CN106227040A - Servosystem input offset method based on limiting control - Google Patents
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Abstract
Servosystem input offset method based on limiting control, relates to control system and optimizes field.Being to solve servosystem under the initial conditions of sinusoidal signal, the bandwidth of system is promoted limited by traditional controller design method, the problem having very amplitude decay and delayed phase under high frequency sinusoidal input signal.The present invention utilizes extremum search control method that the input of servosystem compensates the purpose reaching to improve system tracking performance under sinusoidal initial conditions.The overall structure of method is to add to compensate network outside original closed loop servo-control system, compensation way is the cosine signal of superposition and former sinusoidal input same frequency amplitude, and cosine and sine signal is given respectively different weights, weights are obtained by extreme control method, and the input signal after compensating preferably is exported as the input that system is new.The present invention is applicable to control system and optimizes occasion.
Description
Technical field
The present invention relates to control system and optimize field, be specifically related to a kind of servosystem input offset based on limiting control
Technology.
Background technology
Extreme control method is a kind of self-adaptation control method being not based on model, and the requirement to control condition is relatively low, no
Can be affected by parameter uncertainty or unknown parameters, be there is principle simple, the advantages such as amount of calculation is little.This control method is
For the method searched for and keep system (or function) extreme value.In simple terms, it is simply that deposit between system output and system input
In maximum or minima relation, when the output of system can represent with certain cost function, extremum search is used to control permissible
When the most accurately knowing or being unaware of structure or the mathematical expression of system to be searched, system input is carried out extreme value and searches
Rope, when system input variable to be searched arrives extreme point, can be so that the output of system obtains maximum or minima.?
In actual control system, due to control system parameter time varying and probabilistic feature so that between reference quantity and output
Functional relationship be difficult to be known, at this moment use extreme control method can preferably obtain desired target.At present, extreme value control
Method processed is at home and abroad obtained for relatively broad application, be mainly used in process control, solar battery array management with
And the field such as regulation of turbine blade angle when water conservancy and wind power generation.
In Servo System Design, bandwidth is the major embodiment of systematic function.High frequency sound for good the most in real time with
The input signal of track system has great significance, and during in particular for higher dynamic property, can servosystem have good
Good tracking performance is particularly important.In Servo System Design, it is the method using cascade compensation than more conventional mode
The frequency response of raising system, also has the mode using complex controll, i.e. LOCAL FEEDBACK to combine with feedforward exactly, but these methods needs
Be designed by model based on control system, they are also extremely limited for the lifting of servosystem tracking performance simultaneously
's.It is a kind of self-adaptation control method being not based on model in view of extremum search control method, it is possible to effectively solve optimizing
Problem, it is possible to utilize extreme control method to carry out Aided Design control system, completes to improve servo under sinusoidal initial conditions
The task of system tracking performance.
Summary of the invention
The present invention is to solve servosystem under the initial conditions of sinusoidal signal, traditional controller design method pair
The bandwidth of system promotes limited, the problem having very amplitude decay and delayed phase under high frequency sinusoidal input signal, thus
A kind of servosystem input offset method based on limiting control is provided.
Servosystem input offset method based on limiting control, the flow process of the method is:
Step one, by initial sinusoids input signal and compensate cosine input signal respectively with its each self-corresponding weights phase
Take advantage of, obtain two-way original input signal；
Step 2, two-way input signal step one obtained are added, it is thus achieved that total input signal；Total input signal is inputted
Servosystem, and export after servo system processes, it is thus achieved that output signal；
Step 3, the output signal described in step 2 is extracted the input signal as limiting control after envelope, and will
Described input signal carries out limiting control together with the amplitude of disturbing signal, is compensated the exploration estimated value of input weights；
Step 4, the process of repeated execution of steps one to three, until the defeated signal of servosystem goes out and original input signal
Difference be 0, using this output signal as preferable output signal, complete servosystem input offset based on limiting control.
Output signal described in step 2 is extracted the input signal as limiting control after envelope, method particularly includes:
Extract total input signal and the output signal of servosystem, it is thus achieved that the amplitude of deviation signal p, by former deviation signal p
Delayed T/4 converted after the cycle that signal q, T are sinusoidal input signal；
Calculate the most time dependentI.e. obtain the envelope of signal p, be designated as m, as extremum search control
Making preferable cost function, this cost function is: the input signal of limiting control.
