CN108832836A - A kind of supersonic motor servo-control system sliding-mode control - Google Patents
A kind of supersonic motor servo-control system sliding-mode control Download PDFInfo
- Publication number
- CN108832836A CN108832836A CN201811067088.3A CN201811067088A CN108832836A CN 108832836 A CN108832836 A CN 108832836A CN 201811067088 A CN201811067088 A CN 201811067088A CN 108832836 A CN108832836 A CN 108832836A
- Authority
- CN
- China
- Prior art keywords
- control
- supersonic motor
- function
- parameter
- error
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 claims abstract description 21
- 238000009415 formwork Methods 0.000 claims abstract description 12
- 230000008878 coupling Effects 0.000 claims abstract description 10
- 238000010168 coupling process Methods 0.000 claims abstract description 10
- 238000005859 coupling reaction Methods 0.000 claims abstract description 10
- NJPPVKZQTLUDBO-UHFFFAOYSA-N novaluron Chemical compound C1=C(Cl)C(OC(F)(F)C(OC(F)(F)F)F)=CC=C1NC(=O)NC(=O)C1=C(F)C=CC=C1F NJPPVKZQTLUDBO-UHFFFAOYSA-N 0.000 claims abstract description 10
- 230000000694 effects Effects 0.000 claims abstract description 7
- 238000013178 mathematical model Methods 0.000 claims abstract description 4
- 230000003044 adaptive effect Effects 0.000 claims description 18
- 238000005183 dynamical system Methods 0.000 claims description 11
- 230000001133 acceleration Effects 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims description 6
- 238000012886 linear function Methods 0.000 claims description 6
- 230000006978 adaptation Effects 0.000 claims description 3
- 238000004422 calculation algorithm Methods 0.000 claims description 3
- 238000012885 constant function Methods 0.000 claims description 3
- 239000013256 coordination polymer Substances 0.000 claims description 3
- 230000003247 decreasing effect Effects 0.000 claims description 3
- 230000007547 defect Effects 0.000 claims description 3
- 238000006073 displacement reaction Methods 0.000 claims description 3
- 230000005611 electricity Effects 0.000 claims description 3
- 238000001914 filtration Methods 0.000 claims description 3
- 238000012905 input function Methods 0.000 claims description 3
- 230000009897 systematic effect Effects 0.000 claims description 3
- 238000005312 nonlinear dynamic Methods 0.000 claims 1
- 238000010586 diagram Methods 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000002604 ultrasonography Methods 0.000 description 1
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/0005—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing non-specific motion; Details common to machines covered by H02N2/02 - H02N2/16
- H02N2/0075—Electrical details, e.g. drive or control circuits or methods
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
- H02N2/14—Drive circuits; Control arrangements or methods
Landscapes
- Feedback Control In General (AREA)
Abstract
The present invention relates to a kind of supersonic motor servo-control system sliding-mode controls.One supersonic motor servo-control system is provided, supersonic motor including pedestal and on pedestal, supersonic motor side output shaft is connected with photoelectric encoder, supersonic motor other side output shaft is connected with flywheel inertia load, the flywheel inertia load output shaft is connected through shaft coupling with torque sensor, and the signal output end of the photoelectric encoder, the signal output end of torque sensor are respectively connected to control system；This method is established on the basis of sliding formwork mathematical model, but also servo-system hysteresis is minimum, so as to obtain better input and output controlled efficiency while reducing identification dynamic error.Not only control accuracy is high by the present invention, but also structure is simple, compact, and using effect is good.
Description
Technical field
The invention belongs to electric machine controller fields, in particular to a kind of supersonic motor servo-control system sliding formwork control side
Method.
