CN106067747B - A kind of design method of sliding formwork disturbance observer for servo system control - Google Patents
A kind of design method of sliding formwork disturbance observer for servo system control Download PDFInfo
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- CN106067747B CN106067747B CN201610382613.5A CN201610382613A CN106067747B CN 106067747 B CN106067747 B CN 106067747B CN 201610382613 A CN201610382613 A CN 201610382613A CN 106067747 B CN106067747 B CN 106067747B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P7/00—Arrangements for regulating or controlling the speed or torque of electric DC motors
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Abstract
The present invention provides a kind of design method of the sliding formwork disturbance observer for servo system control, friction interference problem when for servo-drive system low speed and the error and uncertain problem for considering system modelling.Using common DC motor model, disturbance observer is combined with Sliding mode variable structure control, designs sliding formwork disturbance observer.The size of observation moment of friction is gone first with disturbance observer, then according to obtained moment of friction design sliding mode controller.The switching item gain of sliding mode controller can be reduced to the observation of moment of friction, reduce chattering phenomenon.By sliding formwork disturbance observer realize low speed servo system to dead zone, creep, the inhibition of the non-linear phenomenas such as self-oscillation, reduce the requirement to modeling accuracy, and there is good robustness.
Description
Technical field
The present invention relates to a kind of design methods of the sliding formwork disturbance observer for servo system control.
Background technology
In low speed servo system, moment of friction causes the dynamic property of servo-drive system and seriously affects.And cause
Some non-linear phenomenas, such as rotating speed zero crossing dead zone, low speed jerking motion phenomenon, stagnant sliding self-oscillation etc..In order to eliminate this
A little non-linear phenomenas need to compensate moment of friction.There are two types of compensation ways on the whole at present, and one is based on friction
The compensation method of model, such as Stribeck models, LuGre models.Process is estimated first with the speed of acquisition, location information
Model parameter is counted, real-time moment of friction size is obtained, corresponding offset is then added in the controller.This method due to
It needs the method by test or on-line identification to determine model parameter in advance, causes control law more complicated.Another kind is base
In the friciton compensation mode of non-model, friction is considered as disturbing signal and is eliminated.Disturbance observer is a kind of common non-mould
The friciton compensation mode of type, it is widely used to observe and compensate frictional force on torque motor, but model relatively
There is no application note on complicated direct current generator.In addition, disturbance observer compensation way is very high to the required precision of system modelling,
Compensation effect can degenerate in the case of having error if there is Unmarried pregnancy or modeling.
Sliding mode variable structure control has the characteristics that insensitive to the parameter and shock wave of system, and robustness is stronger.But
If rubbing larger servo-drive system with Sliding mode variable structure control, it can make sign function therein that there is higher gain and cause
Larger chattering phenomenon, therefore consideration friction factor is had to when designing sliding mode controller.
Invention content
The present invention be directed to servo-drive system low speed when friction interference problem and consider system modelling error and do not know
Sex chromosome mosaicism provides a kind of design method of the sliding formwork disturbance observer for servo system control.
The present invention adopts the following technical scheme that：A kind of design side of sliding formwork disturbance observer for servo system control
Method, steps are as follows：
(1) state equation for initially setting up servo-drive system is as follows：
Wherein, state variable x1Indicate corner, x2Indicate rotating speed, CeIt is the back EMF coefficient of motor, u is control input,
KuIt is the amplification coefficient of pwm driver, KmIt is torque coefficient, J is rotary inertia, and R is armature resistance, TfIndicate friction perturbed force
Square；
(2) sliding formwork control rate is designed
R indicates that Setting signal, the tracking error of Angle Position and angular speed are respectively
E=r-x1(2)
Design switching function s
Wherein c indicates the parameter of diverter surface, and c is bigger, keeps the response speed of system faster, but stability can be affected；
Using exponentially approaching rule
Wherein ε>0, k>0, ε is constant speed approach term coefficient, and k is exponential approach term coefficient, is required for artificial appropriate selection, knot
Box-like (1) and (4)
The expression formula of control rate u is obtained according to formula (5) (6)
In addition to moment of friction T in above formulafOutside, remaining physical quantity is all known, below by the way of disturbance observer
To observe moment of friction；
(3) according to the modelling disturbance observer of direct current generator, the output valve of disturbance observer is equivalent to arrive servo system
The estimated value of the equivalent friction torque of system input terminalFollowing formula illustrates its relationship with other physical quantitys,
WhereinIt is motor speed, Gn-1(s) it is the inverse of controlled device name transmission function, U (s) is the defeated of controller
Go out, Q (s) indicates that a low-pass filter, expression formula are selected as
Wherein timeconstantτ is suitably chosen according to the bandwidth of system；
Formula (8) is multiplied by coefficientThe estimated value of realistic tribological torque is obtained later,
The control rate that final convolution (7) and formula (10) obtain completes the design of sliding formwork disturbance observer.
