CN104638999A - Segment neural network friction model based dual-motor servo system control method - Google Patents

Abstract

The invention relates to a segment neural network friction model based dual-motor servo system control method and belongs to the technical field of electromechanical control. The method includes: firstly, analyzing a dual-motor drive servo system with friction, and establishing a mathematical model of the dual-motor drive servo system with friction according to a mechanism modelling method as well as the structures of motors and the physical law; secondly, analyzing a friction term fi in the mode, and utilizing a segment neural network to establish a friction model of the nonlinear friction fi so as to obtain a segment neural network friction model; thirdly, utilizing a terminal sliding mode control algorithm to acquire a synchronous motor speed control law, and performing synchronous tracking control on the dual-motor servo system according to the control law. By the method, influence on the dual-motor system due to friction can be eliminated, the dual-motor system has better transient performance, tracking response speed of the dual-motor servo system is increased effectively, and fast synchronization of the dual-motor system can be guaranteed.

Description

Based on the dual-servo-motor system control method of segmentation neural net friction model

Technical field

The present invention relates to a kind of bi-motor friciton compensation synchronization and tracking control method, belong to technical field of electromechanical control.

Background technology

Along with the develop rapidly of modern science and technology, single motor servo system is the more and more difficult demand meeting high-power system from power, performance, adopts multiple electric motors to combine and drives the method for load to address this problem very well.In many motor servo systems, non-linear in tribology result in many negative effects, and such as, Stribeck effect and speed dead band, have a strong impact on the tracking accuracy of servo system under the low speed.This makes to utilize traditional controller to be difficult to ensure that many motor servo systems obtain good control effects.How to ensure that high precision tracking and the Synchronization Control of many motor servo systems have become a hot issue.

Friction is unavoidable problem in motor servo system.For high-precision servo tracking system, the existence of friction link is the obstacle improving systematic function.Frictional force shows as the impact of static system performance and exports response and have larger static difference or the concussion of stable state limit cycle, occurs wave distortion phenomenon when creeping (shake) phenomenon and speed zero passage when showing as low speed to the impact of dynamic performance.Friction has a strong impact on low-speed performance and the tracking accuracy of electromechanical servo system.For solving the impact rubbed on servo system location and tracking accuracy, reply friction is carried out modeling and is designed corresponding dynamic compensation scheme.Researcher successively proposes multiple friction model, as the Coulomb friction+viscous friction model, Dahl model, Karnop model, LuGre model, Leuven model, Maxwell-slip model etc. of classics.Wherein, LuGre model can be complicated in accurate description friction process static and dynamic performance, as creeped, limit cycles oscillations, sliding before distortion, friction as lag, change static friction and Stribeck curve etc., a kind of friction model the most often adopted when having become the current friciton compensation based on model.

Because LuGre model can describe complicated friction phenomenon well, many scholars have done more research in the Friction Modeling and compensatory control of LuGre model.Such as, doctor Muvengei of Kenya have studied the discrimination method of LuGre friction model and model parameter.In order to overcome frictional influence better and improve the control precision of control system, Japanese Hoshino doctor D utilizes observer to carry out friciton compensation control.Domestic aspect, representational have doctor Xiang Hongbiao of Institutes Of Technology Of Tianjin to utilize inversion algorithm to propose a kind of methods such as Adaptive Compensation Control based on friction model.

In addition, along with improving constantly of requiring motor servo system control precision, servo system high accuracy controls the focus also becoming this area.In this regard, doctor Wang Xiaojing of Harbin Institute of Technology proposes a kind of tracking control unit based on null phase error, effectively improves interference free performance and the frequency domain performance of servo system; The Liu Zhi of Central South University proposes initiatively Disturbance Rejection control method based on BP neural net; A shake for Hong Kong University proposes a kind of method that can realize many motor speeds Fast synchronization.

But most tracking or the multi-drive synchronization problem all only studying separately band friciton compensation of these methods existing, the method that can solve this two problems there is not yet invention and has mentioned simultaneously.

Summary of the invention

The object of the invention is to the high precision tracking of motor and Synchronization Control, to propose a kind of dual-servo-motor system control method based on segmentation neural net friction model in order to realize in dual-servo-motor system control process.

The general principle of the inventive method is: utilize and replace LuGre stable state friction model based on discontinuous segmentation neural net expression friction model, thus better approaching to reality friction, realize friciton compensation.In order to make dual motors system can Fast synchronization and can controlling by high precision tracking, proposing in the method for fast terminal sliding formwork and representing the variable coefficient of sync rates, and carrying out friciton compensation control based on it.

For achieving the above object, the technical solution adopted in the present invention is as follows:

Based on a dual-servo-motor system control method for segmentation neural net friction model, comprise the following steps:

Step one, the Dual-motors Driving Servo System containing friction to be analyzed, and according to modelling by mechanism method, according to structure and the physical law of motor, set up the Mathematical Modeling of the Dual-motors Driving Servo System containing friction.The object setting up this model is the characteristic in order to better understand dual motors system, and then design synchronization and tracking control method realizes Fast synchronization and accurate tracking.Specific as follows:

According to modelling by mechanism method, according to structure and the physical law of motor, set up the Mathematical Modeling of the Dual-motors Driving Servo System containing friction, specific as follows:

