CN110032145A - A kind of servo system identification method based on relay position feedback phase path curve matching - Google Patents
A kind of servo system identification method based on relay position feedback phase path curve matching Download PDFInfo
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Abstract
The present invention discloses a kind of servo system identification method based on relay position feedback phase path curve matching, it is related to the fields such as servo control, this method is based on relay feedback technology and optimization curves fitting is realized, implementation step are as follows: setting experiment parameter and relay parameter；Relay position pump back test is carried out, record displacement and speed data obtain practical phase plane trajectory；The initial value of cost function parameter is set；It carries out curve fitting and according to fitting result corrected parameter initial value, until matched curve is consistent with actual curve；Determine servo system models and its parameter.The present invention can avoid the shortcomings that least squares identification servo-system requires acceleration information, there is no the Approximation Problems based on describing function method frequency domain identification, it can be with the less higher identification precision of servo-system acquisition of information, and have runing time short, easily realize on site, the advantages that debugging process is flexible provides foundation to improve movenent performance and the system reliability of servo-system.
Description
Technical field
The present invention relates to movement control technology fields, more particularly to a kind of relay position feedback phase path curve that is based on to intend
The servo system identification method of conjunction.
Background technique
With the development of manufacture and control technology, the servo-system with precise speed and position control potential is widely applied
In modern industry, the effect of control core is played.But the precision of servo-system due to external interference, frictional force etc. because
Element is restricted, and the method that some compensators, System design based on model device etc. improve servo system control precision has obtained
To extensive use, but these methods are mostly based on what high-precision servo parameter was designed and developed, therefore high-precision watch
Dress system discrimination method receives the concern of numerous control field exploitation designers.
Servo system identification method can be divided into on-line identification and off-line identification two major classes.On-line identification method such as recursion
Least square method (RLS) etc. mainly recognizes the identification of the model parameter of some time-varying and the transient state convergence of parameter identification, offline
Discrimination method least square method, frequency sweep method etc. are widely applied in the identification field of the constant parameter of clock synchronization, but
It is least square method in the presence of the shortcomings that needing acceleration information, and outer using needs when the identification such as least square method, frequency sweep method
Boundary's pumping signal.Relay feedback identification method is by KJAnd TIt was proposed in 1984, this method is not required to the external world
Pumping signal can carry out servo-system identification, therefore the concern and research of simplicity and validity by numerous scholars.The party
Method is applied earliest and process control, because the delay of servo-system is smaller, it is difficult to evoke the oscillation that can be observed, therefore use
Artificial delay (Artificial Delay Time) need to be introduced when relay feedback identification method.
It is found through being retrieved to existing literature, Chinese Patent Application No. 200910051179.2, it is entitled " anti-based on relay
The AC servo automatic setting method of feedback " and Chinese Patent Application No. are 201010131841.8, entitled " anti-based on relay
The servo system control method of feedback ", which recognizes servo parameter by describing function method, and devises PID controller,
Achieve preferable control effect, but because describing function method there are approximate processing caused by error, thus controlled servo-system
Model Distinguish precision is restricted.C.Liu etc. is in document " A Relay Shaping Method for Servo
It is proposed in Mechanical System Identification " (a kind of servo system identification method of filter shape) a kind of whole
The method of shape filtering makes it closer to sine wave to reduce approximation accidentally by exporting progress shaping filter to relay module
Difference improves describing function method with this, although this method can effectively reduce approximate error and improve identification precision, increases
The workload of design filter.
Find that J.Liu etc. is in document " Servo system identification using relay through retrieval again
In feedback:A time-domain approach " (carrying out a kind of servo-system identification: time domain approach using relay feedback)
A kind of temporal signatures based on relay velocity feedback are proposed, this method can be avoided the approximate error of describing function method, but
There are the influences of the quantization error bring of velocity feedback.Chinese Patent Application No. is 201310647691.X, a kind of entitled " base
In the servo system identification method of relay position feedback temporal signatures ", which feeds back temporal signatures by relay position
It is recognized, avoids the quantization error of above-mentioned document velocity feedback and the approximate error of describing function method, but still be to pass through
Relay feedback experiment is only the certain features for obtaining limit cycle, there is a problem of that data user rate is lower.
