CN108594646A - A kind of unstable Continuous-time System Identification method based on filtering about point-score - Google Patents
A kind of unstable Continuous-time System Identification method based on filtering about point-score Download PDFInfo
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- CN108594646A CN108594646A CN201810201437.XA CN201810201437A CN108594646A CN 108594646 A CN108594646 A CN 108594646A CN 201810201437 A CN201810201437 A CN 201810201437A CN 108594646 A CN108594646 A CN 108594646A
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract
The present invention relates to a kind of unstable Continuous-time System Identification methods based on filtering about point-score, including：The input and output signal of acquisition system, by the model to be identified of unstable continuous system after the filter filtering of setting, the unstable pole in model to be identified is set to be reduced by filter, the system converting systems stabilisation for original system same order, then System Discrimination is carried out by particle swarm optimization algorithm.Compared with prior art, the present invention converts time-dependent system to systems stabilisation, can solve the identification problems of model of Linear Invariant Unstable Systems using the dynamic reduction of a fraction technology that identification model is filtered is treated；The optimizing to identification of Model Parameters is completed using particle swarm optimization algorithm to work, and has many advantages, such as that search speed is fast, efficient.
Description
Technical field
The present invention relates to a kind of system identifying methods, more particularly, to a kind of unstable continuous system based on filtering about point-score
System discrimination method.
Background technology
With the development of automation science and technology, the requirement to industrial stokehold precision is also higher and higher.Obtain and establish work
The mathematical model of industry process control objects is not only the key precondition of Control System Design and analysis, and established model is accurate
Property also has large effect to control effect.So the accurate model for establishing control object has become urgent being essential of automation science and technology
It wants.The mathematical model for establishing control object needs to use system identifying method.But current system identifying method is only limitted to surely
Determine system；There are problems that identification calculates diverging for time-dependent system.And in actual industrial stokehold, exist quite
More unstable control objects, as chemical plant polymerization process, helicopter pitch control process, water turbine governing process,
Magnetic-suspension automobile engine valve control process etc..So the identification problem research for erratic process has important show
Sincere justice.
Many scholars conduct a research also directed to erratic process identification problem and achieve certain achievement.For unstable
System Discrimination has scholar to propose a kind of two-step method：Estimate the sensitivity simultaneously using reference input, outputting and inputting for process first
Sensitivity function is supplied, model is then estimated using the output of process of the input of process estimation and first step acquisition.But it should
Method is difficult to estimate non-dominant pole when noise is bigger.There is scholar's proposition is a kind of to use Degree Reduction Algorithm by High-order Transfer Functions
It is reduced to the discrimination method of the transmission function of predetermined structure, but this method depends on the dynamic characteristic of process and controller.Also learn
Person proposes that a kind of subspace state space system identification carrys out identification model, but when containing there are two when unstable pole in the presence of loss numerical precision
Problem simultaneously leads to estimate that the phase diagram of model deviates realistic model.Therefore, the identification problem of erratic process is needed newly
Discrimination method.
Invention content
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide one kind based on filtering reduction of a fraction
The unstable Continuous-time System Identification method of method.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of unstable Continuous-time System Identification method based on filtering about point-score, including：Acquisition system is output and input
Signal makes the shakiness in model to be identified by the model to be identified of unstable continuous system after the filter filtering of setting
Determine pole to be reduced by filter, the system converting systems stabilisation for original system same order, then is carried out by particle swarm optimization algorithm
System Discrimination.
Preferably, the model to be identified is：
Wherein, y (t) is the output signal of system, and u (t) is the input signal of system, and A (p) is the transmission operator G of system
(p) denominator polynomials, B (p) is the molecule multinomial of G (p), and A (p) and G (p) is relatively prime polynomial, and τ is delaying for system
Time constant, v (t) are noise signal.
Preferably, the transmission operator of the filter is：
Wherein, Bf(p) it is Gf(p) molecule multinomial is unstable in the denominator polynomials by the transmission operator of system
The multinomial that pole is constituted；Af(p) it is Gf(p) denominator polynomials are and Bf(p) multinomial of same order, and Af(p) feature
The real part of root is respectively less than 0.
Preferably, the setting of time constant filter is gathered using examination in the denominator polynomials of the transmission operator of the filter
Method.
Preferably, the process that System Discrimination is carried out by particle swarm optimization algorithm includes：
S1：According to the characteristic of system, population size and search space dimension are determined, and initialize speed and the position of group
It sets；
S2：Calculate the new speed of each particle and position；
S3：The fitness of the particle of calculating parameter identification；
S4：To each particle, its fitness value is made comparisons with the desired positions that it is lived through, if preferably, by it
As current desired positions, otherwise carry out in next step；
S5：To each particle, its fitness value is made comparisons with the desired positions that the overall situation is undergone, if preferably, it will
Otherwise it is carried out in next step as current global desired positions；
S6：Judge whether algorithm meets end condition, algorithm stops if reaching end condition, and current optimum individual is made
For parameter identification result；Otherwise, circulation step S2~S5.
