CN108333933A - A kind of single order pure delay system closed-loop identification method - Google Patents
A kind of single order pure delay system closed-loop identification method Download PDFInfo
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Abstract
The invention discloses a kind of single order pure delay system closed-loop identification methods.For single order pure delay system, connect proportional component k, adds unit step, and regulation and control k makes system be in boundary stable state, according to final-value theorem and Nyquist criterion, realizes the identification of systematic parameter.Original control loop need not be disconnected compared with traditional open cycle system discrimination method, reduce security risk by the present invention；Meanwhile compared to legacy system discrimination method, calculating error smaller of the invention, especially after adding noise, closed-loop identification method of the invention shows more preferably accuracy.
Description
Technical field
The invention belongs to identification technology fields, more particularly to a kind of single order pure delay system closed-loop identification method.
Background technology
Modern thermal power plant is the large-scale thermal process for being typically related to thermal energy conversion and utilizing, due to electrical energy production
Importance and electric energy cannot store on a large scale, automatic control technology be to ensure that power plant safety, economy and totally produce it is required
Technological means.In these production processes, the determination of controlled device is particularly important, and the identification of characteristic parameter determines controller
Design, therefore ensure safety on the basis of, accurately recognize controlled device characteristic parameter be that basis automatically controls neck
The research emphasis in domain.
For the System Discrimination for being in series with pure delay link in modern times open-loop transfer function, generally using the single rank of addition
Jump, profit recognize wherein parameter with the following method:For open-loop transfer function
Adding unit-step function, i.e. u (∞)=1 observes curve of output, obtains stationary value y (∞), it can thus be concluded thatRecord the starting point x of the X-axis of curve of output0, the as value of parameter τ；0.632y (∞) is found on curve of output
The value x of corresponding X-axis1, then parameter T0=x1-x0。
Although discrimination method as above is simple, premise needs to disconnect original control loop, i.e., before such method
It carries in the case of being open loop, for actual control system, there are security risks for this, if in addition, around there are the disturbances such as noise, meetings
Lead to the unstable of curve of output, to x0It is difficult to recognize and make τ that can not determine so that the identification result of other characteristic parameters increases
Error is added.Be presently recognized that, Open-loop Identification there are certain defect and closed-loop identification series connection pure delay link urgently realize.
Invention content
In order to solve the technical issues of above-mentioned background technology proposes, the present invention is intended to provide a kind of single order pure delay system is closed
Ring discrimination method, realize closed-loop case under, deposit in disturbance cases accurate system identification.
In order to achieve the above technical purposes, the technical scheme is that：
A kind of single order pure delay system closed-loop identification method, which is characterized in that include the following steps：
(1) set the open-loop transfer function of system asWherein, k0For the ratio of open-loop transfer function
Gain, T0For inertial element time constant, τ is the pure delay time, and s is Laplace operator；Connect proportional component k, adds rank
Jump response, forms closed loop negative feedback system
(2) proportional component k is adjusted, until the curve of output self-sustained oscillation of closed loop negative feedback system, and computing system is in
The frequency when stable state of boundaryWherein, T is the period of system output curve at this time；
(3) reduce k values, closed loop negative feedback system is made to reach stable state, it is fixed according to final value if the value of k is k' at this time
Reason, acquires parameterWherein, y (∞) is the final value of system output curve；
(4) s=j ω are enabled, then the open loop frequency characteristic of system isWherein, j is
Imaginary unit；According to Nyquist criterion, when boundary is stablized, G (j ω) is obtained system by point (- 1, j0)：
θ (ω)=- (arctan T0ω+ω τ)=- π
Wherein, M (ω) is system amplitude, and θ (ω) is system phase；
(5) by the frequencies omega that step (2) obtains and the parameter k that step (3) obtains0It substitutes into the M (ω) of step (4), asks
Go out parameter T0, then parameter T0It substitutes into the θ (ω) of step (4), finds out parameter τ, complete System Discrimination.
Further, in step (1), the step response of addition is unit step response.