In step 3, described input signal is carried out together with disturbing signal amplitude limiting control, be compensated input power
The exploration estimated value of value, method particularly includes:
Two-way extremum search process is used to search for sinusoidal input signal respectively and compensate the weights of cosine input signal；
Each road extremum search process is:
Step 3 one, by the input signal of limiting control through high pass filter filters, it is thus achieved that filtered signal；
Step 3 two, demodulated signal sin (ω t) is multiplied with the filtered signal described in step 3 one, obtains gradient letter
Breath；Wherein ω is demodulated signal angular frequency；
Step 3 three, the gradient information described in step 3 two is processed by integrator, it is thus achieved that believe after Integral Processing
Number；
After step 3 four, the Integral Processing that step 3 three is obtained signal and disturbing signal make and, it is thus achieved that the extreme value of estimation
Point, using this extreme point as the exploration estimated value compensating input weights.
In step 3, the preparation method of the amplitude of disturbing signal is:
Extract envelope according to step 3, envelope signal currency is done ratio with envelope signal maximum, by envelope signal
It is limited between 0 to 1, then passes through nonlinear transformation:
A=f (u)=B (1-e-Cu)
Obtain the amplitude of the disturbing signal changed with envelope signal；Wherein B, C are constant value set in advance；U is by envelope
Signal is limited in the value between 0-1.
The present invention utilizes extremum search control method, and the input to servosystem compensates to reach to input bar at sine
The purpose of system tracking performance is improved under part.Method is to compensate on the basis of the former sinusoidal input of servosystem, compensation side
Formula is the cosine signal of superposition same frequency amplitude, and cosine and sine signal gives different weights respectively, and weights pass through extreme value
Control method obtains, and the input signal after compensating preferably is exported as the input that system is new.
Extreme control method used in the present invention is without the concrete model of aware control system, so the most permissible
The sinusoidal input signal of optional frequency is compensated, so that output can be good at following the tracks of input signal.The present invention is entering
After row compensates, the amplitude of system output signal is consistent with input signal with phase place, has followed the tracks of input signal the most well.
Accompanying drawing explanation
Fig. 1 is the servosystem input offset principle schematic based on limiting control of the present invention；
Wherein: symbolRepresent addition relation,Representative is multiplied relation, Ar sin(ωrT) it is that the sinusoidal of system inputs letter
Number, Ar cos(ωrT) for the cosine signal compensated, ArFor input signal amplitude, ωrFor input signal angular frequency, k1,k2It is long-pending
Divide gain, h1,h2For High Pass Filter Cutoff Frequency, ω1,ω2For disturbing signal angular frequency, a is disturbing signal amplitude, and T is defeated
Entering the signal period, B Yu C is constant value to be designed, and p, q, m, u are the pilot process variable of method, and s is that Laplace transform is calculated
Son；
Fig. 2 is that the servo-control system of the embodiment of the present invention does not adds extreme value proposed by the invention under 10Hz sine inputs
The input and output contrast schematic diagram of control method；
Fig. 3 is that the servo-control system of the embodiment of the present invention applies compensation side proposed by the invention under 10Hz sine inputs
The input and output contrast schematic diagram of method；
Fig. 4 is the input and output bias envelope signal change curve schematic diagram of the embodiment of the present invention；
Fig. 5 is the compensation weights change curve schematic diagram of the embodiment of the present invention.
Detailed description of the invention
Detailed description of the invention one, combine Fig. 1 to 4 illustrate this detailed description of the invention, present invention is generally directed to servosystem
Input signal is this situation of sinusoidal signal, compensates input, improves the tracking performance of system.The main think of of embodiment of the present invention
Wanting to combine width phase control with limiting control, width phase control is used for compensated input signal, and limiting control provides width phase
Weights required for control.
In servosystem, when the input signal of system is sinusoidal signal, it is ω for signal frequencyrInput signal
For, due to the restriction of bandwidth, output signal often has the error in certain delayed phase and amplitude, and input signal
Frequency the biggest, delayed phase is the most obvious with the change of amplitude.
Assume that input signal is:
R=Ar sin(ωrt)
Wherein ArIt is amplitude and the angular frequency of input signal respectively with ω, so the output of system can be expressed as:
AyWithThe amplitude of the most corresponding output signal and delayed phase.
