood. In 10 male subjects who rested in supine position under normothermic condition, we measured skin blood flow index (by laser-Doppler flowmetry) at the dorsum pedis, and vasoconstrictor skin SNA (by microneurography) that was confirmed to innervate the same region as the flow index. We determined the transfer and coherence functions from the neural activity input to the flow and quantified the contribution and predictability from the input to output by system engineering technique. The results showed that in frequency-domain analysis, the transfer function from vasoconstrictor skin SNA to skin blood flow had low-pass filter characteristics with 3.6+/-0.1s of pure time delay. The coherence function was approximately 0.5 between 0.01 and 0.1Hz and less above 0.1Hz. In time-domain analysis, the predictability from the SNA to the skin blood flow was approximately 50%. These findings indicate that at normothermic rest, the decoding rule from vasoconstrictor skin SNA to skin blood flow of skin is characterized by low-pass filter with 3-4s of pure time delay, and that the vasoconstrictor skin SNA contributes to a half of fluctuation of skin blood flow in the condition. The incomplete dependence of skin blood flow on vasoconstrictor skin SNA may confirm nonneural mechanisms to control cutaneous circulation even at normothermic rest.

Markovian jump delayed Hopfield networks with multiplicative noise

A non-symmetric version of Hopfield networks subject to state-multiplicative noise, pure time delay and Markov jumps is considered. Such networks arise in the context of visuo-motor control loops and may, therefore, be used to mimic their complex behavior. In this paper, we adopt the Lur’e–Postnikov systems approach to analyze the stochastic stability and the L 2 gain of generalized Hopfield networks including these effects.

Fast Step-response Evaluation of Linear Continuous-time Systems With Time Delay in the Feedback Loop

The simulation of step, impulse and ramp responses of linear continuous-time time-invariant single-input single-output systems with a pure time delay in the feedback loop is tackled. Contrary to systems without time delay where a conversion from Laplace transform to z transform with a zero-order hold allows for an exact response, delay in the feedback loop requires either an unbounded number of states or approximations. This paper proposes an approximation which fulfills a set of criteria, including exactness of the response over a specified multiple of the delay and the conservation of the stability or lack of stability. The approach is illustrated with examples.

Design of decentralized IMC‐PID controller based on dRI analysis

AbstractA simple yet effective method for designing decentralized PID controller, which is based on dynamic interaction analysis and internal model control principle, is proposed. On the basis of structure decomposition, the dynamic relative interaction is defined and represented by the process model and controller explicitly. Using the initial controllers designed for the diagonal elements, the multiplicate model factor is derived, and then simplified to a pure time delay function at the neighborhood of each control loop critical frequency to obtain the equivalent transfer function for the particular control loop. Consequently, appropriate parameters of individual controller are determined by applying the IMC‐PID tuning rules for the equivalent‐transfer function. Simulation results for a variety of 2 × 2, 3 × 3 and 4 × 4 systems show that the design technique results better overall control performance than those of existing design methods. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Binaural and cochlear disparities

Binaural auditory neurons exhibit "best delays" (BDs): They are maximally activated at certain acoustic delays between sounds at the two ears and thereby signal spatial sound location. BDs arise from delays internal to the auditory system, but their source is controversial. According to the classic Jeffress model, they reflect pure time delays generated by differences in axonal length between the inputs from the two ears to binaural neurons. However, a relationship has been reported between BDs and the frequency to which binaural neurons are most sensitive (the characteristic frequency), and this relationship is not predicted by the Jeffress model. An alternative hypothesis proposes that binaural neurons derive their input from slightly different places along the two cochleas, which induces BDs by virtue of the slowness of the cochlear traveling wave. To test this hypothesis, we performed a coincidence analysis on spiketrains of pairs of auditory nerve fibers originating from different cochlear locations. In effect, this analysis mimics the processing of phase-locked inputs from each ear by binaural neurons. We find that auditory nerve fibers that innervate different cochlear sites show a maximum number of coincidences when they are delayed relative to each other, and that the optimum delays decrease with characteristic frequency as in binaural neurons. These findings suggest that cochlear disparities make an important contribution to the internal delays observed in binaural neurons.

Force dynamic response of tibialis anterior–ankle joint unit in humans

The aim of this study was to estimate the dynamic response of a human muscle joint unit by means of the analysis of the torque signal recorded during electrical stimulation of the tibialis anterior (TA). Ten subjects (age: 23–50 years, 7 males, 3 females) volunteered for the study. The leg was fixed in an ergometer designed for isometric contraction of the ankle dorsiflexors and the detection of the generated torque. The amplitude of a 30 Hz stimulation train administered at the TA motor point was varied sinusoidally, thus changing the number of the recruited motor units, and hence the tension at the tendon, in the same fashion. A sequence of 14 frequencies (0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 4.0, 5.0, and 6.0 Hz) was administered. Results: (a) at the 14 frequencies the sinusoidal responses presented distortions always below 2%; (b) from the Bode plots reporting the average gain attenuation and phase shift at each of the 14 input frequencies, it was possible to model the force dynamic response as the one of a critically damped II order system with two real coincident poles (at 2.04 Hz) and a pure time delay (15.6 ms). The possibility to obtain, by means of the system input–output transfer function, data regarding the in vivo mechanics of the muscle–joint unit may represent a novel tool to investigate the functional features of different muscle groups. It may be useful for designing functional electrical stimulation programs as well as training and rehabilitation procedures.