Therefore, those skilled in the art is dedicated to developing a kind of based on relay position feedback phase path curve matching
Servo system identification method is managed by converting optimization curves fitting problems for servo-system identification problem using optimizing
It carries out curve fitting by and by phase path expression formula that the servo-system differential equation obtains, obtains servo-system ginseng to be identified
Number.
Summary of the invention
In view of the above drawbacks of the prior art, the technical problem to be solved by the present invention is to by recognizing servo-system
Problem is converted into optimization curves fitting problems, utilizes Optimum Theory and the phase path obtained by the servo-system differential equation
Expression formula carries out curve fitting, and obtains servo parameter to be identified.
To achieve the above object, the present invention provides a kind of servos based on relay position feedback phase path curve matching
System identifying method, comprising the following steps:
Step 1: being divided into linear and nonlinear two parts for servo system models, Frictional model using Coulomb friction and
Viscous friction model, with second-order modelIt is micro- according to servo-system as servo-system linear segment model
Equation is divided to obtain phase path expression formula；
Step 2: setting experiment parameter and relay module parameter, the experiment parameter include sampling time ST and total
Testing time T, the relay module parameter include artificial delay D and relay output amplitude h；
Step 3: in total testing time T, it is anti-that relay position is carried out using the artificial delay D and initial magnitude
Feedback experiment, and record displacement and the practical phase plane trajectory of speed data acquisition；
Step 4: converting optimization problem for parameter identification problem, using the optimal method of entitled interior point method, setting
The initial value of cost function parameter, a plurality of negative half-cycle track and phase path expression formula matched curve in conjunction with practical phase path,
And by fitting result corrected parameter initial value carry out cyclic curve fitting until fitting phase path it is consistent with practical phase path and
Cost function approaches 0, obtains servo system models and parameter.
Further, it is expressed described in the step 1 by the phase path of independent variable of servo parameter to be identified
Formula, when ignoring small asymmetric interference, phase path is symmetrical for positive value or negative value about relay output, therefore only need to be to positive half cycle
Phase or negative half-cycle carry out curve fitting；By deriving phase when can obtain relay output-h to the servo-system differential equation
The expression formula of track.
Further, the expression formula of phase path when relay output-h is specifically:
In formula, m is quality to be identified, fcFor Coulomb friction to be identified, b is viscous friction coefficient to be identified, and x is
Displacement, x0Expression formula for constant term, λ isH is relay output
Amplitude, the value range of h are h > fcAndWhile meeting the establishment condition of ln () function,
Meet the condition for generating stable limit cycle.
Further, in the step 2 experiment parameter and relay parameter selection, the suggestion of sampling time ST takes 1ms,
Reduce the quantization error for seeking generating when speed data；The standard of total testing time T setting are as follows: long enough is stable to obtain
Oscillating curve；Artificial delay D and relay output amplitude h is that driving servo-system generates the setting vibrated back and forth in a certain range
Parameter, relay output amplitude h need to meet condition described in claim 3；Artificial delay D is according to effective row of controlled device
Cheng Jinhang selection.
Further, in the step 4 negative half-cycle phase path be relay output be-h when phase path, using more
A negative half-cycle can effectively avoid the influence of the other factors in relay feedback experiment；By carrying out curve fitting to phase path,
Data user rate is higher, thus improves identification precision.
Further, optimization problem is converted by parameter identification problem in the step 4, the parameter of cost function is
Constant term x in servo parameter and phase path expression formula to be identified0, specifically:
Wherein [LB, UB] indicates the bound of cost function parameter, and subject to expression is limited to, i.e., in formula
Three infinitives are using the constraint condition during optimization matched curve after subject to.
Further, the value of the cost function is better more approaching 0 fitting result, i.e., cost function to a certain extent can table
Show the precision of identification result.
