WO2004010157A1

WO2004010157A1 - Method for measuring a physical or chemical operating parameter for an analysis system

Info

Publication number: WO2004010157A1
Application number: PCT/DE2003/002346
Authority: WO
Inventors: Peter Jörg PLATH; Ernst-Christoph Hass; Uwe Sydow; Magnus Buhlert
Original assignee: Mir-Chem Gmbh
Priority date: 2002-07-12
Filing date: 2003-07-11
Publication date: 2004-01-29
Also published as: AU2003254628A1; DE10393346D2

Abstract

The invention relates to a method for measuring a physical or chemical operating parameter for an analysis system, in particular an electrochemical cell. According to said method, the analysis system is repeatedly subjected to excitation with the aid of excitation impulses of a physical variable, in order to achieve a non-steady state that can be relaxed. The analysis system can be relaxed from said non-steady state with relation to the physical or chemical operating parameter into a steady state during a relaxation period that is characteristic of the physical or chemical operating parameter of the analysis system and the physical or chemical operating parameter is measured during the relaxation of the analysis system. The analysis system is subjected to successive excitation impulses of an excitation function, during which the successive excitation impulses excite the analysis system at intervals that are shorter than the relaxation period that is characteristic of the physical or chemical operating parameter of said system.

Description

Method for measuring a physical / chemical operating parameter for an examination system

The invention lies in the field of measuring methods in which a physical and / or chemical operating parameter for an examination system is measured in order to obtain information about characteristic properties of the examination system.

Such measurement methods are used in a wide variety of applications to characterize simple or complex systems. For example, the publication WO 03/041209 describes a device for measuring an operating parameter of an electrochemical cell in a spatially and time-resolved manner. In the known method, different measuring arrangements are used to analyze the dynamic behavior of an electrochemical cell. For this purpose, polarization changes are made to the plate elements of a battery, so that the battery relaxes several times from a non-stationary state into a stationary state. This process is repeated each time the polarization changes. It can be provided here that the polarization change is carried out several times in succession in order to obtain information about the behavior of the battery with periodic excitation.

The object of the present invention is to provide an improved method for measuring a physical / chemical operating parameter of an examination system, which extends the analysis options with regard to characteristic physical / chemical properties of the examination system.

According to the invention, this object is achieved by a method for measuring a physical / chemical operating parameter for an examination system, in particular an electrochemical cell, in which the examination system is acted upon several times with the aid of excitation pulses of a physical quantity influencing the examination system, in order to convert it into a relaxable, to be excited in a non-stationary state of the examination system, from which the examination system can relax with respect to the physical / chemical operating parameter in a relaxation time characteristic of the physical / chemical operating parameter, and the physical / chemical operating parameter is measured during excitation and when relaxing the examination system. The examination system is used with successive excitation pulses acted upon in accordance with an excitation function, in which the successive excitation pulses excite the examination system at a time interval which is shorter than the relaxation time characteristic of the physical / chemical operating parameters of the examination system. A complete relaxation takes place in principle after an infinite time. The term relaxation time in the technical meaning used here is the time in which the examination system or the physical / chemical operating parameter has dropped again to about 5% of the maximum size of the excited state or to approximately 95% the desired steady state of the physical / has approached the chemical operating parameters. While in known measuring methods a relaxation of the examination system into a stationary state of the examination system with respect to the physical / chemical operating parameters is observed and only measured afterwards, in the method according to the invention a further excitation takes place with the aid of a following excitation pulse before the examination system relaxes into the stationary state. In this way, a more complex response behavior of the examination system compared to the known method is specifically induced, but this increases the evaluable information content of the measured variables with regard to the properties of the examination system. With the aid of the proposed measuring method, in particular the behavior of the examination system in non-equilibrium states can be analyzed.

The examination system can be any, simply or complexly designed systems for which physical / chemical measured variables are recorded using suitable measuring systems and which are brought at least for measuring purposes from a stationary state into a non-stationary state with the aid of a physical quantity from which the system then relaxes. The relaxation time which is characteristic of the system in this case is known for a wide variety of systems or can be obtained with the aid of known measuring methods in order to take this time constant into account in the manner explained in the newly proposed method. Possible physical / chemical measured variables are basically all measurable parameters of the system under investigation, for example current, voltage, pressure, temperature, intensity of radiation, density or concentration of a substance or the like.