If wishing, the output of system keeps consistent with input signal in amplitude and phase place, needs system input signal
Phase place shifts to an earlier date phase angleAnd change amplitude, if the input value of system is r after Bu Changing simultaneously*, its amplitude is A*, order:
Because A for fixing sinusoidal input signal*,Be constant, institute so that:
r*=w1sin(ωrt)+w2cos(ωrt)
Wherein:
As can be seen from the above equation, the input signal for different frequency and amplitude can take one group of corresponding weight w1And w2
Carry out Indirect method r*, therefore design one compensates network, and the input of this network is respectively the cosine that sinusoidal signal is identical with frequency
Two input signals are weighted by signal respectively, after weighting and as the new input of system, make the output of system for newly
The response of input output desired with system keep consistent, and weights are obtained by extremum search control.
The detailed description of the invention of 1 explanation servosystem input offset method based on limiting control below in conjunction with the accompanying drawings.Side
The overall structure of method is to add to compensate network outside original closed loop servo-control system.
It will be seen that whole system block diagram can be divided into five parts from accompanying drawing 1:
1), importation is compensated.This part by initial sinusoids input signal with compensate cosine input signal and the most right
Answer weights composition, the cosine and sine signal amplitude of input is identical with frequency, after being multiplied with respective weights be added arrive and conduct
The input that servosystem is new.
2), servo-control system.This part is servo-control system, and general has the common servos such as permagnetic synchronous motor
Control object, this part includes that system input is first through the controller that traditional approach (cascade compensation, the feedforward etc.) designs
Total input that part obtains, and exported accordingly through servosystem.
3), envelope extracts part.The effect of this part is the input (cost function) obtaining limiting control part.Due to
Servosystem output is that frequency is identical with input with the deviation of input, and the sinusoidal signal that amplitude is continually changing, if taking definitely it
Value, then it has minimum zero.If but directly application is cost function, due to signal oscillating, can to the convergence rate of method very
The extremely judgement to extreme point all adversely affects, so needing to extract the amplitude of deviation signal.In order to make extremum search control
Cost function in system is the most smooth, it would be desirable to the amplitude extracting deviation signal is used as cost function.For one
For the sinusoidal deviation signal p that amplitude is continually changing, its envelope can be obtained by Hilbert transform, i.e. to former letter
Number carry out the phase shift of preferable 90 degree.Here in order to simplify calculating, by delayed for former deviation signal p T/4, (T is sinusoidal input signal
Cycle) converted after signal q, calculate the most time dependentI.e. obtain the envelope of signal p, be designated as
M, controls preferable cost function as extremum search.
4), extremum search controls part.This part comprises two identical extremum search frameworks of structure, is respectively used to search
Sinusoidal and the weights of cosine input signal, respectively include signals below and link: cost function: cost function is extremum search control
The input of part；High pass filter:Wherein s is Laplace operator, and h is High Pass Filter Cutoff Frequency, limiting control
The input of part first passes through high pass filter；Demodulated signal: sin (ω t), wherein ω is demodulated signal angular frequency, demodulation letter
Number signal multiplication obtained with high pass filter obtains gradient information；Integrator and storage gain:Wherein s is Laplce
Operator, k is storage gain, and gradient information needs the effect through integrator；Disturbing signal: a sin (ω t), wherein ω is for disturbing
Dynamic signal angular frequency, the angular frequency with demodulated signal is identical, and a is disturbing signal amplitude；Estimating extreme point, this is extremum search
Control the output of part, made and obtained the extreme point estimated by integrator output and disturbing signal, namely to compensate in servo
Exploration weights on system input signal.
5), limiting control disturbing signal amplitude self-adaptative adjustment part.The input of this part is the 3rd) bag of extracting section
Network signal, is output as amplitude a of disturbing signal a sin (ω t).
This part is constructed fuction relation between disturbing signal amplitude and envelope signal, first, uses envelope signal current
Value and envelope signal maximum do than form, envelope signal is limited between 0 to 1, is designated as u；Then by non-linear change
Change a=f (u)=B (1-e-Cu), wherein B, C are constant value set in advance, it is thus achieved that with the disturbing signal amplitude of envelope signal change.
