Pure Time Delay Research Articles

Mode analysis of physiological oscillators intercoupled via pure time delays

The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.

未知のむだ時間を有する系に対する適応オブザーバ

未知のむだ時間を有する系に対する適応オブザーバ

The linear dynamic properties of phototransduction in the fly compound eye.

1. Photoreceptor cells in the compound eye of the fly Phormia regina were stimulated with a green light emitting diode whose output was modulated by a pseudo-random noise generator while the resulting fluctuations in membrane potential were measured with intracellular microelectrodes. 2. The responses to repeated sequences of identical pseudorandom patterns were averaged together to give frequency response functions having a significantly improved signal to noise ratio at frequencies where the response has not previously been characterized accurately. 3. Measured frequency response functions could not be fitted by a set of simple exponential time constants but could be well fitted by a model including two under-damped second order time constants. 4. The phase data had no detectable asymptote and could only be accounted for by a model which includes a pure time delay. 5. Residual fluctuations in the phase data with frequency suggest that a small portion of the recorded signal arises from a delayed interaction with lateral or proximal cells.

Oscillatory phenomena in a model of infectious diseases

Oscillations of the number of cases around an average endemic level are common in several infectious diseases. In this paper we study simple deterministic models, where the oscillations arise either solely from periodically varying contact rates or from the combined effect of large initial perturbation, small periodic variation of the contact rate, and the destabilizing nature of infectious and latent periods when described as time delays. The main results are: (a) For a model with a periodically varying contact rate and a recovery rate, a threshold amplitude of variation is found by numerical and analytic methods at which 2-year subharmonic resonance appears. (b) Approximate analytic relationships are derived for the amplitude and phase of the forced 1-year oscillations below this threshold and for the 2-year oscillations above it—in terms of the reproduction rate of the infection. (c) Similar calculations are performed when the recovery rate is replaced by a fixed infectious period represented by a pure time delay. The threshold amplitude of variation in the contact rate is found here to be smaller than in the recovery rate model. (d) A model with a fixed infectious period and a constant contact rate is considered. The nontrivial steady state is shown to be locally stable for the parameter range of interest. However, the ratio of the imaginary to real parts of the eigenvalues in the characteristic equation is increased as compared to the corresponding model with a recovery rate. (e) For the model with a fixed infectious period and a constant contact rate an approximation method indicates consistency in a certain range of contact rates with the existence of an unstable periodic solution about the locally stable steady state. The actual existence of such a solution is not verified. The interpretation is that the destabilizing effect of the introduction of a pure delay into the model becomes more significant as the distance in the variables space from the endemic steady state is increased. (f) For a fixed infectious period and very small subthreshold variation in the contact rate, two different types of solutions are found numerically: yearly small-amplitude oscillations about an endemic average and large-amplitude oscillations of a subharmonic period. The pattern seen depends on the initial conditions. For a sufficiently large initial deviation from the endemic level even very small seasonal variations lead to regular recurrent outbreaks of the disease. The effect of latent periods and of changing the form of the interaction are also considered.

The design of reduced-order systems

A reduction method is proposed based on the elimination of poles and zeros and the use of compensators and pure-time delays. The reduced systems are shown to be extremely useful in control system design. Examples are included dealing with both SISO and MIMO systems.

Phototransduction in the fly compound eye exhibits temporal resonances and a pure time delay.

Photoreceptor cells in both vertebrates and invertebrates respond to a flash of light with a slow graded change in membrane potential, which is generally depolarising in invertebrates and hyperpolarising in vertebrates. Although some of the early photochemical and biochemical stages of the transduction process have been elucidated in both cases, these reactions are fast compared with the time course of the electrical response, which is typically hundreds of milliseconds long. To explain this slow response in the eye of Limulus, Fuortes and Hodgkin proposed a mechanism in which the light signal passes through a cascade of simple low pass filters. The model was later defined more specifically in terms of a chain of chemical reactions linked together through products and reactants, and has been used with small modifications and different numbers of stages to account for the behaviour of various vertebrate and invertebrate photoreceptors including the fly compound eye. I have now obtained evidence that phototransduction in the fly in small signal conditions involves underdamped resonance behaviour and a significant pure time delay, neither of which can be accounted for by the conventional cascade model.