Further, the cost function expression formula specifically:
Wherein n indicates experimental data sum, xr (i)Indicate i-th of actual displacement in curve fitting process, x(i)Indicate root
It is displaced according to calculated i-th of expression formula,Indicate the average value of actual displacement in curve fitting process.
Further, cyclic curve is fitted in the step 4, and since cost function is non-convex about its parameter, there are multiple
Minimal point makes matched curve deviate reality to avoid unsuitable initial parameter value and range that identification result is caused to fall into minimal point
Phase path can constantly correct the initial value of cost function polytomy variable according to fitting result, finally make the phase path and reality of fitting
Border phase path is consistent.
Further, the value of cost function decides whether as the servo parameter finally recognized in the step 4,
The value value range is specifically but not limited to less than 0.001.
Compared with prior art, beneficial outcomes of the invention are as follows: the speed of servo-system is only needed relative to least square method
And displacement information, without seeking acceleration information；Relative to describing function method, its existing approximation can be effectively avoided accidentally
Difference；No longer it is to test the certain features for obtaining limit cycle by relay feedback relative to time domain approach, there is higher data benefit
With rate, and one group of relay feedback experiment is only needed to be obtained with one group of identified parameters, opposite describing function method need two groups after
Electric pump back test identification has higher efficiency for obtaining one group of identified parameters.Thus the present invention has data user rate height, efficiency
Height, identification precision is higher, and runing time is short, debugs the advantages that flexible.
It is described further below with reference to technical effect of the attached drawing to design of the invention, specific structure and generation, with
It is fully understood from the purpose of the present invention, feature and effect.
Detailed description of the invention
Fig. 1 is relay position feedback system block diagram of the invention；
Fig. 2 is the experiment porch of a preferred embodiment of the invention；
Fig. 3 is the operational flowchart of a preferred embodiment of the invention；
Fig. 4 is the relay module output figure of a preferred embodiment of the invention；
Fig. 5 is the displacement signal figure of a preferred embodiment of the invention；
Fig. 6 is the speed signal figure of a preferred embodiment of the invention；
Fig. 7 is the negative half-cycle phase path figure of a preferred embodiment of the invention；
Fig. 8 is the curve-fitting results figure of a preferred embodiment of the invention；
Fig. 9 is the system block diagram that a preferred embodiment of the invention is applied to feedforward compensation；
Figure 10 is tracking error when not compensating；
Figure 11 is based on the compensated tracking error of describing function method；
Figure 12 is based on the compensated tracking error of the present invention.
Specific embodiment
Multiple preferred embodiments of the invention are introduced below with reference to Figure of description, keep its technology contents more clear and just
In understanding.The present invention can be emerged from by many various forms of embodiments, and protection scope of the present invention not only limits
The embodiment that Yu Wenzhong is mentioned.
In the accompanying drawings, the identical component of structure is indicated with same numbers label, everywhere the similar component of structure or function with
Like numeral label indicates.The size and thickness of each component shown in the drawings are to be arbitrarily shown, and there is no limit by the present invention
The size and thickness of each component.Apparent in order to make to illustrate, some places suitably exaggerate the thickness of component in attached drawing.
Fig. 1 show a system block diagram, including relay module and servo-system, and the experiment porch of the present embodiment is ball
The servo-system of lead screw connection, including host, switch, DSPACE controller and servo mechanism, as shown in Figure 2.It should be based on relay
The servo system identification method process of position feedback phase path curve matching is as shown in figure 3, the specific implementation steps are as follows:
Step 1: building system block diagram as shown in Figure 1 in MATLAB, watches by the way that DSPACE control is as shown in Figure 2
Mechanism is taken, the quantity that load block is placed in servo mechanism is 5, and the starting of servo mechanism stops through the switch control in Fig. 2.
Step 2: setting sampling time ST is set as 1ms and seeks the quantization error generated when speed data to reduce；Setting is total
Testing time T be 3min to generate stable limit cycle；Artificial delay D is set as according to the effective travel of controlled device
0.04s；Adjustment relay output amplitude h meets condition required in step 1, is set to servo motor nominal torque
0.3, as shown in Figure 4.