Background technique
Due to the presence of torque-speed hysteresis in the design of existing supersonic motor servo-control system, so that system
Performance be affected, to period repeating signal control when have certain error.In order to improve the control effect followed, Wo Menshe
The supersonic motor servo-control system based on hysteresis compensation control is counted.From torque-speed follower implementation result, we
It was found that system is substantially linear in torque velocities relationship, and variation, noise, cross-linked interference and frictional force of parameter etc. because
Element can not almost export torque and impact, therefore the supersonic motor servo-control system based on hysteresis compensation control can have
The controlled efficiency of the enhancement system of effect, and system is further reduced for probabilistic influence degree, therefore the torque of motor
Preferable dynamic characteristic can be obtained with speed control.
Summary of the invention
The purpose of the present invention is to provide a kind of supersonic motor servo-control system sliding-mode controls, and not only control is quasi-
Exactness is high, and structure is simple, compact, and using effect is good.
To achieve the above object, the technical scheme is that：A kind of supersonic motor servo-control system sliding formwork control
Method provides a supersonic motor servo-control system, the supersonic motor including pedestal and on pedestal, the ultrasonic wave
Motor side output shaft is connected with photoelectric encoder, and supersonic motor other side output shaft is connected with flywheel inertia load,
The flywheel inertia load output shaft is connected through shaft coupling with torque sensor, the signal output end of the photoelectric encoder,
The signal output end of torque sensor is respectively connected to control system；This method is established on the basis of sliding formwork mathematical model, is being reduced
But also servo-system hysteresis is minimum, so as to obtain better input and output controlled efficiency while recognizing dynamic error.
In an embodiment of the present invention, the control system includes supersonic motor drive control circuit, the ultrasonic wave
Motor driving controling circuit includes control chip circuit and driving chip circuit, the signal output end of the photoelectric encoder and institute
The respective input for stating control chip circuit is connected, the output end and the driving chip circuit of the control chip circuit
Respective input is connected, and to drive the driving chip circuit, the driving frequency adjustment signal of the driving chip circuit is defeated
Outlet and driving half-bridge circuit adjustment signal output end are connected with the respective input of the supersonic motor respectively.
In an embodiment of the present invention, this method is implemented as follows,
The dynamical equation of supersonic motor drive system can be written as：
Wherein Ap=-B/J, BP=J/Kt> 0, CP=-1/J；B is damped coefficient, and J is rotary inertia, KtFor current factor,
TfIt (v) is frictional resistance torque, TLFor loading moment, U (t) is the output torque of motor, θrIt (t) is to be surveyed by photoelectric encoder
The position signal measured,For speed signal obtained by calculation,For acceleration signal obtained by calculation；
X is the displacement of rotor,Indicate speed,Indicate acceleration；
In order to eliminate influence caused by motor friction hysteresis, using sliding formwork control；
Considering one has hysteresis non-linearity by the controlled system that non-executing mechanism forms, i.e. lag is represented as non-linear
The input of dynamical system, and it is expressed as operator
ω (t)=P [v] (t) (2)
It is input with v (t), ω (t) is output；Above hysteresis non-linearity dynamical system is described with canonical form
Wherein, YiIt is known continuous and linear/non-linear function, parameter aiIt is constant with controller gain b, not lose
It is general, it is assumed that b>0；
Controlling target is design control law v (t), with forced regime vectorFollow desired rail
MarkThat is x → x as t → ∞d；
Consider that lag output ω (t) is written as
ω (t)=p0v(t)-d[v](t) (4)
For convenience's sake, Fr (v) is indicated for given original state ψ ∈ Ψ, Fr [v, ψ]；
If it is known that the lag in system, i.e., any continuous input function v (t) in moment t is provided or can be quasi-
Really estimate p (r) and ψ, then Fr[v] (t) will be confirmed as one group of line segment；The integral of d [v] can be in line computation, and d [v] can be with
Cancel second nonlinear terms of dynamical system as feed-forward compensator；However, in most cases, accurate estimating system
Lag be difficult or even impossible；The lag model of (4) is used, hysteresis non-linearity dynamical system (3) becomes
