CN111539171B - Time constant estimation method independent of initial point - Google Patents
Time constant estimation method independent of initial point Download PDFInfo
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- CN111539171B CN111539171B CN202010316181.4A CN202010316181A CN111539171B CN 111539171 B CN111539171 B CN 111539171B CN 202010316181 A CN202010316181 A CN 202010316181A CN 111539171 B CN111539171 B CN 111539171B
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Abstract
The invention relates to a time constant estimation method in a measurement system, in particular to a time constant estimation method which does not depend on an initial point, comprising the following steps of x And equivalent capacitance C x The measuring circuit of the equivalent circuit and the equivalent circuit of the measured object is composed, and the measuring circuit is composed of an ideal constant voltage source V in (t), relay KV and protection resistor R 0 And measuring resistance R m Composition, and obtaining τ, R according to KCL and KVL laws and formulas (1) - (8) x 、C x And t 0 Values. The method has the advantages of greatly shortening the test time, obviously improving the efficiency of a test system, not depending on the initial point of time, having strong feasibility of a test scheme, eliminating noise and ripple interference by filtering and improving the measurement precision. The method is suitable for measuring the first-order system and is also suitable for a high-order system with only one closed-loop dominant pole.
Description
Technical Field
The invention relates to a time constant estimation method in a measurement system, in particular to a time constant estimation method independent of an initial point.
Background
In the first-order measurement system, noise and errors are inevitably introduced, and if the time constant of the system is large, the measurement system can be stabilized in several minutes or even tens of minutes, which obviously cannot meet the engineering actual measurement requirement. For example, when the insulation resistance is measured in the working gap of the motor, the time constant is large due to the fact that the equivalent capacitance value between windings of the motor and between the windings and the ground is large, and if the time constant is obtained after the system to be measured reaches a steady state, the measuring time is long, and the working efficiency of the measuring system and the motor is reduced. Aiming at the phenomenon, a learner proposes a method for estimating a time constant according to a transient stage mathematical model of a first-order circuit, and the method can accurately estimate the time constant under the condition of defining a time initial point.
Disclosure of Invention
In order to solve the technical problems, the invention provides a time constant estimation method independent of an initial point. The method can greatly shorten the measurement time, remarkably improve the efficiency of a measurement system, does not depend on a time initial point, and has strong feasibility.
The technical scheme adopted by the invention is as follows: a time constant estimation method independent of initial point includes the steps of using equivalent resistor R x And equivalent capacitance C x The measuring circuit of the equivalent circuit and the equivalent circuit of the measured object is composed, and the measuring circuit is composed of an ideal constant voltage source V in (t), relay KV and protection resistor R 0 And measuring resistance R m Composition, and according to KCL and KVL law, the following formula (1) is obtained:
in the above formula (1)，V Rm (t) is the measured voltage, τ is the time constant, R all ＝R 0 +R m ，t 0 As a time initial point after the relay KV is completely closed, the following formula (2) is obtained from the formula (1):
in the above formula (2), n (t) is noise generated by the measurement circuit, and after filtering K (t) and introducing a constant a, the expression of K (t) is the following formula (3):
according to formula (3) and incorporating variable K f (t) to give the following formula (4):
t in the above formula (4) 3 -t 2 ＝t 2 -t 1 =Δt, thereby solving τ.
Further, substituting the above-described solved τ value into the above-described formula (3) yields the following formula (5):
according to any two equations in the above formula (5), the following formula (6) is obtained:
r is obtained from the above formula (6) x And A.
Further, the following formula (7) is obtained from the above formula (6) and formula (1):
from the above 4, the above formula (7) gives C x 。
Further, from the above formula (6) and formula (3), the following formula (8) is obtained:
from the above formula (8), t is obtained 0 。
According to the technical scheme, the test time of the method is greatly shortened, the efficiency of a test system is obviously improved, the method does not depend on a time initial point, the feasibility of the test scheme is strong, noise and ripple interference are eliminated through filtering, and the measurement accuracy is improved. The method is suitable for measuring the first-order system and is also suitable for a high-order system with only one closed-loop dominant pole.
Drawings
Fig. 1 is a circuit diagram of the components of the measuring circuit and the object equivalent circuit of the present invention.
Detailed Description
The invention is described in further detail below in conjunction with fig. 1:
the invention provides a time constant estimation method independent of initial point, which is shown in the figure 1 as an equivalent circuit of a measured object in a dotted line frame, and comprises an equivalent resistor R x And equivalent capacitance C x Composition is prepared. Outside the dotted line box is a measuring circuit which is composed of an ideal constant voltage source V in (t), relay KV and protection resistor R 0 And measuring resistance R m Composition, R 0 By measuring voltage V Rm The clipping of (t) achieves protection of the later stage measurement circuit. Using KCL and KVL laws for the circuit shown in fig. 1 can be expressed as (1):
in the formula (1), tau is a time constant R all ＝R 0 +R m ，t 0 The starting measurement point after the relay KV is completely closed is also the instant initial point. The following formula (2) can be obtained from formula (1):
in the formula (2), n (t) is noise generated by a measuring circuit, in order to avoid that the noise affects the measuring precision, K (t) needs to be filtered, and after the filtering and the introduction of a constant A, the expression of K (t) is as follows formula (3):
according to formula (3) and incorporating variable K f (t) can be represented by the following formula (4):
t in (4) 3 -t 2 ＝t 2 -t 1 =Δt, thereby solving τ.