An expedient development of the invention provides that a spectrum of the excitation function is formed in a frequency space by at least two harmonic functions or two fundamental frequencies. The frequency spectrum of the excitation function is obtained with the help of a Fourier transformation of the temporal course of the successive the stimulus. This has the advantage, on the one hand, that the probability of exciting a natural frequency of the system is increased, and, on the other hand, of inducing a more complex resonance behavior of the answering system. This enables additional statements to be made, for example about the dynamics of the system to be examined.

In order to adapt the measuring method to different applications when analyzing different examination systems, further developments of the invention provide that the examination system is excited with the successive excitation pulses according to a periodic, an asymmetrically periodic or a chaotic excitation function. In this way, an individual adaptation of the measuring method to the complexity of different examination systems is made possible. Periodic excitation patterns are already suitable for measurement and control tasks in which the examination system is alternated between two non-stationary states of one or more operating parameters and the switchover takes place during the relaxation time, so that the system never goes into a steady state reached and thus always kept away from equilibrium in the excited states (driven periodic measurement of non-stationary states).

Asymmetrically periodic excitation patterns can be used for measurement and control tasks in which a non-steady state of one or more operating parameters from a defined steady state is to be examined. If, for example, an excitation function with a short rectangular pulse in the upper level and a subsequent long rectangular pulse in the lower level is used, the examination system is briefly transferred to a non-stationary state from which it cannot relax to "equilibrium", and then in brought a state from which it relaxes, so that the next excitation in the short-term state occurs from the "equilibrium". This method can be used, for example, to determine the behavior of an operating parameter in a non-stationary state.

The use of chaotic excitation patterns makes it possible to comprehensively record and control an examination system with regard to its complexity, which can be attributed in particular to the fact that the excitation occurs chaotically from stationary and non-stationary states. A chaotic excitation function corresponds to a sequence of excitation pulses that is not periodic in a finite time interval. There in one If there is already increased information content in chaotic excitation patterns, conclusions can be drawn from the resonance behavior of the (complex) examination system regarding its own dynamics and thus its control. For example, a simple system follows the excitation pattern, ie the measured operating parameter shows a course corresponding to the excitation function. A complex examination system preferably contains additional characteristic patterns in its response behavior, which go beyond the information content of the excitation pattern and can thus be analyzed and controlled with regard to their complexity; ie chaotic behavior is controlled by means of chaos. There is also the possibility that a complex examination system shows a response behavior with a simpler pattern than the excitation function, ie dampens the information content of the excitation pattern, for example if the excitation function is much faster than the relaxation behavior of the examination system regarding the examined operating parameters. In addition, this allows conclusions to be drawn about the complexity of the investigated system and opens up further possibilities for controlling complex systems and for controlling chaos through chaos.

In an expedient embodiment of the invention it can be provided that a temporally chaotic behavior is measured and evaluated for the physical / chemical operating parameters. As already mentioned in the previous section, this chaotic behavior also reflects small system changes in a characteristic manner and with high sensitivity, so that a corresponding test arrangement can serve as a sensitive measuring probe for the system to be examined.

The invention is explained in more detail below using exemplary embodiments with reference to a drawing. Here show:

Figure 1 is a schematic representation of an electrochemical cell of a lead accumulator, in which a measuring probe is arranged;

FIG. 2 shows a periodic excitation function for several polarization changes in an accumulator;

FIG. 3 shows a time series for the response behavior of a probe

Measuring system in an accumulator on the periodic excitation function in Figure 2; FIG. 4 shows a 3-dimensional delay attractor with the coordinates of measured values M (t), M (t + _τ ) and M (t + 2 _τ ) and for a delay time (delay time) _τ that _results from the Time series in Figure 2 was derived-

FIG. 5 shows an asymmetrical periodic excitation function for multiple polarization changes in an accumulator;

FIG. 6 shows a time series for the response behavior of a probe

Measuring system in an accumulator on the asymmetrical periodic excitation function in Figure 5;

FIG. 7 shows the delay attractor, which was derived from the time series in FIG. 6;

FIG. 8 shows an illustration of a chaotic excitation function for several polarization changes in an accumulator; and

FIG. 9 shows an illustration of a delay attractor that was generated from a time series of a response behavior (not shown) to the chaotic excitation function in FIG. 8.