Searching extreme point due to extreme control method is that the fluctuation by disturbing signal a sin (ω t) scans for, extreme value
In the output that search controls, the fluctuation of sine in superposition all the time, although being finally reached extreme point, vibration also will not disappear, this existing
As referred to as steady oscillation.This part makes disturbing signal amplitude use up when not stablizing from the impact point arrived to be searched i.e. system farther out
May keep relatively big, and less close to disturbing signal amplitude when stablizing, accelerate the convergence rate of system with this measure and solve pole
The steady oscillation problem that value control itself is brought.
In conjunction with the five respective function of part above, the flow process that is embodied as of the present invention can be summarized as: will be just remaining
String signal weights, and weights are initial value, obtain the initial input of system, obtains the output of system through servosystem, extracts envelope
As the input of limiting control part after line, through limiting control process together with the disturbing signal amplitude obtained, it is compensated
The exploration estimated value of input weights, is constantly circulated by this flow process, finally makes the difference of servosystem output and original input signal
Value is 0, obtains preferable output signal, reaches method and improves the purpose of servosystem tracking sinusoidal signal performance.
When method is implemented, amplitude and the frequency information of the initial sinusoids input signal of servosystem that need to obtain is with
And the output signal information of system, the most only need to design each several part parameter in method, build compensation network according to said structure,
Method can automatic compensated input signal, make the tracking input signal that output signal can be good.The parameter needing design has, pole
The storage gain k that value controls1,k2, High Pass Filter Cutoff Frequency h1,h2, disturbing signal angular frequency1,ω2, nonlinear transformation
Coefficient B and coefficient C.Wherein storage gain k1,k2Unsuitable excessive, otherwise the stability of system can be affected, and typically chooses 5 and arrives
Between 20, disturbing signal angular frequency1,ω2Need less than the angular frequency of input signal, be chosen for input signal angular frequency
About 1/10, High Pass Filter Cutoff Frequency is less than disturbing signal angular frequency, and nonlinear transformation coefficient B is defeated with sine
The amplitude entering signal is identical, and coefficient C sets according to practical situation, typically takes 1 to 5.
Below by embodiment checking beneficial effects of the present invention:
For checking effectiveness of the invention, using the internal ring of certain type three-axis simulating table as controlled device, artificial rotary table it is
The semi-physical emulation platform that simulation actual vector rotates, for typical servo-control system, turntable internal ring utilizes series connection the most in advance
Correction and the feedforward are debugged, and meet basic service requirement.
During enforcement, the sinusoidal input signal to turntable is frequency 10Hz, and amplitude is the sinusoidal signal of 0.5 degree, the output of turntable
Signal is the real-time angular of internal ring.When implementing, each for extreme control method link is carried out discretization and is embedded into the control of turntable
In program (sampling period is 0.5ms, uses bilinearity discretization method), in experiment, parameter used is respectively as follows: high pass filter
Cut-off frequency h=3, storage gain k=10, the disturbing signal frequencies omega of sinusoidal signal weights1=6 π rad/s, cosine signal is weighed
The disturbing signal frequencies omega of value2=10 π rad/s, C=6 in nonlinear transformation, then, record real-time defeated in systems in practice
Enter curve of output, and obtain the correlation curve of final result.
Fig. 2 and Fig. 3 gives the correlation curve of system input and output before and after compensating under 10Hz sine inputs, and Fig. 4 is given
Deviation signal envelope variation curve, Fig. 5 gives the search change curve that sine and cosine compensates weights.Figure it is seen that
Under the input of 10Hz sine, between output and the input of system, there is relatively large deviation, but through side proposed by the invention
After method compensates, it is seen in figure 3 that the input/output signal of system is almost completely superposed, in conjunction with the deviation signal shown in Fig. 4
The change curve of envelope can obtain, and the deviation between system input and output tapers into along with the operation of extreme control method,
10 just can be reduced in the shortest time-3The order of magnitude.
So according to the above results, the present invention is by utilizing extreme control method to combine with width phase control, defeated to sine
Enter the input of the servosystem under signal to compensate so that servosystem can be issued to good tracking effect at optional frequency
Really, substantially increase the tracking performance of servosystem, and due to the simple construction features of extreme control method, can be easy to
Apply in servo system control program, make servosystem obtain more preferable tracking performance.