$\left\{\begin{array}{c}J{\stackrel{\·\·}{\mathrm{\θ}}}_i+f_i=u_i\left(t\right)-{\mathrm{\τ}}_i\left(t\right)-{(-1)}^i\mathrm{\ω}\\ J_m{\stackrel{\·\·}{\mathrm{\θ}}}_m+b_m{\stackrel{\·}{\mathrm{\θ}}}_m={\mathrm{\Σ}}_{i=1}^2{\mathrm{\τ}}_i\left(t\right)\end{array}\right.---\left(1\right)$

Wherein, θ _i(i=1,2) and θ _mrepresent the corner of drive end and load end respectively; with represent the rotating speed of drive end and load end respectively; represent the acceleration of drive end and load end respectively; J represents the moment of inertia of drive motors; J _mrepresent the moment of inertia of load end; b _mfor connecting the viscosity of gear; u _iexpression system input torque; ω represents biased moment; τ _it () represents transmission torque between motor and load; f _irepresent the moment of friction of drive motors; T represents the time from signal input; I=1, the drive motors 1 of 2 expression dual motors system and drive motors 2.

In formula (1), if backlash is 2 α, then gear drive moment τ _it () can be expressed as:

${\mathrm{\τ}}_i\left(t\right)=\mathrm{kf}\left(z_i\left(t\right)\right)+\mathrm{cf}\left({\stackrel{\·}{z}}_i\left(t\right)\right)---\left(2\right)$

Wherein, k represents the torque coefficient of gear, and c represents the damping coefficient of gear, f (z _i(t)) represent the nonlinear function containing backlash dead band, be expressed as:

$f\left(z_i\left(t\right)\right)=\left\{\begin{array}{cc}{z}_i\left(t\right)+\mathrm{\&alpha;},& z_i\left(t\right)\&le;-\mathrm{\&alpha;}\\ 0,& -\mathrm{\&alpha;}<z_i\left(t\right)<\mathrm{\&alpha;}\\ z_i\left(t\right)-\mathrm{\&alpha;},& z_i\left(t\right)\&GreaterEqual;\mathrm{\&alpha;}\end{array}\right.---\left(3\right)$

Wherein, z _i(t)=θ _i(t)-θ _mt () is the differential seat angle of drive end and load end.

For convenience of the design of controller, by nonlinear function f (z _i(t)) be rewritten as continuously differentiable function:

$f\left(z_i\left(t\right)\right)=z_i\left(t\right)-\mathrm{\&alpha;}(\frac{2}{1+e^{{-\mathrm{rz}}_i}}-1)---\left(4\right)$

Wherein, r represents normal number.Then gear drive moment τ _it () can be expressed as and can be write as:

${\mathrm{\&tau;}}_i\left(t\right)=k(z_i\left(t\right)-\mathrm{\&alpha;}(\frac{2}{1+e^{-r{z}_i}}-1))+c{\stackrel{\&CenterDot;}{z}}_i\left(t\right)(1-2\mathrm{\&alpha;}\frac{e^{{-\mathrm{rz}}_i}}{{(1+e^{{-\mathrm{rz}}_i})}^2})---\left(5\right)$

Be defined as follows variable x ₁, x ₂, x _3i, x _4i, thus simplify control algorithm design.

$\left\{\begin{array}{c}{x}_1={\mathrm{\&theta;}}_m\\ x_2={\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m\\ x_{3i}=z_i\left(t\right)-\mathrm{\&alpha;}(\frac{2}{1+e^{{-\mathrm{rz}}_i}}-1)\\ x_{4i}={\stackrel{\&CenterDot;}{z}}_i\left(t\right)(1-2\mathrm{\&alpha;}\frac{e^{{-\mathrm{rz}}_i}}{{(1+e^{{-\mathrm{rz}}_i})}^2})\end{array}\right.---\left(6\right)$

Obtained by above-mentioned, gear drive moment is τ _i(t)=kx _3i+ cx _4iso formula (1) is by variable x ₁, x ₂, x _3i, x _4ibe rewritten as:

Wherein,

In consideration formula (7) part, frictional force f _ifor system input u _ithe resistance of (t).

Discuss below and how to utilize segmentation neural net to f _iapproach, produce with frictional force f _ithe moment that size is identical, then utilizes compensatory control mechanism can follow the tracks of desired signal and meets required precision.

Step 2, to the friction term f in step one Modling model _ianalyze, and utilize segmentation neural network non-linear in tribology f _ifriction model;

Moment of friction has had a strong impact on tracking accuracy and the control effects of servo system, in order to eliminate fricative adverse effect, improves the follow-up control of system and robustness, needs to analyze friction phenomenon and carries out the identification of modeling and characterisitic parameter.Frictional force is low-speed stage to the stage that systematic influence is maximum, and now system may present shake or the state of creeping due to the impact of friction.In classical PID controls, overcome the impact of low-speed stage friction on system by increasing control system gain, but usually can produce again the situation of system instability.

The multianalysis non-linear in tribology of bi-motor Properties of Objects and existence in step one, step 2 utilizes segmentation neural net to non-linear in tribology f _iapproach.Segmentation neural net can be approached any zonal cooling linear function, can represent by linear parameterization expression formula.Do not need to do any hypothesis to unknown function, the precision of approaching can by controlling the adjustment of parameter several in formula, and this is the great advantage of segmentation neural net expression formula.