Preferably, the fitness of the particle of the parameter identification is：
Wherein, θ is the parameter of model to be identified, and N is data length, tkIndicate T at timed intervalssThe time of sampling, y
(tk) indicate tkThe output signal at moment,For the estimated value of model to be identified output.
Compared with prior art, the present invention, will be unstable using the dynamic reduction of a fraction technology that identification model is filtered is treated
System converting is systems stabilisation, can solve the identification problems of model of Linear Invariant Unstable Systems；Using particle swarm optimization algorithm
It completes the optimizing to identification of Model Parameters to work, has many advantages, such as that search speed is fast, efficient.
Specific implementation mode
With reference to specific embodiment, the present invention is described in detail.The present embodiment is based on the technical solution of the present invention
Implemented, give detailed embodiment and specific operating process, but protection scope of the present invention be not limited to it is following
Embodiment.
The application is directed to the erratic process in closed-loop control system, proposes a kind of unstable company based on filtering about point-score
Continuous system identifying method, including：The input and output signal of acquisition system passes through the model to be identified of unstable continuous system
After the filter filtering of setting, the unstable pole in model to be identified is made to be reduced by filter, it is system converting to be and original system
The systems stabilisation of same order, then System Discrimination is carried out by particle swarm optimization algorithm (PSO).
System structure to be identified is known, is needed to delay time constant, the zero of system, stable pole in model
Point, filter the parameter of molecule recognized.Wherein, model to be identified is：
In formula, y (t) is the output signal of system, and u (t) is the input signal of system, and A (p) is the transmission operator G of system
(p) denominator polynomials, B (p) is the molecule multinomial of G (p), and A (p) and G (p) is relatively prime polynomial, and τ is delaying for system
Time constant, v (t) are noise signal.
If identification model output isThen the output error of system is as follows：
Since A (p) has unstable pole, then φOE(t) it dissipates.
The transmission operator of the filter set as：
Wherein, Bf(p) it is Gf(p) molecule multinomial is unstable in the denominator polynomials A (p) by the transmission operator of system
The multinomial that fixed pole is constituted；Af(p) it is Gf(p) denominator polynomials are and Bf(p) multinomial of same order, and Af(p)
The real part of characteristic root is respectively less than 0.
It is obtained after the filtered device filtering of system output y (t)：
Because of B in formulaf(p) it is the multinomial being made of pole unstable in A (p), Bf(p) with the common factor of A (p)
For Bf(p), remaining part is denoted as A after the two reduction of a fraction*(p), i.e. A (p)=A*(p)·Bf(p), this process is known as filtering about
Point.
System y after filtered reduction of a fractionf(t) stable polar point of original system is remained, system at this time has been converted into stabilization
System, output error are expressed as：
Since after filtered, G (p) Gf(p) unstable pole is not contained, so φ 'OE(t) it does not dissipate.
The molecule of filter is continually changing in identification process, that is, forms so-called dynamic reduction of a fraction process.Filtering
The molecular parameter of device gradually converges on the unstable pole of system as parameter to be identified with the increase of iterations, but filters
The denominator parameter of wave device then will rule of thumb value, the denominator parameter of filter refers to time constant filter here.As long as filtering
Time constant is selected in appropriate range, so that it may to obtain can converge to the identification result of true value.The transmission operator of filter
The setting of time constant filter uses trial and error procedure in denominator polynomials, specially：When the priori of systematic inertia time constant
When knowledge, time constant filter can be selected by its order of magnitude, when no priori, when first can arbitrarily set a filtering
Between constant debate knowledge and calculate, after obtaining identification result, then substitute into model to be identified the identified parameters value of calculating, to
To the inertia time constant of system, the time constant filter being more suitable for is reset according to obtained inertia time constant and is carried out newly
It debates knowledge to calculate, by the accuracy of input and output signal data verification result, adjusts time constant filter repeatedly until obtaining
Satisfied identification result.
The process that System Discrimination is carried out by particle swarm optimization algorithm specifically includes：
S1：According to the characteristic of system, population size and search space dimension are determined, and initialize speed and the position of group
It sets；
S2：Calculate the new speed of each particle and position；
S3：The fitness of the particle of calculating parameter identification；
S4：To each particle, its fitness value is made comparisons with the desired positions that it is lived through, if preferably, by it
As current desired positions, otherwise carry out in next step；
S5：To each particle, its fitness value is made comparisons with the desired positions that the overall situation is undergone, if preferably, it will
Otherwise it is carried out in next step as current global desired positions；
S6：Judge whether algorithm meets end condition, algorithm stops if reaching end condition, and current optimum individual is made
For parameter identification result；Otherwise, circulation step S2~S5.