This leads to the linear relationship of input signal v (t) He shift terms bd [v]；
Wherein, the first item on the right side of formula (6) is the linear function signal v (t) for controlling currently available controller；This
In the case of, currently available controller design can be merged with the lag model of controller design；Such structure is real
It can be becomed more clear on border, and adaptive control algorithm can be designed；
If there is no hysteresis effect in system (6), i.e. d [v] (t)=0,
Building robust controller can be efficiently used for using adaptive sliding-mode observer method, and tracking and steady is carried out to system
It is fixed, even if there are systematic uncertainties；In robust control, bd [v] (t) is generally viewed as interference function；Since d [v] (t) is
One integral function；It is thus impossible to make hypothesis to its boundedness；In addition, it is actually the function of input signal v (t), need
Adaptive controller is designed and carry out specially treated；
By tracking error vectorIt is defined asThe tracking error of filtering is
S (t) can be rewritten asAnd ΛT=[λ(n-1),(n-1)λ(n-2).., 1], it provides in formula (8)
Definition has with properties：
(i) equation s (t)=0 defines tracking error vectorTime-varying hyperplane of the index decreased to zero on it
(ii) ifS (t) |≤ε, and ε is a constant, then
(iii) ifS (t) |≤ε, then x (t) will converge to Ω in time constant (n-1)/λε；
In sliding formwork control design, controller includes discontinuous nonlinear function sat ()；Due to the reality of switching device
Defect and delay can cause to shake；In order to eliminate shake, a tuning error s is introducedε, it is shown below：
Wherein, ε is any normal number, and sat () is saturation function；When filtered error s is less than ε, tuning error sεDisappear
It loses；
When developing adaptive control law, system and lag have been made it is assumed hereinafter that：
Assuming that 1：Required trackIt is continuously available；
Assuming that 2：There are known 0 < b of constantmin≤bmax, so that the control gain b in (3) meets b ∈ [bmin,bmax]
Assuming that 3：It determines
Thenθi minAnd θi maxIt is known real number；
Assuming that 4：For r ∈ [0, R], there is known constant P0 minAnd P0 max, make P0> P0 minAnd Pr> P0 max；
Assuming that 3 define a new parameter vector θ；Assuming that 3 mean that system parameter a is known in advancei, i=1 ..., k
Range；This is the reasonable assumption to system prior knowledge；For assuming 4, it is based on the attribute of density function p (r), is set p (r)
Upper limit P0 maxIt is reasonable；It needs exist for meeting P0 min> 0；
When proposing Robust Adaptive Control method, need defined below：
It is the evaluated error of θ (t),It is the estimation of θ (t),It isEstimation,It isEstimation
Error,It is the evaluated error of p (t, r),It is the estimation of p (t, r)；It allows
And the estimation of B (t)ByIt provides, this causes
Meaning be B (t) evaluated error；It is limited by above-mentioned in view of system and lag model it is assumed that and paying attention to
To the d [v] (t) and F in (4)r[v] (t) be it is integrated, propose following control law：
kdFor the coefficient of saturation function, work as kd> 0,
When, parameterAnd functionIt will be updated by following adjustment procedure
Wherein, parameter γ, η and q is the normal number of determining adaptation rate, and Proj () is a projection operator, and definition is such as
Under：
Projection operator needs parameter θ,With the upper and lower bound of p (t, r)；But these parameters are only used for specified projection and calculate
The parameter variation range of son；As long as estimation parameter has boundary, these ranges would not be restricted；
vh(t) the compensation component of representative function d [v] (t)；It is assumed that d [v] (t) is constant function or known function, d [v]
(t) it is integral equation, its boundedness is not assumed；Density function p (r) is not the function of time, therefore this can be considered as
The parameter of lag model, and the law of an estimation is formulated thus；
ForCalculating simply can replace accumulating with R using numerical technique
Point, i.e., by R divided by size closely-spaced, that wherein determination is spaced by N；The selection of the size of space depends on required precision；(6),
(15) and the stability of closed-loop system described in (18)-(20) is identified below；
System for being provided in equation (3), be by PI model (4) propose hysteresis non-linearity, it is assumed that for 1-4 with
IfWithThen equation (15) and (18)-(20)
Specified Robust adaptive controller ensures that all closed signals are all bounded, when t → ∞, the error and expectation of state vector
TrackIt converges to
In an embodiment of the present invention, the shaft coupling is yielding coupling.