Optimal Control of an Object in Pulp and Paper Industry by a Combined Criterion

A new method is proposed for the synthesis of an optimal control system by a combined criterion “energy-time”. It is illustrated on a concrete object in paper industry - paper machine producing wrapping paper. As an example of control, one of the channels for regulation of the steam pressure coming in the machine, is chosen. The model is a consecutive combination of an aperiodic and an integrating unit with a pure time delay. The optimal criterion is a minimum steam expenditure per a fixed time of the transition process. The synthesis applies the phase plane method. The original quality of the method applied for the synthesis of optimal control is that another modified switch-off line is used, invariant to input effects. The new switch-off line depends only on the time given to the transition process and the parameters of the object. An equation is deduced for the modified switch-off line in the case in discussion. Its construction is represented by a graphic method which may be used for all second order systems. A method can be applied for compensation of time delay where the parameters of auto-variations are minimal in the system. The control lines for switch-off and -on are approximated by some sequences by the method of the equivalent signurn functions. This formulation facilitates considerably the technical realization of the system. A digital modelling is made to the transition process in the steam regulating channel with a synthesized control equipment. It is shown, that the synthesized quasi-optimal control equipment forms effects close to the optimal in form and duration, for the whole range of variation of input effects. The comparison made between the optimal and the quasi-optimal systems shows that the steam expenditure does not differ for the two systems. The time of completion of the process remains constant at that.

Optimal control of an object in pulp and paper industry by a combined criterion

A new method is proposed for the synthesis of an optimal control system by a combined criterion “energy-tim”. It is illustrated on a concrete object in paper industry - paper machine producing wrapping paper. As an example of control, one of the channels for regulation of the steam pressure coming in the machine, is chosen. The model is a consecutive combination of an aperiodic and an integrating unit with a pure time delay. The optimal criterion is a minimum steam expenditure per a fixed time of the transition process. The synthesis applies the phase plane method. The original quality of the method applied for the synthesis of optimal control is that another modified switch-off line is used, invariant to input effects. The new switch-off line depends only on the time given to the transition process and the parameters of the object. An equation is deduced for the modified switch-off line in the case in discussion. Its construction is represented by a graphic method which may be used for all second order systems. A method can be applied for compensation of time delay where the parameters of auto-variations are minimal in the system. The control lines for switch-off and -on are approximated by some sequences by the method of the equivalent signum functions. This formulation facilitates considerably the technical realization of the system. A digital modelling is made to the transition process in the steam regulating channel with a synthesized control equipment. It is shown, that the synthesized quasi-optimal control equipment forms effects close to the optimal in form and duration, for the whole range of variation of input effects. The comparison made between the optimal and the quasi-optimal systems shows that the steam expenditure does not differ for the two systems. The time of completion of the process remains constant at that.

Parameter adaptive control of stochastic distributed systems

Abstract The parameter adaptive control problem of linear stochastic distributed-parameter systems is considered and treated by invoking the partitioning/non-linear separation approach. Both continuous-time and discrete-time systems are studied, with volume and/or boundary control and disturbance inputs. The following cases are considered: spatially-continuous and point-wise measurements/control actions, continuous and quantized parameter space, non-gaussian initial state, uncertainty in continuous and point-wise measurements, cost-function with spatial-derivative penalties, systems with pure time delays, composite distributed- and lumped-parameter systems, scanning-type control, and simultaneous adaptive system and measurement control. The uncertain parameters are assumed to be time-and-space independent, but the spatial independence can be alleviated as will be shown elsewhere.

On-Line Computer Control of a Nuclear Reactor Using Optimal Control and State Estimation Methods

The paper discusses an on-line computer control system for a nuclear reactor using optimal state feedback based on the linear quadratic regulator and state estimation using a Kalman filter. Practical methods are presented for selecting the gain of the state estimator. It is shown that when pure time delays occur in the output states it is possible to use the Kalman filter to virtually eliminate the effects of the time delay on the control loop performance. The experimental results obtained using the control scheme show that the control scheme designed using modern control techniques has improved performance compared with conventional reactor control methods having greater speed of response, wider stability margins and significantly improved noise filtering properties

A Nonlinear Model Describing Driver Behavior on Straight Roads

Experiments on a CRT driving simulator are used to develop a closed-loop human operator model for straight road driving in the absence of any externally applied disturbance such as side wind gusts or road roughness. It is shown that a significant portion of the driver's control characteristics can be represented by a stationary, nonlinear system with a single visual input. The driver's visual input is considered to be the angle subtended between the heading axis and a line connecting a point on the lane center at a preview distance with his eyes. An optimization procedure is used to evaluate the model parameters, and it is found that the driver's action can be best represented by a pure time delay cascaded with a classical hysteresis nonlinearity. The self-excited limit cycle frequency and amplitudes of this model system are shown to agree closely with respective quantitative aspects of the experimental data confirming the validity of the model.

Adaptive observer for systems with pure time delay

This note is concerned with the application of adaptive techniques for simultaneous parameter identification and state estimation to the design of an adaptive observer for systems having unknown pure time delay and parameters.

A Simplified Method of Pure Time Delay Generation

A method of time delay generation is described that is not dependent on a Pade or similar approximation. It is shown that the use of a serial analogue to digital conversion technique known as Delta Modulation can result in a simple and low cost alternative to the parallel conversion methods normally applied and it is stated that the time delay system described can be used on a low cost analogue computer with the addition of only one shift register.