Advantages of the present invention：The friction for enabling disturbance observer to observe common DC motor by Structural Transformation is interfered,
Rather than just torque motor.Disturbance observer can reduce the jitter problem of sliding formwork control to the observation of moment of friction, and slide
The use of mould controller can be effectively improved the shortcomings that disturbance observer, reduce the requirement to modeling accuracy, improve system
Robustness and anti-interference ability, the two bring out the best in each other.
Description of the drawings
Fig. 1 is the sliding formwork control figure containing friction servo system；
Fig. 2 is the schematic diagram of disturbance observer；
Fig. 3 is the structure chart of sliding formwork disturbance observer；
Fig. 4 is the speed curves figure of the lower PID control of sinusoidal input；
Fig. 5 is the speed curves figure of the lower sliding formwork disturbance observer control of sinusoidal input；
Fig. 6 is the site error curve graph that step position inputs lower two kinds of control strategies；
Fig. 7 is the response curve of two kinds of control strategies under low speed ramp input.
Specific implementation mode
The present invention is further explained below according to Figure of description citing：
Embodiment 1
A kind of design method of sliding formwork disturbance observer for servo system control, steps are as follows：
1. the design of sliding mode controller
Such as Fig. 1 shows using sliding mode controller to control a servo-drive system by frictional influence, servo system is initially set up
Shown in the state equation of system such as formula (1)：
Wherein r (t) is command signal, and u is control input, CeIt is the back EMF coefficient of motor, KuIt is pwm driver
Amplification coefficient, R are armature resistance, KmIt is torque coefficient, J is rotary inertia, TfIndicate friction disturbance torque.State variable x1Table
Show corner, x2Indicate rotating speed.
The tracking error of Angle Position and angular speed is respectively
E=r-x1 (2)
Design switching function
Using exponentially approaching rule
Wherein ε>0,k>0.Convolution (1) and (4) can obtain
The expression formula of control rate u can be obtained according to formula (5) (6)
In addition to moment of friction T in above formulafOutside, remaining physical quantity is all known.Below by the way of disturbance observer
To observe moment of friction.
2. the principle of disturbance observer
The schematic diagram of disturbance observer as shown in Fig. 2, n indicates interference signal in figure,Indicate the observation of interference, Gp(s)
Indicate controlled device transmission function, Gn -1(s) indicate that the inverse of controlled device nominal plant model, ξ indicate output end noise, Q (s) is one
A low-pass filter.Usual Q (s) can be selected
Direct current generator shown in FIG. 1 is needed to carry out since its friction interference being subject to is located at the inside of controlled device
Certain Mathematical treatment.If still according to the structure design disturbance observer of Fig. 2, the output valve of disturbance observer is not
It is true moment of friction, but it is in the equivalence value T of servo-drive system input terminaleq.Equivalent friction torque TeqWith original frictional force
Square TfRelationship be
Ignore the influence of inductance, approximation has
3. the design of sliding formwork disturbance observer
In conjunction with the method for Sliding mode variable structure control and disturbance observer, the control block diagram for obtaining servo-drive system is as shown in Figure 3.
The estimated value of moment of friction is obtained by disturbance observer firstSince the output valve of interference observer is equivalent friction torque
Estimated valueAccording to formula (10), it is multiplied by coefficientThe estimated value of realistic tribological torque is obtained later
The sliding formwork control rate of controller is finally designed according to formula (7).
Embodiment 2
The parameter of known controlled motor servo system：R=14.7 Ω, Km=1.134Nm/A, Ce=0.119V/ (r/
Min), J=1.79*10-6kg*m2, Ku=12.