If the equivalent resistance, the equivalent capacitance and the time initial point of the measured object need to be further obtained, the method can be carried out according to the following steps:
substituting τ into formula (3) yields formula (5):
according to any two of the equations (5) (suggesting selection of t 1 And t 3 Correlation equation), R is obtained by solving the following equation (6) x And A:
from the formulae (6) and (1), formula (7) is obtained, and C is further obtained x (II), (III), (V), (; from the formulae (6) and (3), formula (8) is obtained, furtherObtaining t 0 ：
In order to verify the effectiveness of the estimation method, a test system and a tested object are equivalent to be a combination of ideal components, and the values of the components are as follows: r is R 0 ＝2MΩ，R m ＝2kΩ，t 0 ＝5.5s，R x ＝100MΩ，C x =0.5 uF. Then, V at each time point is obtained by the formula (3) Rm . The results obtained by using this estimation method are shown in the following table. The n-th set of the amounts to be calculated in the table is obtained by the (n-2), (n-1), n-th set of the known amounts. For example, the 3 rd set of variables is determined from the 1 st, 2 nd, and 3 rd set of known variables. The table shows τ, R, which are obtained by any of the three known sets of quantities x 、C x And t 0 The values are consistent with the preset values, thereby verifying the validity of the estimation method.
The above embodiments are provided for illustrating the present invention and not for limiting the present invention, so that those skilled in the relevant art can make various changes and modifications without departing from the spirit and scope of the present invention, and all equivalent technical solutions shall fall within the scope of the present invention.
Claims (4)
1. A time constant estimation method independent of initial point includes the steps of using equivalent resistor R x And equivalent capacitance C x The equivalent circuit of the measured object and the measuring circuit of the equivalent circuit are formed, and the measuring circuit is characterized in that: the measuring circuit is composed of an ideal constant voltage source V in (t), relay KV and protection resistor R 0 And measuring resistance R m Composition, and according to KCL and KVL law, the following formula (1) is obtained:
in the above formula (1), V Rm (t) is the measured voltage, τ is the time constant, R all ＝R 0 +R m ，t 0 As a time initial point after the relay KV is completely closed, the following formula (2) is obtained from the formula (1):
in the above formula (2), n (t) is noise generated by the measurement circuit, and after filtering K (t) and introducing a constant a, the expression of K (t) is the following formula (3):
according to formula (3) and incorporating variable K f (t) to give the following formula (4):
t in the above formula (4) 3 -t 2 ＝t 2 -t 1 =Δt, thereby solving τ.
2. The initial point-independent time constant estimation method according to claim 1, wherein: substituting the above-described solved τ value into the above-described formula (3) to obtain the following formula (5):
according to any two equations in the above formula (5), the following formula (6) is obtained:
r is obtained from the above formula (6) x And A.
3. The initial point-independent time constant estimation method according to claim 2, wherein: the following formula (7) is obtained from the above formula (6) and formula (1):
from the above formula (7), C is obtained x 。
4. A time constant estimation method independent of an initial point as claimed in claim 2 or 3, wherein: from the above formula (6) and formula (3), the following formula (8) is obtained:
from the above formula (8), t is obtained 0 。
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| CN107656140A (en) * | 2017-08-11 | 2018-02-02 | 中国科学院地质与地球物理研究所 | A kind of method and circuit that resistance is measured using embeded processor digital port |
| CN110096780A (en) * | 2019-04-23 | 2019-08-06 | 西安交通大学 | A kind of super capacitor single order RC network equivalent circuit and parameter determination method |
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2020
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| US4952808A (en) * | 1988-06-07 | 1990-08-28 | U.S. Philips Corp. | Thermal radiation detection apparatus |
| CN1551501A (en) * | 2003-05-12 | 2004-12-01 | 因芬尼昂技术股份公司 | Apparatus and method for calibrating resistance/ capacitor filter circuit |
| CN1543912A (en) * | 2003-11-18 | 2004-11-10 | 华中科技大学 | Method and apparatus for measuring biological tissue multi-frequency impedance |
| CN104198813A (en) * | 2014-05-09 | 2014-12-10 | 杭州电子科技大学 | Device and method for measuring impedance angle of ultrasonic energy transducer through orthogonal correlation method |
| CN107656140A (en) * | 2017-08-11 | 2018-02-02 | 中国科学院地质与地球物理研究所 | A kind of method and circuit that resistance is measured using embeded processor digital port |
| CN110096780A (en) * | 2019-04-23 | 2019-08-06 | 西安交通大学 | A kind of super capacitor single order RC network equivalent circuit and parameter determination method |
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| Anjali Chauhan ; Bahgat Sammakia ; Furat Afram ; Kanad Ghose ; Gamal Refai-Ahmed ; Dereje Agonafer.Analysing real time power of the microprocessor to estimate thermal time constant of the hotspot.13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems.2012,全文. * |
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