Wherein, the fitness of the particle of parameter identification is：
In formula, θ is the parameter of model to be identified, and N is data length.Under normal conditions, data are output and input with discrete
Time sampling obtains, tkIt indicates to press constant time intervals TsThe time of sampling, y (tk) indicate tkThe output signal at moment,For the estimated value of model to be identified output.
Embodiment
Contain the unstable second order system of a unstable pole for some, it is assumed that its accurate model is
Assuming that being to carry out System Discrimination under closed-loop system, the controller in closed-loop control system is PID controllerIn the present embodiment, the parameter of PID controller is Kp=3.6622, Ki=1.3469,
Kd=2.4628.
In the present embodiment, using MATLAB softwares, with Ts=1ms is the sampling interval, and identification number is obtained by l-G simulation test
According to { uk,yk, it is approaching to reality process, coloured noise has been superimposed in l-G simulation testWherein ε (t)
The white noise for being zero for mean value.
Filter Gf(p) denominator is set as 1.5s+1, to the Identification Data that emulation experiment obtains, using particle group optimizing
Algorithm carries out System Discrimination, using iterations as algorithm end condition, PSO parameter settings：Iterations G=200, population
S=30, inertia weight ω linearly decrease to 0.4 by 0.9.Identification result as shown in Table 1 is obtained, the System Discrimination phase in table 1
It is to percentage error residual quantity
Wherein, θiFor i-th of parameter of model to be identified,For the estimated value of i-th of parameter of model to be identified.
1 System Discrimination result of table
| Parameter | K | T1 | T2 | τ | δ % |
| Actual value | -2 | -1 | 1.5 | 0.2 | 0 |
| Identification result | -2.0000 | -0.9999 | 1.4981 | 0.1994 | 0.0739% |
As seen from the results in Table 1, for the present embodiment unstable second order system to be identified, with the System Discrimination side of the present invention
The identification result of approximate unbiased can be obtained in method, and error percentage δ % are within 0.1%, it was demonstrated that the system that the application proposes is distinguished
The validity that knowledge method recognizes continuous time-dependent system.
Claims (6)
1. a kind of unstable Continuous-time System Identification method based on filtering about point-score, which is characterized in that including：Acquisition system it is defeated
Enter and output signal makes model to be identified by the model to be identified of unstable continuous system after the filter filtering of setting
In unstable pole reduced by filter, the system converting systems stabilisation for original system same order, then pass through particle group optimizing
Algorithm carries out System Discrimination.
2. a kind of unstable Continuous-time System Identification method based on filtering about point-score according to claim 1, feature exist
In the model to be identified is：
Wherein, y (t) is the output signal of system, and u (t) is the input signal of system, and A (p) is the transmission operator G's (p) of system
Denominator polynomials, B (p) is the molecule multinomial of G (p), and A (p) and G (p) is relatively prime polynomial, and τ is the delay time of system
Constant, v (t) are noise signal.
3. a kind of unstable Continuous-time System Identification method based on filtering about point-score according to claim 2, feature exist
In the transmission operator of the filter is：
Wherein, Bf(p) it is Gf(p) molecule multinomial is pole unstable in the denominator polynomials by the transmission operator of system
The multinomial of composition；Af(p) it is Gf(p) denominator polynomials are and Bf(p) multinomial of same order, and Af(p) characteristic root
Real part is respectively less than 0.
4. a kind of unstable Continuous-time System Identification method based on filtering about point-score according to claim 3, feature exist
In the setting of time constant filter is using trial and error procedure in the denominator polynomials of the transmission operator of the filter.
5. a kind of unstable Continuous-time System Identification method based on filtering about point-score according to claim 1, feature exist
In the process for carrying out System Discrimination by particle swarm optimization algorithm includes：
S1：According to the characteristic of system, population size and search space dimension are determined, and initialize speed and the position of group；
S2：Calculate the new speed of each particle and position；
S3：The fitness of the particle of calculating parameter identification；
S4：To each particle, its fitness value is made comparisons with the desired positions that it is lived through, if preferably, as
Otherwise current desired positions carry out in next step；
S5：To each particle, its fitness value is made comparisons with the desired positions that the overall situation is undergone, if preferably, made
For current global desired positions, otherwise carry out in next step；
S6：Judge whether algorithm meets end condition, algorithm stops if reaching end condition, using current optimum individual as ginseng
Number identification result；Otherwise, circulation step S2~S5.
6. a kind of unstable Continuous-time System Identification method based on filtering about point-score according to claim 5, feature exist
In the fitness of the particle of the parameter identification is：
Wherein, θ is the parameter of model to be identified, and N is data length, tkIndicate T at timed intervalssThe time of sampling, y (tk) table
Show tkThe output signal at moment,For the estimated value of model to be identified output.
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