The piecewise linear function f (v, w) of given arbitrary l dimension, (V ∈ R ^l-1, w ∈ R), the domain of definition is then be expressed as following form:

D is divided into the subdomain D of N number of non-overlapping copies _r(r=1 ..., N) and then f (v, w are represented as:

$f(v,w)=f(v,{\mathrm{\&alpha;}}_0\left(v\right))+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_r{\mathrm{\&sigma;}}_r(0,w-{\mathrm{\&alpha;}}_r\left(v\right),{\mathrm{\&beta;}}_r\left(v\right)-{\mathrm{\&alpha;}}_r\left(v\right))---\left(9\right)$

Wherein, α _r(v) and β _r(V) be respectively r subdomain about v ∈ R ^l-1the upper bound and lower bound.α _rv () is relative to domain of definition D, about the minimum lower bound of v.P _rthe unknowm coefficient needing in expression formula to estimate, σ _r(0, w-α _r(V), β _r(v)-α _rv () is basic function, its concrete form is:

σ(a，b，c)＝max(a，min(b，c)) (10)

As the special case of above-mentioned theory, one dimension segmentation neural net expression formula form is:

$f\left(h\right)=p_0+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_r{\mathrm{\&sigma;}}_r(0,h-{\mathrm{\&alpha;}}_r,{\mathrm{\&beta;}}_r-{\mathrm{\&alpha;}}_r)\&ForAll;h\&Element;R---\left(11\right)$

Wherein, basic function σ (0, h-α _r, β _r-α _r) be a special zonal cooling linear function, be expressed as: σ (0, h-α _r, β _r-α _r)=max (0, h-α _r)-max (0, h-max (α _r, β _r)), α _rand β _rat r subinterval shangguan in the upper bound of h ∈ R and lower bound respectively, p _r(r=1 ..., N) and be the unknowm coefficient needing to estimate.And unknowm coefficient p _rin fact be exactly local linear function σ _r=h-α _rat α _r≤ h≤β _rtime unknown slope, as h < α _rtime have σ _r=0; As h>=β _rtime, σ _r=β _r-α _r.The adequate condition that use formula (11) approaches 1 dimension zonal cooling linear function the domain of definition of independent variable h is divided into the subinterval of non-overlapping copies and boundary point α _rand β _rmeet α _r< β _rand β _r=α _r+1.

Consider the special nature of friction, above-mentioned segmentation neural net expression formula sets up friction model also to be needed to do following process.Dynamically present segmented characterizing owing to rubbing, the method that formula (11) sets up friction model only considers frictional force and is similar to the feature presented with the linear relationship of speed at high-speed region, have ignored the impact of low-speed stage.Consider at low-speed stage, Coulomb friction and Stribeck effect become the factor of major effect friction, and have stronger nonsmooth nonlinearities characteristic, friction time especially near zero-speed also exists hopping phenomenon when turning to.The problem of frictional force can not be described to solve low-speed stage segmentation neural net very well, in formula (11), doing following process: add saltus step item h ₁(v) and exponential term h ₂(v).Wherein, saltus step item h ₁v () is relevant to maximum static friction force, with frictional force hopping phenomenon when solving break-in; Exponential term h ₂v () is with solving approaching of low speed Stribeck effect.Therefore, no matter can approach frictional force completely in high regime or low speed segment segmentation neural net, expression formula (11) can be rewritten as:

$f\left(v\right)=d_0+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}[d_r{\mathrm{\&rho;}}_r(0,v-{\mathrm{\&alpha;}}_r\left(v\right),{\mathrm{\&beta;}}_r\left(v\right)-{\mathrm{\&alpha;}}_r\left(v\right))+h_1\left(v\right)]+d_{N+1}{h}_2\left(v\right)---\left(12\right)$

Wherein, v and f (v) is speed and frictional force respectively; N (>=2) represents the number excursion of speed v being divided gained; α _r, β _rthe bound in r subinterval, h ₁v () is saltus step item, form is: $h_1\left(v\right)=\left\{\begin{array}{c}2F_s,v\&GreaterEqual;0\\ 0,v<0\end{array}\right.,$ H ₂v () describes Stribeck effect, form is: wherein F _srepresent stiction, v _crepresent speed when moment of friction is minimum.

Conveniently process, formula (12) rewritten compact expression formula:

Wherein, D=[d ₀, d ₁..., N, d _n+1] ^trepresent parameter vector, represent basis function vector.Parameter D can be calculated by recurrent least square method method of estimation.

In order to verify that segmentation neural net has the discontinuous function of jump to have fine approximation capability to non-linear in tribology is this kind of, segmentation neural net is used to approach conventional LuGre model:

$F\left(v\right)=F_c\mathrm{sign}\left(v\right)+(F_s-F_c)e^{{-(v/v_c)}^2}\mathrm{sign}\left(v\right)+F_{v}v(F_s=2.4N,F_c=0.8N,v_c=1.05/s,F_v=0.8N),$

Result is as Fig. 2.Can show that from figure segmentation neural net can approach non-linear in tribology very well.

Described speed interval v _cacquisition methods be:

Respectively choose at the both forward and reverse directions of dual-servo-motor system and be no less than 10 friction speed values; Meanwhile, adopt PI to control to motor, make motor rotation speed keep constant; When motor uniform motion, the size of frictional force equals the size of motor output torque, and the size of motor output torque is proportional to controller and exports the size of control voltage, exported the size of controlled quentity controlled variable by recording controller, the size of motor friction under present speed can be obtained; 3 above-mentioned process are no less than to each speed sample point, to the whole frictional force results averaged obtained, as actual frictional force suffered by system under present speed; Finally obtain the size of frictional force during positive and negative both direction at least 10 friction speeds, then data acquisition least square fitting is respectively organized to positive and negative both direction, speed interval v can be obtained _c.