In an embodiment of the present invention, the supersonic motor, photoelectric encoder, torque sensor are respectively through ultrasonic wave electricity
Machine fixes the fixed bracket of bracket, photoelectric encoder, the fixed bracket of torque sensor is fixed on the pedestal.
Compared to the prior art, the invention has the advantages that：The present invention improves the accuracy of control, can obtain
Obtain preferable dynamic characteristic.In addition, device design is rationally, structure is simple, compact, and manufacturing cost is low, has very strong practical
Property and wide application prospect.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of the embodiment of the present invention.
Fig. 2 is the control circuit schematic diagram of the embodiment of the present invention.
In figure, 1- photoelectric encoder, the fixed bracket of 2- photoelectric encoder, 3- supersonic motor side output shaft, 4- ultrasound
Wave motor, the fixed bracket of 5- supersonic motor, 6- supersonic motor other side output shaft, 7- flywheel inertia load, 8- flywheel are used
Property load output shaft, 9- yielding coupling, 10- torque sensor, the fixed bracket of 11- torque sensor, 12- pedestal, 13- control
Chip circuit, 14- driving chip circuit, 15,16,17- photoelectric encoder output A, B, Z phase signals, 18,19,20,21- drive
The driving frequency adjustment signal that dynamic chip circuit generates, the driving half-bridge circuit adjustment signal that 22- driving chip circuit generates,
23,24,25,26, the 27, signal for the driving chip circuit that 28- control chip circuit generates, 29- supersonic motor drive control
Circuit.
Specific embodiment
With reference to the accompanying drawing, technical solution of the present invention is specifically described.
The present invention provides a kind of supersonic motor servo-control system sliding-mode controls, provide a supersonic motor and watch
Take control system, the supersonic motor 4 including pedestal 12 and on pedestal 12, supersonic motor side output shaft 3 with
Photoelectric encoder 1 is connected, and supersonic motor other side output shaft 6 is connected with flywheel inertia load 7, and the flywheel inertia is negative
It carries output shaft 8 to be connected through shaft coupling (yielding coupling 9) with torque sensor 10, the signal output of the photoelectric encoder 1
It holds, the signal output end of torque sensor 10 is respectively connected to control system；The control system includes supersonic motor driving control
Circuit 29 processed, the supersonic motor drive control circuit 29 includes controlling chip circuit 13 and driving chip circuit 14, described
The signal output end of photoelectric encoder 1 is connected with the respective input of the control chip circuit 13, the control chip electricity
The output end on road 13 is connected with the respective input of the driving chip circuit 14, to drive the driving chip circuit 14,
The driving frequency adjustment signal output end of the driving chip circuit 14 and driving half-bridge circuit adjustment signal output end respectively with
The respective input of the supersonic motor 4 is connected.The supersonic motor 4, photoelectric encoder 1, torque sensor 10 divide
The base is not scheduled through the fixed bracket 5 of supersonic motor, the fixed bracket 2 of photoelectric encoder, the fixed bracket solid 11 of torque sensor
On seat 12.This method is established on the basis of sliding formwork mathematical model, but also servo-system while reducing identification dynamic error
Hysteresis is minimum, so as to obtain better input and output controlled efficiency.