Identification of linear systems with time-delay operating in a closed loop in the presence of noise

The subject of this short paper is on-line identification of the parameter vector defining a linear dynamical system which operates in a closed loop in the presence of noise, and incorporates a time delay. The method is based on the equation error. Other known subsystems in the closed-loop system increase the dimension of the closed-loop parameter vector which tends to degrade the estimation convergence process. By means of "composite state variables," introduced in this short paper, this increase is prevented and the open-loop parameters are directly identified from closed-loop input-output data. The pure time delay in the closed loop causes a representation problem in the equation error formulation. This is overcome by "composite delayed state variables." The value of the time delay is determined by means of excess parameters provided by a "higher order model" and a simple on-line search procedure. The method is illustrated by simulated examples.

Extremum controller design

An extremum on-off controller whose detailed description is given here is designed to continuously operate an industrial process at the extreme value of the process output. The process investigated consists of the following in cascade: a pure time delay, a parabolic function, and a first-order lag. A simple method is presented for selection of the three controller parameters, a gain, a velocity constant, and a dead time. The gain and the velocity constant are chosen so as to obtain a desired average output for the oscillation cycle. The main advantages of the controller designed are speed in reaching the extremum and low sensitivity to disturbances (because of low value of gain). A step-by-step procedure for the control system design is given.

On the Performance Characteristics of a Vortex Rate Gyro

The static and dynamic performance characteristics of a fluidic angular rate sensor were studied both theoretically and experimentally. It seems that the total time delay of a vortex rate gyro is composed of the time delay associated with the development of a stabilized tangential flow at the vortex chamber periphery plus the pure delay time associated with the fluid transport phenomenon. By this theoretical analysis, the transfer function of a vortex rate gyro was obtained as AeLS/(T2s +1) and thereby, the effects of the vortex rate gyro configuration and supply flow rate on the pure delay time L, time constant T2 and output sensitivity A were clarified. Experiments were conducted varying the vortex chamber thickness and the supply flow rate. It was found that experimental pure delay time L and time constant T2 almost coincide with those obtained theoretically.

Asymptotic approximation method of optimal control applied to a power-system problem

A single machine power system connected to an infinite bus with both voltage regulator and speed governor controls is considered. This system mathematically can be described by an 8th-order nonlinear time-delay model. However, by perturbing a small scalar parameter, this 8th-order model can be reduced to a 3rd-order ordinary model without any pure time delays. An asymptotic approximate solution is constructed with respect to the scalar parameter for the 8th-order time delay model by using the solution of only the 3rd-order ordinary model. Numerical results indicate that the asymptotic solution is close to the optimal solution. Computationally, the asymptotic method is compared with the 2-variation method and is shown to be superior.

Determination of transport lags by using frequency-response tests

An algorithm for the determination of the transport lag of a pure time delay in cascade with a time-invariant linear system is developed and illustrated by an example.

Statistical analysis and interpretation of the initial response of cochlear nucleus neurons to tone bursts.

1. Subject of investigation is the initial response of cochlear nucleus neurons and units presumed to be auditory nerve fibres to CF tone burst stimulation. 2. The initial response is characterized by computing the distribution of the latency of the first spike and of the duration of the first interval in the ensemble of responses to a large number of stimuli. 3. In many of the neurons the properties of both distributions appear to be related. The presumed auditory nerve fibres and spontaneously active cochlear nucleus neurons showing only activation responses to tonal stimuli (A type) exhibit irregularity in both response onset and intervals. Minimum latency and minimum first intervals are short. On the other hand, spontaneously active neurons with both activation and suppression in the response area (AS type) and silent neurons showing only activation (A(S) type) often show a more precisely timed onset of response and narrow interval distributions. In many neurons this leads to oscillations in the PSTH (chopping). In these neurons minimum latency and minimum first interval have higher values. The longer minimum latency cannot be attribute-d to longer pure time delays in these neurons. 4. The results are interpreted as speaking in favour of temporal integration as an important mechanism in many of the AS and A(S) neurons, particularly those in the DCN. The firing patterns of A neurons are thought to indicate virtual absence of this mechanism. 5. Using pure time delay estimates derived from cross-correlation functions, computed from the responses to stationary noise, an attempt is made to estimate the integration time in the cochlear and in the cochlear nucleus neurons.

The Control of a Process Having Appreciable Transport Lag-A Laboratory Case Study

The control of a process characterized by major " pure time delay" or " transport lag" by means of a coentonal analog controller is difficult because of the finite time which must elapse before a change in the controller output produces any measurable change in the process output. Linear predictor control is a well-known theoretical scheme for compensating the dead time; this requires incorporation of dead time in the controller itself and hardware difficulties have limited the use of this scheme in practice. It is shown in this paper that using an approximate-analog model of dead time synthesized from relatively inexpensive electronic components, a controller using the linear predictor approach is quite practicable in a typical process conatrol situation. A design of a control scheme for a laboratory process implementing the linear predictor control principle is given and it is shown that the improvement obtained in the control of the process, using an approximate analog model of dead time, is considerable.