Described maximum static friction force F _sacquisition methods is:

By dual-servo-motor system works under open loop environment, increase Double Motor Control voltage gradually, until motor starts to rotate, be now the maximum static friction of system; Repeat at least 10 operations, get its mean value as maximum static friction torque F _s.

Step 3, the segmentation neural net friction model obtained according to step 2, utilize TSM control algorithm, carry out synchronization and tracking control to dual-servo-motor system.

Friction model is showed by segmentation neural network model by step 2, is f (v) is become f _i, substitute into the design carrying out controller in algorithm.Below for the present invention utilizes fast terminal sliding Mode Algorithm, devise the control algolithm of the dual motors system based on segmentation neural net friciton compensation, thus make dual motors system can ensure the speed sync of two motors, fine tracking performance can be had by proof load end again.

The tracking performance of consideration system, if y (t)=θ _mfor the output signal of system, y _dt reference signal that () is system, then error e (t)=y (t)-y _dt (), obtains the differential of error, second differential and three subdifferentials are respectively:

$\stackrel{\&CenterDot;}{e}=x_2-{\stackrel{\&CenterDot;}{y}}_d---\left(14\right)$

$\stackrel{\&CenterDot;\&CenterDot;}{e}={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d=a_1{\mathrm{\&Sigma;}}_{i=1}^2{\mathrm{\&tau;}}_i\left(t\right)-a_1{b}_m{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d---\left(15\right)$

Fast terminal sliding Mode Algorithm is utilized to obtain:

$\left\{\begin{array}{c}{s}_0=e\\ s_1={\stackrel{\&CenterDot;}{s}}_0+{\mathrm{\&alpha;}}_0{s}_0+{\mathrm{\&beta;}}_0{s}_0^{q_0/p_0}\\ s_2={\stackrel{\&CenterDot;}{s}}_1+{\mathrm{\&alpha;}}_1{s}_1+{\mathrm{\&beta;}}_1{s}_1^{q_1/p_1}\end{array}\right.---\left(17\right)$

Wherein, p _i(i=0,1) is for positive odd number and meet p _i> q _i, and α _i> 0, β _i> 0.

In order to make dual motors system can Fast synchronization and can realize high precision tracking control, the variable coefficient representing bi-motor synchronization extent is proposed in the method for fast terminal sliding formwork, and carry out friciton compensation control based on it, original control law is divided into and ensures speed sync u _siu is followed the tracks of with guarantee _titwo parts.Based on segmentation neural net friction model, control law u _ibe expressed as

u _i＝u _si+ψu _ti(18)

Wherein,

$u_{\mathrm{si}}=\frac{1}{a_{2}c{\mathrm{\&rho;}}_i}[h_1(x_{3i},x_{4i})-c(a_1{b}_m{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m-a_2{f}_i){\mathrm{\&rho;}}_i]---\left(19\right)$

$\mathrm{\&psi;}=\frac{1}{e^{\mathrm{\&eta;}|{\stackrel{\&CenterDot;}{z}}_1-{\stackrel{\&CenterDot;}{z}}_2|}}---\left(21\right)$

Wherein, the control law u of speed sync is ensured _simiddle f _ifor the friction model that segmentation neural net in third step obtains, at input u _iproduce the input variable that can be offset friction effects; And b is a normal number, η is a selectable normal number, h ₁(x _3i, x _4i) be the state feedback item of system, for the sliding formwork item of system, be expressed as

h ₁(x _3i，x _4i)＝a ₂cρ _iτ _i(t)+a ₂cρ _i(-1) ⁱω+ca ₁ρ _i(τ ₁(t)+τ ₂(t))-kx _4i(22)

$\begin{array}{c}{h}_2(s_0,{\stackrel{\&CenterDot;}{s}}_0,{\stackrel{\&CenterDot;\&CenterDot;}{s}}_0,s_1,{\stackrel{\&CenterDot;}{s}}_1)={\mathrm{\&alpha;}}_0{\stackrel{\&CenterDot;\&CenterDot;}{s}}_0/\left(2a_1\right)+{\left({\mathrm{\&beta;}}_0{x}_0^{q_0/p_0}\right)}^{\&prime;\&prime;}/\left({2a}_1\right)+{\left({\mathrm{\&beta;}}_1{s}_1^{q_1/p_1}\right)}^{\&prime;}/\left(2a_1\right)\\ +{\mathrm{\&alpha;}}_1{\stackrel{\&CenterDot;}{s}}_1/\left(2a_1\right)\end{array}---\left(23\right)$

According to control law u _i, synchronization and tracking control is carried out to dual-servo-motor system, realizes object of the present invention and original intention thus.

Beneficial effect

Control method of the present invention has following beneficial effect:

1, for dual-servo-motor system, segmentation neural net friction model has better None-linear approximation ability, with high accuracy, frictional behavior can be described, therefore the present invention devises the friciton compensation controller based on segmentation neural net, the nonlinear interaction brought is cancelled out each other with rubbing, final realization compensates object, eliminates the impact of friction on dual motors system.