Supersonic motor servo-control system sliding-mode control of the present invention is implemented as follows,
The dynamical equation of supersonic motor drive system can be written as：
Wherein Ap=-B/J, BP=J/Kt> 0, CP=-1/J；B is damped coefficient, and J is rotary inertia, KtFor current factor,
TfIt (v) is frictional resistance torque, TLFor loading moment, U (t) is the output torque of motor, θrIt (t) is to be surveyed by photoelectric encoder
The position signal measured,For speed signal obtained by calculation,For acceleration signal obtained by calculation；
X is the displacement of rotor,Indicate speed,Indicate acceleration；
In order to eliminate influence caused by motor friction hysteresis, using sliding formwork control；
Considering one has hysteresis non-linearity by the controlled system that non-executing mechanism forms, i.e. lag is represented as non-linear
The input of dynamical system, and it is expressed as operator
ω (t)=P [v] (t) (2)
It is input with v (t), ω (t) is output；Above hysteresis non-linearity dynamical system is described with canonical form
Wherein, YiIt is known continuous and linear/non-linear function, parameter aiIt is constant with controller gain b, not lose
It is general, it is assumed that b>0；
Controlling target is design control law v (t), with forced regime vectorFollow desired rail
MarkThat is x → x as t → ∞d；
Consider that lag output ω (t) is written as
ω (t)=p0v(t)-d[v](t) (4)
For convenience's sake, for given original state ψ ∈ Ψ, Fr[v, ψ] indicates Fr(v)；
If it is known that the lag in system, i.e., any continuous input function v (t) in moment t is provided or can be quasi-
Really estimate p (r) and ψ, then Fr[v] (t) will be confirmed as one group of line segment；The integral of d [v] can be in line computation, and d [v] can be with
Cancel second nonlinear terms of dynamical system as feed-forward compensator；However, in most cases, accurate estimating system
Lag be difficult or even impossible；The lag model of (4) is used, hysteresis non-linearity dynamical system (3) becomes
This leads to the linear relationship of input signal v (t) He shift terms bd [v]；
Wherein, the first item on the right side of formula (6) is the linear function signal v (t) for controlling currently available controller；This
In the case of, currently available controller design can be merged with the lag model of controller design；Such structure is real
It can be becomed more clear on border, and adaptive control algorithm can be designed；
If there is no hysteresis effect in system (6), i.e. d [v] (t)=0,
Building robust controller can be efficiently used for using adaptive sliding-mode observer method, and tracking and steady is carried out to system
It is fixed, even if there are systematic uncertainties；In robust control, bd [v] (t) is generally viewed as interference function；Since d [v] (t) is
One integral function；It is thus impossible to make hypothesis to its boundedness；In addition, it is actually the function of input signal v (t), need
Adaptive controller is designed and carry out specially treated；
By tracking error vectorIt is defined asThe tracking error of filtering is
S (t) can be rewritten asAnd ΛT=[λ(n-1),(n-1)λ(n-2).., 1], formula provides in (8)
Definition have with properties：
(i) equation s (t)=0 defines tracking error vectorTime-varying hyperplane of the index decreased to zero on it
(ii) ifS (t) |≤ε, and ε is a constant, then
(iii) ifS (t) |≤ε, then x (t) will converge to Ω in time constant (n-1)/λε；
In sliding formwork control design, controller includes discontinuous nonlinear function sat ()；Due to the reality of switching device
Defect and delay can cause to shake；In order to eliminate shake, a tuning error s is introducedε, it is shown below：
Wherein, ε is any normal number, and sat () is saturation function；When filtered error s is less than ε, tuning error sεDisappear
It loses；
When developing adaptive control law, system and lag have been made it is assumed hereinafter that：
Assuming that 1：Required trackIt is continuously available；
Assuming that 2：There are known 0 < b of constantmin≤bmax, so that the control gain b in (3) meets b ∈ [bmin,bmax]
Assuming that 3：It determines
Thenθi minAnd θi maxIt is known real number；
Assuming that 4：For r ∈ [0, R], there is known constant P0 minAnd P0 max, make P0> P0 minAnd Pr> P0 max；