Further, it in step (3), takesWherein, k1For system output curve self-sustained oscillation when corresponding k
Value.
Further, it in step (2), is used there are when noise disturbance around systemIt is right when seeking frequency
In the determination of cycle T, selection at least five cycle time is needed to be averaging the period again.
Further, in step (3), the wave crest and trough difference of disturbance are taken there are when noise disturbance around system
5 points are at least taken, are averaged respectively, obtain wave crest mean value and trough mean value, then to wave crest mean value and trough mean value group mean, obtain
To the final value y (∞) of system output curve.
The advantageous effect brought using above-mentioned technical proposal：
The present invention is a kind of Identification of Closed-loop Systems, need not be by this compared with traditional open cycle system discrimination method
The control loop come disconnects, and reduces security risk；Meanwhile compared to legacy system discrimination method, calculating error of the invention
Smaller, especially after adding noise, closed-loop identification method of the invention shows more preferably accuracy.
Description of the drawings
Fig. 1 is the change curve of the steady timing output y in closed-loop system boundary in embodiment；
Fig. 2 is the change curve of the steady timing output y of closed-loop system in embodiment；
Fig. 3 is the change curve of the steady timing output y in closed-loop system boundary after addition noise in embodiment；
Fig. 4 is the change curve of the steady timing output y of closed-loop system after addition noise in embodiment；
Fig. 5 is the change curve for exporting y in embodiment after addition noise in Open-loop Identification；
Fig. 6 is the flow chart of the present invention.
Specific implementation mode
Below with reference to attached drawing, technical scheme of the present invention is described in detail.
The present embodiment utilizes identification of the Mtlab softwares to pure delay open-loop transfer function, first sets a transmission function：
This transmission function is in the identification process of the present embodiment, each parameter：k0=1.6, T0=10 and τ=3 conduct
Unknown quantity, this discrimination method determine k by the change curve in conjunction with the stable and steady timing output y in boundary0、T0With the value of τ, then
It is compared with setup parameter value.
Closed loop negative feedback system, i.e. a proportional component k series connection G are made in SimulinkKAnd negative-feedback is formed, remember K0
=k0K constantly changes the value of k until so that the change curve of output y is self-sustained oscillation, curve as shown in Figure 1, i.e. closed loop system
System is in boundary stable state, at this time proportional component k=3.6816.The point of two troughs, coordinate value is taken to be respectively in Fig. 1
(122, -0.0788) and (176.1, -0.0789), and 5 periods are differed, take multiple periods to be herein to take being averaged for period
It is worth and makes calculated value more acurrate./ 5th of the difference of 2 abscissas are the period, then according to the following formula can calculated rate ω：
Solve ω=0.5807.
Then reduce the value of k so that this closed-loop system reaches stable, this example takesOutput is bent at this time
Line reaches a stationary value, and curve as shown in Figure 2 passes through y (∞)=0.7465 known to curve.According to final-value theorem：
I.e.
K'=1.8408 and y (∞)=0.7465 is substituted into, k can be obtained0=1.5997.By result of calculation as it can be seen that at this
K under discrimination method0Calculated value and setting value 1.6 differ very little, identification result is correct.
According to K0=k0K obtains K0=5.8895.According toCalculate T0, i.e.,：
Substitute into K0=5.8895 and ω=0.5807, T can be obtained0=9.9948.Setting value T0=10, therefore this example
The result and setting value that middle identification obtains are close, then identification result almost indifference.
According to θ (ω)=- (arctanT0ω+ω τ)=- π, it can obtain：
Substitute into T0=9.9948 and ω=0.5807, τ=2.9988 can be obtained, the setting value of τ is 3, therefore this is recognized
Method can accurately recognize the open-loop transfer function of series connection pure delay link.
The variation of curve of output when adding noise in Simulink emulation, while observing boundary stabilization and stablizing is gone forward side by side
The identification of row open-loop transfer function.