2, while carrying out friciton compensation, consider the synchronous and tracing control of the dual-servo-motor system containing segmentation neural net friction model, utilize fast terminal sliding Mode Algorithm, the rapidity of following the tracks of can be ensured, systematic steady state precision can be ensured again.The present invention can make dual motors system have better mapping, effectively improves the tracking response speed of dual-servo-motor system.

3, the present invention is directed to the characteristic that dual-servo-motor system is not easily synchronous, fast terminal sliding mode controller is devised based on segmentation neural net friciton compensation, propose variable coefficient to represent synchronization extent, the method can ensure the Fast synchronization of dual motors system, and control algolithm of the present invention has comparatively strong robustness.

A variable coefficient ψ is devised in fast terminal sliding Mode Algorithm, solve the coordination problem of the synchronous and tracing control of bi-motor well, the size of variable coefficient ψ is regulated by the speed discrepancy of two drive motors, thus ensure the synchronous of bi-motor and tracking effect: when the speed discrepancy of two drive motors is larger, variable coefficient ψ is less, thus ensures synchronous velocity control rule u _siplay a major role, first make two drive motors speed sync as quickly as possible; After synchronous, the speed discrepancy of two drive motors diminishes, and variable coefficient ψ, close to equaling 1, ensures tracing control rule u _tiplay a part main, make dual motors system have very high tracking accuracy.Therefore control program of the present invention can ensure that dual motors system reaches effect that is synchronous and that follow the tracks of simultaneously.

Accompanying drawing explanation

Fig. 1 is typical dual-servo-motor Control system architecture figure;

Fig. 2 is that segmentation neural net approaches friction model figure;

Fig. 3 is the bi-motor speed-friction curve figure in embodiment;

Fig. 4 is bi-motor friction testing curve chart in embodiment;

Fig. 5 is the tracking effect figure utilizing fast terminal sliding mode controller in embodiment under segmentation neural net friciton compensation;

Fig. 6 is the tracking error figure utilizing fast terminal sliding mode controller in embodiment under segmentation neural net friciton compensation;

Fig. 7 is the synchronous effect figure utilizing two drive motors in fast terminal sliding mode controller dual-servo-motor system in embodiment;

Fig. 8 utilizes synchronous error figure in fast terminal sliding mode controller dual-servo-motor system in embodiment.

Embodiment

Below in conjunction with drawings and Examples, the method for the invention is further elaborated.

Based on a motor servo system control method for segmentation neural net friction model, comprise the following steps:

Step one, the Dual-motors Driving Servo System containing friction to be analyzed, and according to modelling by mechanism method, according to structure and the physical law of motor, set up the Mathematical Modeling of the Dual-motors Driving Servo System containing friction, specific as follows:

Wherein,

${\mathrm{\&tau;}}_i\left(t\right)=k(z_i\left(t\right)-\mathrm{\&alpha;}(\frac{2}{1+e^{{-\mathrm{rz}}_i}}-1))+c{\stackrel{\&CenterDot;}{z}}_i\left(t\right)(1-2\mathrm{\&alpha;}\frac{e^{{-\mathrm{rz}}_i}}{{(1+e^{{-\mathrm{rz}}_i})}^2})---\left(26\right)$

In formula (24), formula (25), formula (26), θ _i(i=1,2) and θ _mrepresent the corner of drive end and load end respectively; with represent the rotating speed of drive end and load end respectively; with represent the acceleration of drive end and load end respectively; J represents the moment of inertia of drive motors; J _mrepresent the moment of inertia of load end; b _mfor connecting the viscosity of gear; u _iexpression system input torque; ω represents biased moment; τ _it () represents transmission torque between motor and load; f _irepresent the moment of friction of drive motors; T represents the time from signal input; I=1, the drive motors 1 of 2 expression dual motors system and drive motors 2; z _i(t)=θ _i(t)-θ _mt () represents the differential seat angle of drive end and load end;

Step 2, to the friction term f in step one Modling model _ianalyze, and utilize segmentation neural network non-linear in tribology f _ifriction model, specific as follows:

One dimension segmentation neural net expression formula form is:

$f\left(h\right)=p_0+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_r{\mathrm{\&sigma;}}_r(0,h-{\mathrm{\&alpha;}}_r,{\mathrm{\&beta;}}_r-{\mathrm{\&alpha;}}_r)\&ForAll;h\&Element;R---\left(27\right)$

Wherein, basic function σ (0, h-α _r, β _r-α _r) be a special zonal cooling linear function, be expressed as: σ (0, h-α _r, β _r-α _r)=max (0, h-α _r)-max (0, h-max (α _r, β _r)), α _rand β _rat r subinterval shangguan in the upper bound of h ∈ R and lower bound respectively, p _r(r=1 ..., N) and be need to estimate to obtain unknowm coefficient;

The adequate condition that use formula (27) approaches one dimension zonal cooling linear function is: the domain of definition of independent variable h is divided into the subinterval of non-overlapping copies and boundary point α _rand β _rmeet α _r< β _rand β _r=α _r+1;

Following process is done further to formula (27):

Saltus step item h is added in formula (27) ₁(v) and exponential term h ₂(v); Wherein, saltus step item h ₁v () is relevant to maximum static friction force, with frictional force hopping phenomenon when solving break-in; Exponential term h ₂v () is with solving approaching of low speed Stribeck effect; Formula (27) becomes as described below:

$f\left(v\right)=d_0+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}[d_r{\mathrm{\&rho;}}_r(0,v-{\mathrm{\&alpha;}}_r\left(v\right),{\mathrm{\&beta;}}_r\left(v\right)-{\mathrm{\&alpha;}}_r\left(v\right))+h_1\left(v\right)]+d_{N+1}{h}_2\left(v\right)---\left(28\right)$

Wherein, v and f (v) is speed and frictional force respectively; N (>=2) represents the number excursion of speed v being divided gained; α _r, β _rthe bound in r subinterval, h ₁v () is saltus step item, form is: $h_1\left(v\right)=\left\{\begin{array}{c}2F_s,v\&GreaterEqual;0\\ 0,v<0\end{array}\right.,$ H ₂v () describes Stribeck effect, form is: wherein F _srepresent stiction, v _crepresent speed when moment of friction is minimum;

By formula (28), conversion is as follows further:

Wherein, D=[d ₀, d ₁..., N, d _n+1] ^trepresent parameter vector, represent basis function vector; Parameter D is calculated by recurrent least square method method of estimation;

Described speed interval v _cacquisition methods be:

15 friction speed values are respectively chosen at the both forward and reverse directions of dual-servo-motor system; Meanwhile, adopt PI to control to dual motors system, make the speed of system keep constant; When motor uniform motion, the size of motor output torque is the size of frictional force, and the size that the size of motor output torque and controller export control voltage is directly proportional, export the size of controlled quentity controlled variable by recording controller, the size of motor friction under present speed can be obtained; 5 above-mentioned process are carried out to each speed sample point, to the whole frictional force results averaged obtained, as actual frictional force suffered by system under present speed; Finally obtain the size of frictional force during positive and negative both direction 15 friction speeds, then data acquisition least square fitting is respectively organized to positive and negative both direction, speed interval v can be obtained _c.With speed-friction curve that the matching of least square method algorithm obtains, as Fig. 3.

Described maximum static friction force F _sacquisition methods is:

By dual-servo-motor system works under open loop environment, increase Double Motor Control voltage gradually, until motor starts to rotate, be now the maximum static friction of system; Repeat 10 operations, get its mean value as maximum static friction torque F _s.The rate signal gathered and controller output voltage signal drafting pattern, as Fig. 4, namely observable draws stiction size.

Step 3, the segmentation neural net friction model obtained according to step 2, utilize TSM control algorithm, carry out synchronization and tracking control to dual-servo-motor system, method is as follows:

If y (t)=θ _mfor system output signal, y _dt () is system reference signal, then error obtain error differential, second differential and three subdifferentials are respectively:

$\stackrel{\&CenterDot;}{e}=x_2-{\stackrel{\&CenterDot;}{y}}_d---\left(30\right)$

$\stackrel{\&CenterDot;\&CenterDot;}{e}={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d=a_1{\mathrm{\&Sigma;}}_{i=1}^2{\mathrm{\&tau;}}_i\left(t\right)-a_1{b}_m{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d---\left(31\right)$

Fast terminal sliding Mode Algorithm is utilized to obtain:

$\left\{\begin{array}{c}{s}_0=e\\ s_1={\stackrel{\&CenterDot;}{s}}_0+{\mathrm{\&alpha;}}_0{s}_0+{\mathrm{\&beta;}}_0{s}_0^{q_0/p_0}\\ s_2={\stackrel{\&CenterDot;}{s}}_1+{\mathrm{\&alpha;}}_1{s}_1+{\mathrm{\&beta;}}_1{s}_1^{q_1/p_1}\end{array}\right.---\left(33\right)$

Wherein, p _i(i=0,1) is for positive odd number and meet p _i> q _i, and α _i> 0, β _i> 0;

Now, original control law is divided into guarantee speed sync u _siu is followed the tracks of with guarantee _titwo parts, control law u _ibe expressed as

u _i＝u _si+ψu _ti(34)

Wherein,

$u_{\mathrm{si}}=\frac{1}{a_{2}c{\mathrm{\&rho;}}_i}[h_1(x_{3i},x_{4i})-c(a_1{b}_m{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m-a_2{f}_i){\mathrm{\&rho;}}_i]---\left(35\right)$

$\mathrm{\&psi;}=\frac{1}{e^{\mathrm{\&eta;}|{\stackrel{\&CenterDot;}{z}}_1-{\stackrel{\&CenterDot;}{z}}_2|}}---\left(37\right)$

Wherein, the control law u of speed sync is ensured _simiddle f _ifor the friction model that segmentation neural net in step 2 obtains, at input u _iproduce the input variable that can be offset friction effects; B, η are positive number, h ₁(x _3i, x _4i) be system mode feedback term, for system sliding formwork item, be expressed as

h ₁(x _3i，x _4i)＝a ₂cρ _iτ _i(t)+a ₂cρ _i(-1) ⁱω+ca ₁ρ _i(τ ₁(t)+τ ₂(t))-kx _4i(38)

$\begin{array}{c}{h}_2(s_0,{\stackrel{\&CenterDot;}{s}}_0,{\stackrel{\&CenterDot;\&CenterDot;}{s}}_0,s_1,{\stackrel{\&CenterDot;}{s}}_1)={\mathrm{\&alpha;}}_0{\stackrel{\&CenterDot;\&CenterDot;}{s}}_0/\left(2a_1\right)+{\left({\mathrm{\&beta;}}_0{x}_0^{q_0/p_0}\right)}^{\&prime;\&prime;}/\left({2a}_1\right)+{\left({\mathrm{\&beta;}}_1{s}_1^{q_1/p_1}\right)}^{\&prime;}/\left(2a_1\right)\\ +{\mathrm{\&alpha;}}_1{\stackrel{\&CenterDot;}{s}}_1/\left(2a_1\right)\end{array}---\left(39\right)$

According to control law u _i, synchronization and tracking control can be carried out to dual-servo-motor system.