Formula omitted]-optimal digital redesign method

The plant input mapping (PIM) method is a digital redesign technique which guarantees the closed-loop stability for all non-pathological sampling periods. The PIM method, however, has some possible drawbacks observed in the closed-loop step response: (1) a steady-state error, and (2) a pure time delay. The first problem might occur when the plant is unstable, and the second one occurs, when the analog controller is not bi-proper. In the present study, we first modify the original PIM method such that these two drawbacks are resolved. Although the PIM method does not, in general, lead to undesirable inter-sample ripples, yet, its formulation does not explicitly address the inter-sample behavior of the resulting digital control system. Therefore, the main contribution of the paper is to extend the idea of the PIM method in the context of sampled-data systems, so that the inter-sample behavior can be taken into account explicitly. For this purpose, we consider a standard sampled-data setting, in which the H ∞ norm of the discretization error is minimized. The effectiveness of the proposed methods is demonstrated through benchmark examples.

MODAL CONTROL FOR SAMPLED-DATA SYSTEMS WITH GENERALIZED HIGHER-ORDER HOLD AND TIME DELAY

The paper defines the modal digital control problem for a continuous-time LTI process with m inputs and n outputs and real-valued pure time delay. A generalized higher-order hold is applied as an extrapolator. The paper introduces the concept of modal controllability for such a process. Necessary and sufficient conditions are derived under which the modal controllability takes place. Moreover, for modal controllable processes, a method is provided that allows to build the set of all controllers which place the closed-loop modes on prescribed locations. The investigations base on the discrete backward model of the process.

Process control of pH neutralization based on adaptive algorithm of universal learning network

This paper presents an adaptive algorithm of universal learning network (ULN) and its application to identify pure time delay of a plant model. Universal learning network can be used in model predictive control for stabilizing a class of nonlinear systems with long time delay. Depending on ULN model with single neuron controller, the control architectures are introduced and applied to pH neutralization process. Simulation results prove the applicability and effectiveness of the ULN model. The general architecture and adaptive learning algorithm give ULN more representing abilities to model and control the nonlinear black box systems with long time delay.

Accuracy of Identification and Control Performance in 3 Parameter Process Model Approximations(Identification by Prony's Method and Examination through Model-Driven PID Control System Design)

In this paper, very simple method based on Prony method, which is known as one of the most representative methods in the exponential analysis method, is presented by which transfer function models for processes can easily be obtained. Here, the method is reformed and applied to obtain the so-called 3 parameter model (first-order transfer function with pure time delay model) from the data of the step response of the process system. The method gives different process models by changing the identification interval. Here the relation between the accuracy of identification and identification interval is considered from the viewpoint of integrated absolute error and integrated squared error. The obtained results are examined by applying it to the design of model-driven PID control of a typical test batch process model.

Effect of renal perfusion pressure on responses of intrarenal blood flow to renal nerve stimulation in rabbits.

1. We investigated how sympathetic nerve activity and renal perfusion pressure (RPP) interact in controlling renal haemodynamics in pentobarbitone-anaesthetized rabbits. 2. Renal blood flow (RBF) was reduced by electrical renal nerve stimulation (0.5-8 Hz), with RPP set using an extracorporeal circuit to 65, 100 and 135 mmHg. 3. Responses of RBF and cortical laser Doppler flux to renal nerve stimulation were blunted by increased RPP. For example, 4 Hz stimulation reduced RBF by 68 +/- 7% with baseline perfusion pressure approximately 65 mmHg, but only by 22 +/- 3% at approximately 135 mmHg. Medullary laser Doppler flux was less responsive than cortical laser Doppler flux to renal nerve stimulation and its response was not dependent on perfusion pressure. 4. When perfusion pressure was clamped at its baseline level during renal nerve stimulation, responses of RBF and cortical laser Doppler flux, but not medullary laser Doppler flux, were still blunted with increased baseline perfusion pressure. 5. A frequency rich stimulus was applied to assess the effects of perfusion pressure on dynamic neural control of RBF. Renal blood flow responded similarly at each level of perfusion pressure, as a low-pass filter with a pure time delay. 6. Our results suggest that, in the rabbit extracorporeal circuit model, increased RPP blunts the ability of steady state renal nerve stimulation to reduce cortical, but not medullary perfusion. However, in this model the level of RPP appears to have little impact on dynamic neural control of RBF.