Step 3: carrying out relay position pump back test, and records displacement and the practical phase plane trajectory of speed data acquisition,
Displacement is as shown in figure 5, speed signal is as shown in Figure 6.This method only needs to obtain practical phase rail by one group of relay feedback experiment
Mark can follow the steps below to obtain one group of servo parameter identification result, and the present embodiment relay feedback experiment gained is practical
Phase path is as shown in Figure 7.
Step 4: the expression formula of the optimization problem as obtained by the conversion of parameter identification problem are as follows:
[LB, UB] indicates the bound of cost function parameter in formula, and subject to expression is limited to, i.e., in formula
Three infinitives are using the constraint condition during optimization matched curve after subject to.
Cost function parameter is set: being by the upper bound that the constraint condition of above formula optimization problem can obtain viscous friction coefficient bCoulomb friction fcThe upper bound be h, according to m, b, fcPhysical significance known to its lower bound be 0；Pass through servo to be identified
Mechanism estimates that the order of magnitude of quality m to be identified is 100, and the upper bound that can obtain m is 100, not because of phase path expression formula constant term range
Know, when first fit is set as infinitely great.It therefore can be by cost function parameter (b, fc,m,x0) bound be set as LB=[0,0,
0,0,inf]；Initial value is set as initial value=[0,0,0,0].Parameter is set
After the completion of setting, carry out curve fitting in conjunction with interior point method and phase path expression formula to multiple negative half-cycles of practical phase path, because of x0
Bound is excessive and the initial value of viscous friction force coefficient b is too small, thus identification result falls into minimal point, obtains identification knot
Fruit (b, fc, m) and it is (2.1757,32.4137,0.2648), the value of cost function is 0.9904.
Pass through identification result corrected parameter initial value: x0The upper bound is set as x in identification result0Twice, lower bound and upper bound of symbol
On the contrary, the initial value of b is greater than the b value (can be set as 2 times or so) in identification result.Restart curve matching, and recycles amendment
Initial parameter value carries out curve fitting until fitting phase path is consistent with practical phase path and cost function approaches 0.Finally repair
Positive parameter bound are as follows: LB=[0,0,0,0, inf]；Initial value: initial value
=[0,0,0,0], obtained fitting result is as shown in figure 8, servo parameter (b, the f that identification obtainsc, m) be
(111.8821,49.6168,26.5488), the value of cost function are 0.0007.
To do comparison and verifying the validity of identification result, equally applicable describing function method is to servo-system shown in Fig. 2
It recognizes, servo parameter (b, the f recognizedc, m) be (103.1878,43.1648,29.2331), by the present invention and
The identification result of describing function method is applied to feedforward compensation, the system block diagram of feedforward compensation as shown in figure 9, its input is harmonic wave,
Find no matter which kind of method can greatly reduce tracking error, but based on compensation of the invention by comparison diagram 10- Figure 12
Profile error can be eliminated, and maximum tracking error can be reduced by 30% or so relative to the compensation based on describing function method,
With better compensation effect.
The present embodiment absolutely proves that the present invention rapidly and efficiently and with good identification precision can pick out servo-system
Parameter, provide foundation for the control precision and reliability of servo-system.
The preferred embodiment of the present invention has been described in detail above.It should be appreciated that the ordinary skill of this field is without wound
The property made labour, which according to the present invention can conceive, makes many modifications and variations.Therefore, all technician in the art
Pass through the available technology of logical analysis, reasoning, or a limited experiment on the basis of existing technology under this invention's idea
Scheme, all should be within the scope of protection determined by the claims.