Above-mentioned result is emulated, obtains tracking effect and synchronous effect figure.From the analogous diagram of contrast, segmentation neural net friciton compensation controller has very high output tracking accuracy.In dual-servo-motor system segment neural networks compensate synchronized tracking emulation experiment, the parameter of drive motors, load and friction is as shown in table 1.

Table 1 simulation parameter

Emulate segmentation neural net friciton compensation algorithm under the above parameter of electric machine, the tracking effect of offset of sinusoidal input signal and tracking error are as shown in the figure.Fig. 5 and Fig. 6 is sinusoidal signal tracking effect figure, Fig. 7 and Fig. 8 is bi-motor synchronous effect figure.From simulation result, control algolithm of the present invention has very high tracking performance and net synchronization capability, dual motors system can be made synchronous quickly and with high precision tracking input signal.

Contemplated by the invention the dual-servo-motor system synchronization containing segmentation neural net friction model and tracking control problem.Set up segmentation neural net friction model, can approach the non-linear in tribology of servo system very well, this model not only can describe high regime frictional behavior, and also has good effect at low speed segment.Based on segmentation neural net friction model CONTROLLER DESIGN, and propose in the algorithm of fast terminal sliding formwork and represent the variable coefficient of synchronization extent, can make dual motors system can Fast synchronization and high-precision tracing control can be realized.Can be found out by emulation experiment, the inventive method has good control performance.

Claims (2)

1., based on the dual-servo-motor system control method of segmentation neural net friction model, it is characterized in that, comprise the following steps:

Step one, the Dual-motors Driving Servo System containing friction to be analyzed, and according to modelling by mechanism method, according to structure and the physical law of motor, set up the Mathematical Modeling of the Dual-motors Driving Servo System containing friction, specific as follows:

Wherein,

${\mathrm{\&tau;}}_i\left(t\right)=k(z_i\left(t\right)-\mathrm{\&alpha;}(\frac{2}{1+e^{{-\mathrm{rz}}_i}}-1))+c{\stackrel{\&CenterDot;}{z}}_i\left(t\right)(1-2\mathrm{\&alpha;}\frac{e^{{-\mathrm{rz}}_i}}{{(1+e^{{-\mathrm{rz}}_i})}^2})---\left(3\right)$

In formula (1), formula (2), formula (3), θ _i(i=1,2) and θ _mrepresent the corner of drive end and load end respectively; with represent the rotating speed of drive end and load end respectively; with represent the acceleration of drive end and load end respectively; J represents the moment of inertia of drive motors; J _mrepresent the moment of inertia of load end; b _mfor connecting the viscosity of gear; u _iexpression system input torque; ω represents biased moment; τ _it () represents transmission torque between motor and load; f _irepresent the moment of friction of drive motors; T represents the time from signal input; I=1, the drive motors 1 of 2 expression dual motors system and drive motors 2; z _i(t)=θ _i(t)-θ _mt () represents the differential seat angle of drive end and load end;

Step 2, to the friction term f in step one Modling model _ianalyze, and utilize segmentation neural network non-linear in tribology f _ifriction model, specific as follows:

One dimension segmentation neural net expression formula form is:

$f\left(h\right)=p_0+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_r{\mathrm{\&sigma;}}_r(0,h-{\mathrm{\&alpha;}}_r,{\mathrm{\&beta;}}_r-{\mathrm{\&alpha;}}_r)\&ForAll;h\&Element;R---\left(4\right)$

Wherein, basic function σ (0, h-α _r, β _r-α _r) be a special zonal cooling linear function, be expressed as: σ (0, h-α _r, β _r-α _r)=max (0, h-α _r)-max (0, h-max (α _r, β _r)), α _rand β _rat r subinterval shangguan in the upper bound of h ∈ R and lower bound respectively, p _r(r=1 ..., N) and be need to estimate to obtain unknowm coefficient;

The adequate condition that use formula (4) approaches one dimension zonal cooling linear function is: the domain of definition of independent variable h is divided into the subinterval of non-overlapping copies and boundary point α _rand β _rmeet α _r< β _rand β _r=α _r+1;

Following process is done further to formula (4):

Saltus step item h is added in formula (4) ₁(v) and exponential term h ₂(v); Wherein, saltus step item h ₁v () is relevant to maximum static friction force, with frictional force hopping phenomenon when solving break-in; Exponential term h ₂v () is with solving approaching of low speed Stribeck effect; Formula (4) becomes as described below:

$f\left(v\right)=d_0+\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}[d_r{\mathrm{\&rho;}}_r(0,v-{\mathrm{\&alpha;}}_r\left(v\right),{\mathrm{\&beta;}}_r\left(v\right)-{\mathrm{\&alpha;}}_r\left(v\right))+h_1\left(v\right)]+d_{N+1}{h}_2\left(v\right)---\left(5\right)$