Claims (10)
1. servosystem input offset method based on limiting control, is characterized in that: the flow process of the method is:
Step one, by initial sinusoids input signal with compensate cosine input signal be multiplied with its each self-corresponding weights respectively,
To two-way original input signal；
Step 2, two-way input signal step one obtained are added, it is thus achieved that total input signal；Total input signal is inputted servo
System, and export after servo system processes, it is thus achieved that output signal；
Step 3, the output signal described in step 2 is extracted the input signal as limiting control after envelope, and by described
Input signal carries out limiting control together with the amplitude of disturbing signal, is compensated the exploration estimated value of input weights；
Step 4, the process of repeated execution of steps one to three, until the defeated signal of servosystem goes out the difference with original input signal
Value is 0, using this output signal as preferable output signal, completes servosystem input offset based on limiting control.
Servosystem input offset method based on limiting control the most according to claim 1, it is characterised in that step one
In, original sine-signal is the most identical with compensating the amplitude of cosine input signal, frequency.
Servosystem input offset method based on limiting control the most according to claim 1, it is characterised in that step 2
In, total input signal, through servo system processes, specifically includes former controller and the controlled device of servosystem, controller comprise but
It is not limited to cascade compensation and the feedforward.
Servosystem input offset method based on limiting control the most according to claim 1, it is characterised in that step 3
In, the output signal described in step 2 is extracted the input signal as limiting control after envelope, method particularly includes:
Extract total input signal and the output signal of servosystem, it is thus achieved that the amplitude of deviation signal p, by delayed for former deviation signal p
T/4 converted after the cycle that signal q, T are sinusoidal input signal；
Calculate the most time dependentI.e. obtain the envelope of signal p, control preferable generation as extremum search
Valency function, this cost function is: the input signal of limiting control.
Servosystem input offset method based on limiting control the most according to claim 1, it is characterised in that step 3
In, described input signal is carried out together with disturbing signal amplitude limiting control, is compensated the exploration estimated value of input weights,
Method particularly includes:
Two-way extremum search process is used to search for sinusoidal input signal respectively and compensate the weights of cosine input signal；
Each road extremum search process is:
Step 3 one, by the input signal of limiting control through high pass filter filters, it is thus achieved that filtered signal；
Step 3 two, demodulated signal sin (ω t) is multiplied with the filtered signal described in step 3 one, obtains gradient information；Its
Middle ω is demodulated signal angular frequency；
Step 3 three, the gradient information described in step 3 two is processed by integrator, it is thus achieved that signal after Integral Processing；
After step 3 four, the Integral Processing that step 3 three is obtained signal and disturbing signal make and, it is thus achieved that the extreme point of estimation, will
This extreme point is as the exploration estimated value compensating input weights.
Servosystem input offset method based on limiting control the most according to claim 5, it is characterised in that step 3
In, the preparation method of the amplitude of disturbing signal is:
Extract envelope according to step 3, envelope signal currency is done ratio with envelope signal maximum, envelope signal is limited
Between 0 to 1, then pass through nonlinear transformation:
A=f (u)=B (1-e-Cu)
Obtain the amplitude of the disturbing signal changed with envelope signal；Wherein B, C are constant value set in advance；U is by envelope signal
The value being limited between 0-1.
Servosystem input offset method based on limiting control the most according to claim 6, it is characterised in that step 3
In one, the expression formula of high pass filter is:Wherein: s is Laplace operator, h is High Pass Filter Cutoff Frequency.
Servosystem input offset method based on limiting control the most according to claim 7, it is characterised in that step 3
In three, the expression formula of integrator is:Wherein: s is Laplace operator, k is storage gain.
Servosystem input offset method based on limiting control the most according to claim 8, it is characterised in that step 3
In two, demodulated signal angular frequency is less than sinusoidal input signal or compensates cosine input signal angular frequency.
Servosystem input offset method based on limiting control the most according to claim 9, it is characterised in that B with just
The amplitude of string input signal is identical, and C takes the real number of 1 to 5.
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| CN114706305A (en) * | 2022-03-31 | 2022-07-05 | 哈尔滨工业大学 | Adaptive filter design method based on preset basis function and servo system |
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Application publication date: 20161214 |