When closed-loop system, which is in boundary, to be stablized, the curve for exporting y is as shown in Figure 3.Due to the addition of noise, curve occurs
Fluctuation but stability are simultaneously unaffected.Likewise, take two points for being separated by five periods, coordinate be respectively (67.75 ,-
0.1482), (121.7, -0.1582).Thus it acquires：
It can obtain ω1=0.5823.K'=1.8408, curve of output is taken to reach stable simultaneously, as shown in figure 4, but this
When due to noise influence, steady component curve fluctuation it is very big, it is difficult to determine, therefore, take the wave crest mean value and wave of the curve of cyclical fluctuations
Paddy mean of mean, wave crest and trough take five points to seek its mean value, and the coordinate of this ten points is as shown in figure 4, therefore
It can calculate：
Further according to formulaIt can be in the hope of after adding noise, k01=1.6023, result of calculation and
Setting value 1.6 is approximate, therefore the addition of noise influences less even without influence this discrimination method.
Then according to K01=k01K obtains K01=5.8989, and then obtain T01=9.9837, τ1=2.9901.It is distinguished from this
From the point of view of the result of calculation of knowledge method, T01And τ1Value and almost equal with setting value is acquired, in conclusion noise is in this example
Discrimination method does not have an immense impact on, and identification result is also without prodigious deviation.
It is an advantage of the present invention that for the system after addition noise jamming, using conventional method, i.e., in background technology
Open-loop Identification mode, for the parameter value emulated with actual setpoint there are larger difference, Open-loop Identification method is as follows：
Unit step u is added under open loop situations, obtains simulation data value y curves, as shown in Figure 5.
First, determine that output valve y starts increased coordinate points, due to the presence of noise so that the growth of starting stage is deposited
It is difficult to determine coordinate points in fluctuation, it is that y values increase starting point (3.3,0.0074) that growth rate maximum point is chosen in this example, therefore
τ'1=3.3, increase 10% compared to setting value 3, it can be seen that, in surrounding there are in the case of noise, conventional open-loop recognizes
For method to the determination of delay time there are prodigious error, this error is unavoidable.
It determines that the stationary value after noise is added is similar with this example, the average value disturbed after stablizing is taken, as Fig. 5 takes ten at random
A coordinate points, are calculated：
Therefore,This calculated value is more accurate.
A coordinate points, corresponding time coordinate and τ ' are determined at the 62.3% of stationary value1Difference be time constant T
'01.According to above formula 0.632*y'1(∞)=1.0094, then time constant respective coordinates are (13.03,1.01).Thus may be used
Obtain T'01=13.03-3.3=9.73.This result of calculation and setting value difference are larger, this and τ '1Selection also have much relations,
Illustrate that the interference of noise makes conventional open-loop discrimination method lose higher accuracy.
When noise is added in list observation in simulations, the difference for the load transfer function coefficient that Open-loop Identification goes out with closed-loop identification is such as
Shown in table 1：
Table 1
| Parameter | k0 | T0 | τ |
| Setting value | 1.6 | 10 | 3 |
| Closed-loop identification | 1.6023 | 9.9837 | 2.9901 |
| Open-loop Identification | 1.5972 | 9.73 | 3.3 |
It is observed with being apparent from from table 1, the parameter that closed-loop identification method of the invention picks out and setting value are more
It is close.The entire flow of the present invention is as shown in Figure 6.
Embodiment is merely illustrative of the invention's technical idea, and cannot limit protection scope of the present invention with this, it is every according to
Technological thought proposed by the present invention, any change done on the basis of technical solution, each falls within the scope of the present invention.