FIG. 1 shows a schematic illustration of a lead accumulator 100 with a Pb electrode 101 and a PbO ₂ electrode 102. The two electrodes 101, 102 are arranged in an electrolyte solution 103 based on H ₂ SO ₄ . A separator 104 is positioned between the two electrodes 101, 102. A measuring probe 106, on which a measuring tip 107 is formed, is arranged in a space 105 between the two electrodes 101, 102. The measuring probe 106 is connected via a high-resistance measuring unit 108 to a circuit 109 which connects the two electrodes 101, 102. The measuring unit 108 is used to create a measuring circuit 110 for measuring a potential in the area of the measuring tip 107 opposite the Pb electrode 101. The circuit shown is closed via a load resistor 111.

In order to obtain information about the state of the lead accumulator 100, the measuring tip 107 can be positioned in any spatial points in the space 105 between the two electrodes 101, 102. In this way, local potential measurements can be carried out in the different spatial points. The measuring points can be located in the space 105 in any local positions which are relatively displaced in height or laterally with respect to the position of the measuring tip 107 shown. In the following, exemplary embodiments of a measuring method are explained with reference to FIGS. 2 to 9, in which the current is measured which flows through a measuring probe 106 between the two electrodes 101, 102 in the lead accumulator 100 when the polarization changes. The polarization change is carried out periodically (FIG. 2), asymmetrically periodically (FIG. 5) and chaotically (FIG. 7). The switching of the polarity is specified using a trigger circuit (not shown). The current which flows against the electrodes 101 or 102 when the polarity of the probe 106 is reversed can be measured, for example, as a voltage drop across a suitable shunt resistor (not shown in FIG. 1). Since this voltage drop (and also the current) is very small, a suitable amplifier is expediently used, for example based on the lock-in technique.

Depending on the given excitation function / trigger sequence (periodic, asymmetrical periodic, chaotic), a characteristic response behavior is obtained. FIG. 3 shows, by way of example, the basic response behavior of the measured variable M (for example the current measured as a voltage drop) as a function of time to a periodic trigger signal 200 according to FIG. 2. In the example, the relaxation time of the measured current is approximately Is and the time between two polarity reversals approx. 0.3s. The excitation of the examination system induced with the aid of the polarity reversal thus takes place at time intervals which are shorter than the relaxation time of the current. In parallel, it is possible that other operating parameters (e.g. a local concentration) than the measured current after the polarity reversal relax in a shorter time than the measured current, so that the excitation pulse indicated by polarity reversal is given up for the other operating parameters after the relaxation time has expired.

Switching the polarization - indicated in FIG. 3 by dashed vertical lines 201 - of the measuring probe 106 alternately produces a positive deflection 202 and a negative deflection 203 of the measured variable M, which corresponds to a capacitive current, ie a charge flow caused by the change in polarization , In Figure 3, three measured values M (t), M (t + _τ ) and M (t + 2 _τ ) are shown as an example, which result at equal time intervals _τ at the times t, t + _τ and t + 2 _τ , where _{τ is} the Delay time is.

FIG. 4 shows a graphic representation of the time profile of an overall variable P derived from the measured values M (t), M (t + _τ ) and M (t + 2 _τ ) according to FIG. 3 in a so-called delay phase space. The measured values M (t), M (t + _τ ) and M (t + 2 _τ ) span a 3-dimensional, orthogonal coordinate system in which each point P is divided by three by vector addition. measured values offset from one another by the delay time _τ . This is shown in FIG. 4 as an example for the point P (M (t), M (t + _τ ), M (t + 2 _τ )), which results from the corresponding three measured values from FIG. 3. Arrows 204 indicate the direction of movement of the time course of point P. The diversity that results from the movement of this point P, the so-called attractor of the system, reflects the properties in a characteristic manner, particularly with regard to the dynamics of the system.

The attractor shown in FIG. 4 is typical of an (unstable) examination system that oscillates around a fixed point but does not run into it. This corresponds to the fact that the examination system is always disturbed before entering a stationary state, i.e. is driven into the reversed, non-stationary state. Furthermore, it can be concluded from the property of the attractor in FIG. 4 that the point P, due to a period of the trigger signal, ends up near the original position after a revolution, but not exactly there, that it is potentially a chaotic investigation system is. Quantitative information about the dynamics and thus also the chaotic properties of the system can be obtained from the Lyapunov exponents of the time series, which characterize their long-term behavior in a linear approximation. If the maximum Lyapunov exponent is positive, the system exhibits chaotic dynamics; and the magnitude of its value (for equal observation intervals) is a measure of the predictability of the system.