Assuming that 3 define a new parameter vector θ；Assuming that 3 mean that system parameter a is known in advancei, i=1 ..., k
Range；This is the reasonable assumption to system prior knowledge；For assuming 4, it is based on the attribute of density function p (r), is set p (r)
Upper limit P0 maxIt is reasonable；It needs exist for meeting P0 min> 0；
When proposing Robust Adaptive Control method, need defined below：
It is the evaluated error of θ (t),It is the estimation of θ (t),It isEstimation,It isEstimation
Error,It is the evaluated error of p (t, r),It is the estimation of p (t, r)；It allows
And the estimation of B (t)ByIt provides, this causes
Meaning be B (t) evaluated error；It is limited by above-mentioned in view of system and lag model it is assumed that and paying attention to
To the d [v] (t) and F in (4)r[v] (t) be it is integrated, propose following control law：
kdFor the coefficient of saturation function, work as kd> 0,
When, parameterAnd functionIt will be updated by following adjustment procedure
Wherein, parameter γ, η and q is the normal number of determining adaptation rate, and Proj () is a projection operator, and definition is such as
Under：
Projection operator needs parameter θ,With the upper and lower bound of p (t, r)；But these parameters are only used for specified projection
The parameter variation range of operator；As long as estimation parameter has boundary, these ranges would not be restricted；
vh(t) the compensation component of representative function d [v] (t)；It is assumed that d [v] (t) is constant function or known function, d [v]
(t) it is integral equation, its boundedness is not assumed；Density function p (r) is not the function of time, therefore this can be considered as
The parameter of lag model, and the law of an estimation is formulated thus；
ForCalculating simply can replace accumulating with R using numerical technique
Point, i.e., by R divided by size closely-spaced, that wherein determination is spaced by N；The selection of the size of space depends on required precision；(6),
(15) and the stability of closed-loop system described in (18)-(20) is identified below；
System for being provided in equation (3), be by PI model (4) propose hysteresis non-linearity, it is assumed that for 1-4 with
IfWithThen equation (15) and (18)-(20)
Specified Robust adaptive controller ensures that all closed signals are all bounded, when t → ∞, the error and expectation of state vector
TrackIt converges to
The above are preferred embodiments of the present invention, all any changes made according to the technical solution of the present invention, and generated function is made
When with range without departing from technical solution of the present invention, all belong to the scope of protection of the present invention.
Claims (5)
1. a kind of supersonic motor servo-control system sliding-mode control, which is characterized in that provide a supersonic motor servo
Control system, the supersonic motor including pedestal and on pedestal, supersonic motor side output shaft and photoelectric coding
Device is connected, and supersonic motor other side output shaft is connected with flywheel inertia load, the flywheel inertia load output shaft warp
Shaft coupling is connected with torque sensor, and the signal output end of the photoelectric encoder, the signal output end of torque sensor divide
Control system is not connected to it；This method establish on the basis of sliding formwork mathematical model, reduce recognize dynamic error while but also
Servo-system hysteresis is minimum, so as to obtain better input and output controlled efficiency.
2. a kind of supersonic motor servo-control system sliding-mode control according to claim 1, which is characterized in that institute
Stating control system includes supersonic motor drive control circuit, and the supersonic motor drive control circuit includes control chip electricity
Road and driving chip circuit, the signal output end of the photoelectric encoder are connected with the respective input of the control chip circuit
It connects, the output end of the control chip circuit is connected with the respective input of the driving chip circuit, to drive the drive
Dynamic chip circuit, the driving frequency adjustment signal output end of the driving chip circuit and driving half-bridge circuit adjustment signal output
End is connected with the respective input of the supersonic motor respectively.