Claims (5)
1. a kind of single order pure delay system closed-loop identification method, which is characterized in that include the following steps：
(1) set the open-loop transfer function of system asWherein, k0Increase for the ratio of open-loop transfer function
Benefit, T0For inertial element time constant, τ is the pure delay time, and s is Laplace operator；Connect proportional component k, adds step
Response forms closed loop negative feedback system
(2) proportional component k is adjusted, until the curve of output self-sustained oscillation of closed loop negative feedback system, and computing system is in boundary
Frequency when stable stateWherein, T is the period of system output curve at this time；
(3) reduce k values, closed loop negative feedback system is made to reach stable state, if the value of k is that k' is asked according to final-value theorem at this time
Obtain parameterWherein, y (∞) is the final value of system output curve；
(4) s=j ω are enabled, then the open loop frequency characteristic of system isWherein, j is imaginary number
Unit；According to Nyquist criterion, when boundary is stablized, G (j ω) is obtained system by point (- 1, j0)：
θ (ω)=- (arctanT0ω+ω τ)=- π
Wherein, M (ω) is system amplitude, and θ (ω) is system phase；
(5) by the frequencies omega that step (2) obtains and the parameter k that step (3) obtains0It substitutes into the M (ω) of step (4), finds out parameter
T0, then parameter T0It substitutes into the θ (ω) of step (4), finds out parameter τ, complete System Discrimination.
2. single order pure delay system closed-loop identification method according to claim 1, which is characterized in that in step (1), addition
Step response be unit step response.
3. single order pure delay system closed-loop identification method according to claim 1, which is characterized in that in step (3), takeWherein, k1For system output curve self-sustained oscillation when corresponding k values.
4. single order pure delay system closed-loop identification method according to claim 1, which is characterized in that exist around system and make an uproar
When acoustic disturbance, in step (2), useWhen seeking frequency, the determination for cycle T needs to choose at least five period
Time is averaging the period again.
5. single order pure delay system closed-loop identification method according to claim 1, which is characterized in that exist around system and make an uproar
When acoustic disturbance, in step (3), takes the wave crest of disturbance and trough at least to take 5 points respectively, be averaged respectively, it is equal to obtain wave crest
Value and trough mean value, then to wave crest mean value and trough mean value group mean, obtain the final value y (∞) of system output curve.
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| CN111061150A (en) * | 2019-10-23 | 2020-04-24 | 南京大学 | Hardware implementation method and system of Laplace frequency response |
| CN112180801A (en) * | 2020-10-13 | 2021-01-05 | 郑州大学 | Control method of process control system |
| CN112198789A (en) * | 2020-09-11 | 2021-01-08 | 匙慧（北京）科技有限公司 | Object recognition method in closed loop system, electronic device, and computer-readable storage medium |
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| CN111061150A (en) * | 2019-10-23 | 2020-04-24 | 南京大学 | Hardware implementation method and system of Laplace frequency response |
| CN111061150B (en) * | 2019-10-23 | 2020-11-27 | 南京大学 | Hardware implementation method of Laplace frequency response |
| CN112198789A (en) * | 2020-09-11 | 2021-01-08 | 匙慧（北京）科技有限公司 | Object recognition method in closed loop system, electronic device, and computer-readable storage medium |
| CN112180801A (en) * | 2020-10-13 | 2021-01-05 | 郑州大学 | Control method of process control system |
| CN112180801B (en) * | 2020-10-13 | 2021-07-09 | 郑州大学 | Control method of process control system |
| CN113050419A (en) * | 2021-03-03 | 2021-06-29 | 华电莱州发电有限公司 | Closed loop system identification method based on slope response and known time lag and considering feedforward |
| CN113050419B (en) * | 2021-03-03 | 2022-11-08 | 华电莱州发电有限公司 | Closed loop system identification method based on slope response and known time lag and considering feedforward |
| CN113885311A (en) * | 2021-09-18 | 2022-01-04 | 东南大学溧阳研究院 | Closed-loop identification method for combustion chamber model of gas turbine based on generalized frequency method |
| CN113885311B (en) * | 2021-09-18 | 2024-04-16 | 东南大学溧阳研究院 | Gas turbine combustion chamber model closed-loop identification method based on generalized frequency method |
| CN114237043A (en) * | 2021-11-29 | 2022-03-25 | 东南大学溧阳研究院 | Gas turbine equipment transfer function closed-loop identification method based on deep learning |
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