If one applies these considerations to the measuring system shown in FIG. 1, the response behavior of the accumulator 100, which can be registered with the aid of a current measurement, is a function of the physical (temperature) and electrochemical (for example acid density / electrolyte properties) properties of the system , The properties of the accumulator 100 depend on the state of the accumulator 100, which is characterized, for example, by a specific charge / discharge state or state of aging. Depending on the state of the battery, 100 different Lyapunov exponents can be determined. The attractor of a basic response behavior shown in FIG. 4 for a current profile measured as a voltage drop changes its shape in a characteristic manner depending on periodic triggering from non-stationary conditions depending on, for example, the state of charge, the state of aging, the state of stress or the temperature, for example in its space filling. This is of course also expressed in the corresponding Lyapunov exponents. So you can With the help of the evaluation of the current measurement in the case of a periodic change in polarization, information about the state of charge of the battery 100 can be obtained.

An asymmetrical variation of the excitation function / the trigger signal changes the Fourier spectrum of the driving trigger signal, i.e. the excitation function and thus also the response behavior of the overall system, which includes the accumulator 100 and the measuring probe 106. FIG. 5 shows an example of an asymmetrically periodic trigger sequence 205, and FIG. 6 shows in principle the resulting response behavior of the measured variable M. In the selected example, the polarization state is excited only briefly with the positive deflection 206, i.e. the system cannot relax from this into the steady state, while the polarization state with the negative deflection 207 is maintained for a sufficiently long time and the system can relax steady state 208 in this case.

FIG. 7 shows the attractor derived from the time series shown in FIG. 6. This attractor is typical of a system which runs around the fixed point 211 when passing through the positive half space, indicated by the revolving arrow 209, while it runs into the fixed point 211 when passing through the negative half space, indicated by the revolving arrow 210 and is stimulated into the positive half-space only after a certain dwell time.

If one proceeds to the chaotic trigger signal (see FIG. 8), namely a sequence of excitation pulses that is not periodic in a finite time interval, the discrete Fourier spectrum of the example of periodic triggering given above (see FIG. 2) becomes dense in a quasi-continuous spectrum lying frequencies transforms and gives the system the possibility to react to the external stimulation in various ways. As expected, the structure of the chaotic attractor of the response behavior (see FIG. 9) differs for different charge states of the accumulator 100 as well as that of the attractors in the case of periodic and asymmetrically periodic driving.

The features of the invention disclosed in the above description, the claims and the drawing can be of importance both individually and in any combination for realizing the invention in its various embodiments.

Claims

Expectations

1. Method for measuring a physical / chemical operating parameter for an examination system, in particular an electrochemical cell, in which the examination system is acted upon several times with the aid of excitation impulses of a physical quantity influencing the examination system in order to bring the examination system into a relaxable, non-stationary state to be stimulated, from which the examination system regarding the physical / chemical operating parameters can relax into a stationary state of the examination system in a relaxation time characteristic of the physical / chemical operating parameters of the examination system, and the physical / chemical operating parameters are measured when the examination system relaxes, characterized in that the examination system is subjected to successive excitation pulses corresponding to an excitation function in which the successive excitation pulses can excite the examination system at a time interval which is shorter than the relaxation time characteristic of the physical / chemical operating parameters of the examination system.

2. The method according to claim 1, characterized in that a spectrum of the excitation function is formed in a frequency space of at least two harmonic functions.

3. The method according to claim 1 or 2, characterized in that the examination system is excited with the successive excitation pulses of a periodic excitation function accordingly.

4. The method according to claim 1 or 2, characterized in that the examination system is excited with the successive excitation pulses of an asymmetrically periodic excitation function accordingly.

5. The method according to claim 1 or 2, characterized in that the examination system is excited with the successive excitation pulses of a chaotic excitation function accordingly.

6. The method according to any one of the preceding claims, characterized g e k e nn z e i c hn e t that a temporally chaotic behavior is measured and evaluated for the physical / chemical operating parameters.

7. Use of the method according to one of claims 1 to 6 for measuring an electrical parameter with the aid of an electrical measuring probe in an electrochemical cell, in particular a battery, wherein a polarization change between a negative and a positive cell element is carried out by means of the successive excitation pulses.