Wherein, v and f (v) is speed and frictional force respectively; N (>=2) represents the number excursion of speed V being divided gained; α _r, β _rthe bound in r subinterval, h ₁v () is saltus step item, form is: $h_1\left(v\right)=\left\{\begin{array}{c}2F_s,v\&GreaterEqual;0\\ 0,v<0\end{array}\right.,$ H ₂v () describes Stribeck effect, form is: wherein F _srepresent stiction, v _crepresent speed when moment of friction is minimum;

By formula (5), conversion is as follows further:

Wherein, D=[d ₀, d ₁..., N, d _n+1] ^trepresent parameter vector, represent basis function vector; Parameter D is calculated by recurrent least square method method of estimation;

Step 3, the segmentation neural net friction model obtained according to step 2, utilize TSM control algorithm, carry out synchronization and tracking control to dual-servo-motor system, method is as follows:

If y (t)=θ _mfor system output signal, y _dt () is system reference signal, then error e (t)=y (t)-y _dt (), obtains error differential, second differential and three subdifferentials are respectively:

$\stackrel{\&CenterDot;}{e}=x_2-{\stackrel{\&CenterDot;}{y}}_d---\left(7\right)$

$\stackrel{\&CenterDot;\&CenterDot;}{e}={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d=a_1{\mathrm{\&Sigma;}}_{i=1}^2{\mathrm{\&tau;}}_i\left(t\right)-a_1{b}_m{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d---\left(8\right)$

Fast terminal sliding Mode Algorithm is utilized to obtain:

$\left\{\begin{array}{c}{s}_0=e\\ s_1={\stackrel{\&CenterDot;}{s}}_0+{\mathrm{\&alpha;}}_0{s}_0+{\mathrm{\&beta;}}_0{s}_0^{q_0/p_0}\\ s_2={\stackrel{\&CenterDot;}{s}}_1+{\mathrm{\&alpha;}}_1{s}_1+{\mathrm{\&beta;}}_1{s}_1^{q_1/p_1}\end{array}\right.---\left(10\right)$

Wherein, p _i(i=0,1) is for positive odd number and meet p _i> q _i, and α _i> 0, β _i> 0;

Now, original control law is divided into guarantee speed sync u _siu is followed the tracks of with guarantee _titwo parts, control law u _ibe expressed as

u _i＝u _si+ψu _ti(11)

Wherein,

$u_{\mathrm{si}}=\frac{1}{a_{2}c{\mathrm{\&rho;}}_i}[h_1(x_{3i},x_{4i})-c(a_1{b}_m{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m-a_2{f}_i){\mathrm{\&rho;}}_i]---\left(12\right)$

$\mathrm{\&psi;}=\frac{1}{e^{\mathrm{\&eta;}|{\stackrel{\&CenterDot;}{z}}_1-{\stackrel{\&CenterDot;}{z}}_2|}}---\left(14\right)$

Wherein, the control law u of speed sync is ensured _simiddle f _ifor the friction model that segmentation neural net in step 2 obtains, at input u _iproduce the input variable that can be offset friction effects; B, η are positive number, h ₁(x _3i, x _4i) be system mode feedback term, for system sliding formwork item, be expressed as h ₁(x _3i, x _4i)=a ₂c ρ _iτ _i(t)+a ₂c ρ _i(-1) ⁱω+ca ₁ρ _i(τ ₁(t)+τ ₂(t))-kx _4i(15)

$\begin{array}{c}{h}_2(s_0,{\stackrel{\&CenterDot;}{s}}_0,{\stackrel{\&CenterDot;\&CenterDot;}{s}}_0,s_1,{\stackrel{\&CenterDot;}{s}}_1)={\mathrm{\&alpha;}}_0{\stackrel{\&CenterDot;\&CenterDot;}{s}}_0/\left(2a_1\right)+{\left({\mathrm{\&beta;}}_0{x}_0^{q_0/p_0}\right)}^{\&prime;\&prime;}/\left({2a}_1\right)+{\left({\mathrm{\&beta;}}_1{s}_1^{q_1/p_1}\right)}^{\&prime;}/\left(2a_1\right)\\ +{\mathrm{\&alpha;}}_1{\stackrel{\&CenterDot;}{s}}_1/\left(2a_1\right)\end{array}---\left(16\right)$

According to control law u _i, synchronization and tracking control is carried out to dual-servo-motor system.

2. as claimed in claim 1 based on a dual-servo-motor system control method for segmentation neural net friction model, it is characterized in that, the interval v of step 2 medium velocity _cacquisition methods be:

Respectively choose at the both forward and reverse directions of dual-servo-motor system and be no less than 10 friction speed values; Meanwhile, adopt PI to control to dual motors system, make the speed of system keep constant; When motor uniform motion, the size of motor output torque is the size of frictional force, and the size that the size of motor output torque and controller export control voltage is directly proportional, export the size of controlled quentity controlled variable by recording controller, the size of motor friction under present speed can be obtained; 3 above-mentioned process are no less than to each speed sample point, to the whole frictional force results averaged obtained, as actual frictional force suffered by system under present speed; Finally obtain the size of frictional force during positive and negative both direction at least 10 friction speeds, then data acquisition least square fitting is respectively organized to positive and negative both direction, speed interval v can be obtained _c;

Described maximum static friction force F _sacquisition methods is:

By dual-servo-motor system works under open loop environment, increase Double Motor Control voltage gradually, until motor starts to rotate, be now the maximum static friction of system; Repeat at least 10 operations, get its mean value as maximum static friction torque F _s.