The transmission function of motor is
Parameter τ=0.001ms of low-pass filter Q (s) is selected, then
Then according to Q (s) and Gp(s), structure disturbance observer obtains the estimated value of moment of frictionSelect c=30, k
=1, ε=1 is as control parameter design control rate u.
It is emulated by computer simulink, compares the quality of PID control and the control of sliding formwork interference observer.
The two-loop system of operating speed ring and position ring first, the rule that pid parameter is chosen are：Do not consider first
The non-linear friction part of motor determines the PID coefficient of speed ring and position ring using critical proportional band law successively, then right again
Coefficient is finely adjusted, and is obtained close to best tracking performance.It is final to determine that the proportionality coefficient of speed ring is 0.021, integration system
Number is 1.6, since the effect of friction interference makes output end have larger noise, differential term zero；Position ring proportionality coefficient is 6, product
It is 1.8 to divide coefficient, differential term zero.
Given amplitude be 6 ° of frequencies be 2rad/s sinusoidal position input signal θ=6sin2t (o), theoretically its speedometer
It is ω=2cos2t (r/min) up to formula.Fig. 4 illustrates the angular speed change curve under PID control, and speed curves are in zero crossing table
Reveal dead zone phenomenon, dead time is about 0.15s, accounts for the 4.8% of a cycle, this is mainly due to non-linear in tribology to cause
's.Fig. 5 illustrates that the change curve using rotating speed after sliding formwork interference observer, dead time are about 0.02s, accounts for the period
0.64%, illustrate effectively inhibit dead zone phenomenon using sliding formwork disturbance observer.
Given 6 ° of step position input signal, Fig. 6 indicate that the site error of two kinds of control strategies when reaching stable state is bent
Line.There is the free-running phenomenon of stagnant cunning, position deviation in the site error curve of PID control, Position Tracking Systems when reaching stable state
Maximum value is 0.012 °.Using the site error curve of sliding formwork disturbance observer (SMDOB), shake number significantly reduces, and position is inclined
Poor maximum value is 0.001 °, and oscillation amplitude is the 8% of PID control.
The low speed slope position that given slope is 0.01 ° inputs, and the dotted line in Fig. 7 is illustrated using being exported under PID control
The curve that position changes over time shows apparent creeping phenomenon；Solid line is controlled using sliding formwork disturbance observer (SMDOB)
The position response curve of system, creeping phenomenon are substantially eliminated.Illustrate that SMDOB control programs can be good at inhibiting electricity
The creeping phenomenon that machine low speed occurs when running.
Claims (1)
1. a kind of design method of sliding formwork disturbance observer for servo system control, which is characterized in that steps are as follows：
(1) state equation for initially setting up servo-drive system is as follows：
Wherein, state variable x1Indicate corner, x2Indicate rotating speed, CeIt is the back EMF coefficient of motor, u is control input, KuIt is
The amplification coefficient of pwm driver, KmIt is torque coefficient, J is rotary inertia, and R is armature resistance, TfIndicate friction disturbance torque；
(2) sliding formwork control rate is designed
R indicates that Setting signal, the tracking error of Angle Position and angular speed are respectively
E=r-x1 (2)
Design switching function s
Wherein c indicates the parameter of diverter surface, and c is bigger, keeps the response speed of system faster, but stability can be affected；
Using exponentially approaching rule
Wherein ε>0, k>0, ε is constant speed approach term coefficient, and k is exponential approach term coefficient, is required for artificial appropriate selection, convolution
(1) it is obtained with (4)
The expression formula of control rate u is obtained according to formula (5) (6)
In addition to moment of friction T in above formulafOutside, remaining physical quantity is all known, is observed by the way of disturbance observer below
Moment of friction；
(3) according to the modelling disturbance observer of direct current generator, the output valve of disturbance observer is equivalent defeated to servo-drive system
Enter the estimated value of the equivalent friction torque at endFollowing formula illustrates its relationship with other physical quantitys,
WhereinIt is motor speed, Gn-1(s) it is the inverse of controlled device name transmission function, U (s) is the output of controller, Q
(s) indicate that a low-pass filter, expression formula are selected as
Wherein timeconstantτ is suitably chosen according to the bandwidth of system；
Formula (8) is multiplied by coefficientThe estimated value of realistic tribological torque is obtained later,
The control rate that final convolution (7) and formula (10) obtain completes the design of sliding formwork disturbance observer.
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