Describing and compensating gas transport dynamics for accurate instantaneous emission measurement

Instantaneous emission measurements on chassis dynamometers and engine test benches are becoming increasingly usual for car-makers and for environmental emission factor measurement and calculation, since much more information about the formation conditions can be extracted than from the regulated bag measurements (integral values). The common exhaust gas analysers for the “regulated pollutants” (carbon monoxide, total hydrocarbons, nitrogen oxide, carbon dioxide) allow measurement at a rate of one to ten samples per second. This gives the impression of having after-the-catalyst emission information with that chronological precision. It has been shown in recent years, however, that beside the reaction time of the analysers, the dynamics of gas transport in both the exhaust system of the car and the measurement system last significantly longer than 1 s. This paper focuses on the compensation of all these dynamics convoluting the emission signals. Most analysers show linear and time-invariant reaction dynamics. Transport dynamics can basically be split into two phenomena: a pure time delay accounting for the transport of the gas downstream and a dynamic signal deformation since the gas is mixed by turbulence along the way. This causes emission peaks to occur which are smaller in height and longer in time at the sensors than they are after the catalyst. These dynamics can be modelled using differential equations. Both mixing dynamics and time delay are constant for modelling a raw gas analyser system, since the flow in that system is constant. In the exhaust system of the car, however, the parameters depend on the exhaust volume flow. For gasoline cars, the variation in overall transport time may be more than 6 s. It is shown in this paper how all these processes can be described by invertible mathematical models with the focus on the more complex case of the car's exhaust system. Inversion means that the sharp emission signal at the catalyst out location can be reconstructed from a flattened emission signal at the sensor. In this modelling, special focus is put on finding an easy parameterisation for different cars. The process of finding these compensators consists of first describing the process by differential equations of appropriate order and parameterising them, resulting in low pass systems. The following step of inverting these systems results automatically in high pass systems. These kinds of systems, however, amplify measurement noise, thus they need signal filters to smooth their output.

The PIL (Not PID?) Controller as Eigenvalue Assigner and Optimum Stabiliser

For reasons of saturation avoidance and limitation of high frequency noise, the classical PID controller is usually implemented with a lowpass filter on the derivative channel. As pointed out by the author some years ago, this has profound implications for the stability of digital control systems based on discretised analog designs. However, it then ceases to be a PID controller and might be better described as PIL, where L normally stands for phase “lead,” but might in exceptional circumstances be phase “lag.” Such controllers are investigated as eigenvalue assigners for an inherently unstable magnetic levitation (maglev) system and for a first order lag with pure time delay, where the time delay is approximated by a first order Padé approximation for design purposes and then simulated exactly for performance evaluation. Explicit controller designs are derived with all closed loop eigenvalues placed at the same location. It is demonstrated, using root locus arguments, that this gives an optimally stable system in the sense that as any single controller or process parameter is varied with respect to its nominal value, the rightmost eigenvalue, on passage through the nominal parameter setting, is as deep in the left half plane as possible.

Motion control via telecommunication networks: Random time delays and a simple stability design

Motion control and navigation via telecommunications networks as well as the control of other dynamical systems recently again came in the focus by a number of authors world-wide. It has been subject to extensive investigation because of remote motion control applications, and also because of the impact of random time delays caused by telecommunication networking, e.g., Internet. The most essential phenomenon in implementing remote control via Internet networking is that of a random, time varying pure time delay. In turn, this phenomenon gives rise to the issue of closed-loop stability which may cause control performance deterioration, and even instability brake down of such control systems. Within the limitations of using linear models of the dynamics of controlled object - remote motion control process in open-loop system, a through design analysis is feasible and has been elaborated in the course of our research. In order to ensure the system stability, the maximum expected time-delay phenomenon must be observed at design stage of the control system. Hence the main design conclusion is to ensure that system parameters be adjusted according to the maximum expected delay distributions always.

Combined Effects of Nitrous Oxide and Propofol on the Dynamic Cerebrovascular Response to Step Changes in End-tidal Pco2in Humans