Claims (10)
1. a kind of servo system identification method based on relay position feedback phase path curve matching, which is characterized in that including
Following steps:
Step 1: being divided into linear and nonlinear two parts for servo system models, and Frictional model is using Coulomb friction and viscous
Friction model, with second-order modelAs servo-system linear segment model, according to servo-system differential side
Journey obtains phase path expression formula；
Step 2: being arranged experiment parameter and relay module parameter, the experiment parameter include sampling time ST and total test
Time T, the relay module parameter include artificial delay D and relay output amplitude h；
Step 3: in total testing time T, relay position is carried out using the artificial delay D and initial magnitude and is fed back in fact
It tests, and records displacement and the practical phase plane trajectory of speed data acquisition；
Step 4: converting optimization problem for parameter identification problem, and using the optimal method of entitled interior point method, cost is arranged
The initial value of function parameter, a plurality of negative half-cycle track and phase path expression formula matched curve in conjunction with practical phase path, and lead to
Over-fitting modified result initial parameter value carries out cyclic curve fitting up to fitting phase path is consistent with practical phase path and cost
Function approximation obtains servo system models and parameter in 0.
2. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
It is characterized in that, using servo parameter to be identified as the phase path expression formula of independent variable described in the step 1, ignores micro-
When small asymmetric interference, phase path is symmetrical for positive value or negative value about relay output, therefore only need to be to positive half period or negative half
Period carries out curve fitting；The table of phase path when can obtain relay output-h by deriving to the servo-system differential equation
Up to formula.
3. the servo system identification method as claimed in claim 2 based on relay position feedback phase path curve matching,
It is characterized in that, the expression formula of phase path when relay output-h is specifically:
In formula, m is quality to be identified, fcFor Coulomb friction to be identified, b is viscous friction coefficient to be identified, and x is displacement,
x0Expression formula for constant term, λ isH is relay output amplitude, h
Value range be h > fcAndWhile meeting the establishment condition of ln () function, also meets and produce
The condition of raw stable limit cycle.
4. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
It is characterized in that, the selection of experiment parameter and relay parameter in the step 2, the suggestion of sampling time ST takes 1ms, and reduction is sought
The quantization error generated when speed data；The standard of total testing time T setting are as follows: long enough is bent to obtain stable oscillation
Line；Artificial delay D and relay output amplitude h is that driving servo-system generates the setting parameter vibrated back and forth in a certain range,
Relay output amplitude h need to meet condition described in claim 3；Artificial delay D according to the effective travel of controlled device into
Row selection.
5. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
Be characterized in that, in the step 4 negative half-cycle phase path be relay output be-h when phase path, using multiple negative half periods
Phase can effectively avoid the influence of the other factors in relay feedback experiment；By carrying out curve fitting to phase path, data are utilized
Rate is higher, thus improves identification precision.
6. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
It is characterized in that, convert optimization problem for parameter identification problem in the step 4, the parameter of cost function is to be identified
Constant term x in servo parameter and phase path expression formula0, specifically:
Wherein [LB, UB] indicates the bound of cost function parameter, and subject to expression is limited to, i.e. subject in formula
Three infinitives are using the constraint condition during optimization matched curve after to.
7. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
It is characterized in that, the value of the cost function is better more approaching 0 fitting result, i.e., cost function can indicate identification knot to a certain extent
The precision of fruit.
8. the servo system identification method as claimed in claim 7 based on relay position feedback phase path curve matching,
It is characterized in that, the cost function expression formula specifically:
Wherein n indicates experimental data sum, xr (i)Indicate i-th of actual displacement in curve fitting process, x(i)It indicates according to table
It is displaced up to calculated i-th of formula,Indicate the average value of actual displacement in curve fitting process.
9. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
It being characterized in that, cyclic curve is fitted in the step 4, since cost function is non-convex about its parameter, there are multiple minimal points,
Matched curve is set to deviate practical phase path to avoid unsuitable initial parameter value and range that identification result is caused to fall into minimal point,
The initial value that cost function polytomy variable can be constantly corrected according to fitting result finally makes the phase path and practical phase path of fitting
Unanimously.
10. the servo system identification method as described in claim 1 based on relay position feedback phase path curve matching,
It is characterized in that, the value of cost function decides whether as the servo parameter finally recognized in the step 4, the value value
Range is specifically but not limited to less than 0.001.
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