Nitrous oxide (N2O) and propofol exhibit directionally opposite effects on the cerebral circulation, vasodilation and vasoconstriction, respectively. The authors investigated an interaction between the two anesthetic agents on the dynamic cerebrovascular response to step changes in end-tidal pressure of carbon dioxide (PetCO2) in humans. Participants with no systemic diseases were allocated into two groups, each of which was anesthetized sequentially with two protocols. Patients in group 1 were anesthetized with 30% O2 + 70% N2O. A continuous intravenous infusion of propofol (7-10 mg x kg(-1) x h(-1)) was then added to the N2O. Patients in group 2 were anesthetized first with continuous infusion of propofol (10 mg x kg(-1) h(-1)), and then 30% O2 + 70% N2O was added to the propofol anesthesia. Using transcranial Doppler ultrasonography, blood flow velocity at the middle cerebral artery (FV(MCA)) was measured during a step increase (on-response) followed by a step decrease (off-response) in PetCO2, with PetCO2 ranging between approximately 28 and 50 mmHg. The dynamic FV(MCA)-PetCO2 relationship was analyzed using a mathematical model that was characterized with a pure time delay, and a time constant and a gain each for the on- or off-response. The addition of propofol to the N2O anesthesia increased the on-response time constant (P < 0.01), whereas the addition of N2O to the propofol anesthesia increased the time constants for on- (P < 0.01) and off-responses (P < 0.05). However, the addition of either anesthetic did not affect the gains. Propofol and N2O, when one is added to the other, produce similar dynamic FV(MCA) responses to sudden changes in PetCO2. Addition of each anesthetic slows the dynamic response and produces the response whose magnitude is proportional to the baseline FV(MCA).

Interactions between neural and hormonal mediators of renal vascular tone in anaesthetized rabbits.

We investigated how sympathetic nerve activity and vasoactive hormones interact in controlling renal haemodynamics in pentobarbitone-anaesthetized rabbits. Renal blood flow was progressively reduced by electrical stimulation (0.5-3 Hz) of the renal nerves, during renal arterial infusion of saline, vasoconstrictors (angiotensin II and [Phe2,Ile3,Orn8]-vasopressin), or vasodilators (acetylcholine, adrenomedullin and the nitric oxide donor methylamine hexamethylene NONOate (MAHMA NONOate). A frequency-rich stimulus was also applied to test whether the vasoactive agents affect the dynamic control of renal blood flow by sympathetic nerve activity. The vasodilators tended to increase renal blood flow, but only the effect of MAHMA NONOate was statistically significant. [Phe2,Ile3,Orn8]-vasopressin reduced medullary perfusion (by 61 +/- 12 %) but not renal blood flow or cortical perfusion. Angiotensin II reduced renal blood flow (33 +/- 3 %) and cortical perfusion (14 +/- 5 %) but not medullary perfusion. Steady-state responses of renal blood flow and cortical perfusion during renal nerve stimulation were attenuated during infusion of acetylcholine and [Phe2,Ile3,Orn8]-vasopressin, while angiotensin II attenuated responses of medullary perfusion, and MAHMA NONOate and adrenomedullin had no significant effects. The dynamic response to sympathetic nerve activity (renal blood flow responded as a low pass filter with a pure time delay of ~664 ms) was not altered by the vasoactive agents. We conclude that some vasoactive agents can modulate steady-state renal haemodynamic responses to sympathetic nerve activity in a regionally specific manner, independent of their effects on baseline renovascular tone. However, they have little impact on the dynamic response of renal blood flow to sympathetic nerve activity.

Improved unit hydrograph characterisation of the daily flow regime (including low flows) for the River Teifi, Wales: towards better rainfall-streamflow models for regionalisation

Abstract. An established rainfall-streamflow modelling methodology employing a six-parameter unit hydrograph-based rainfall-runoff model structure is developed further to give an improved model-fit to daily flows for the River Teifi at Glan Teifi. It is shown that a previous model of this type for the Teifi, which (a) accounted for 85% of the variance in observed streamflow, (b) incorporated a pure time delay of one day and (c) was calibrated using a trade-off between two model-fit statistics (as recommended in the original methodology), systematically over-estimates low flows. Using that model as a starting point the combined application of a non-integer pure time delay and further adjustment of a temperature modulation parameter in the loss module, using the flow duration curve as an additional model-fit criterion, gives a much improved model-fit to low flows, while leaving the already good model-fit to higher flows essentially unchanged. The further adjustment of the temperature modulation loss module parameter in this way is much more effective at improving model-fit to low flows than the introduction of the non-integer pure time delay. The new model for the Teifi accounts for 88% of the variance in observed streamflow and performs well over the 5 percentile to 95 percentile range of flows. Issues concerning the utility and efficacy of the new model selection procedure are discussed in the context of hydrological studies, including regionalisation. Keywords: unit hydrographs, rainfall-runoff modelling, low flows, regionalisation.

Predictive control of a high temperature–short time pasteurisation process

Modifications on the dynamic matrix control (DMC) algorithm are presented to deal with transfer functions with varying parameters in order to control a high temperature–short time pasteurisation process. To control processes with first order with pure time delay models whose parameters present an exogenous variable dependence, a new method of free response calculation, using multiple model information, is developed. Two methods, to cope with those nonlinear models that allow a generalised Hammerstein model description, are proposed. The proposed methods have been tested, both in simulation and in real cases, in comparison with PID and DMC classic controllers, showing important improvements on reference tracking and disturbance rejection.