3. a kind of supersonic motor servo-control system sliding-mode control according to claim 2, which is characterized in that should
Method is implemented as follows,
The dynamical equation of supersonic motor drive system can be written as：
Wherein Ap=-B/J, BP=J/Kt> 0, CP=-1/J；B is damped coefficient, and J is rotary inertia, KtFor current factor, Tf
It (v) is frictional resistance torque, TLFor loading moment, U (t) is the output torque of motor, θrIt (t) is to be measured by photoelectric encoder
Obtained position signal,For speed signal obtained by calculation,For acceleration signal obtained by calculation；
X is the displacement of rotor,Indicate speed,Indicate acceleration；
In order to eliminate influence caused by motor friction hysteresis, using sliding formwork control；
Considering one has hysteresis non-linearity by the controlled system that non-executing mechanism forms, i.e. lag is represented as non-linear dynamic
The input of system, and it is expressed as operator
ω (t)=P [v] (t) (2)
It is input with v (t), ω (t) is output；Above hysteresis non-linearity dynamical system is described with canonical form
Wherein, YiIt is known continuous and linear/non-linear function, parameter aiIt is constant with controller gain b, it is general not lose
Property, it is assumed that b>0；
Controlling target is design control law v (t), with forced regime vectorFollow desired trackThat is x → x as t → ∞d；
Consider that lag output ω (t) is written as
ω (t)=p0v(t)-d[v](t) (4)
For convenience's sake, for given original state ψ ∈ Ψ, Fr[v, ψ] indicates Fr(v)；
If it is known that the lag in system, i.e., any continuous input function v (t) in moment t is provided or can be accurately
Estimate p (r) and ψ, then Fr[v] (t) will be confirmed as one group of line segment；The integral of d [v] can may be used as in line computation, d [v]
Feed-forward compensator cancels second nonlinear terms of dynamical system；However, in most cases, accurate estimating system it is stagnant
After be difficult or even impossible；The lag model of (4) is used, hysteresis non-linearity dynamical system (3) becomes
This leads to the linear relationship of input signal v (t) He shift terms bd [v]；
Wherein, the first item on the right side of formula (6) is the linear function signal v (t) for controlling currently available controller；In such case
Under, currently available controller design can be merged with the lag model of controller design；Such structure is actually
It can become more clear, and adaptive control algorithm can be designed；
If there is no hysteresis effect in system (6), i.e. d [v] (t)=0,
It can be efficiently used for building robust controller using adaptive sliding-mode observer method system is tracked and stablized, i.e.,
Make that there are systematic uncertainties；In robust control, bd [v] (t) is generally viewed as interference function；Since d [v] (t) is one
Integral function；It is thus impossible to make hypothesis to its boundedness；In addition, it is actually the function of input signal v (t), need pair
Adaptive controller design carries out specially treated；
By tracking error vectorIt is defined asThe tracking error of filtering is
S (t) can be rewritten asAnd ΛT=[λ(n-1),(n-1)λ(n-2).., 1], the definition provided in formula (8)
With with properties：
(i) equation s (t)=0 defines tracking error vectorTime-varying hyperplane of the index decreased to zero on it
(ii) ifS (t) |≤ε, and ε is a constant, then
(iii) ifS (t) |≤ε, then x (t) will converge to Ω in time constant (n-1)/λε；
In sliding formwork control design, controller includes discontinuous nonlinear function sat ()；Due to the actual defects of switching device
And delay, it can cause to shake；In order to eliminate shake, a tuning error s is introducedε, it is shown below：
Wherein, ε is any normal number, and sat () is saturation function；When filtered error s is less than ε, tuning error sεIt disappears；
When developing adaptive control law, system and lag have been made it is assumed hereinafter that：
Assuming that 1：Required trackIt is continuously available；
Assuming that 2：There are known 0 < b of constantmin≤bmax, so that the control gain b in (3) meets b ∈ [bmin,bmax]
Assuming that 3：It determinesThen
θiminAnd θimaxIt is known real number；
Assuming that 4：For r ∈ [0, R], there is known constant P0minAnd P0max, make P0> P0minAnd Pr> P0max；
Assuming that 3 define a new parameter vector θ；Assuming that 3 mean that system parameter a is known in advancei, i=1 ..., the model of k
It encloses；This is the reasonable assumption to system prior knowledge；For assuming 4, it is based on the attribute of density function p (r), sets the upper of p (r)
Limit P0maxIt is reasonable；It needs exist for meeting P0min> 0；
When proposing Robust Adaptive Control method, need defined below：
It is the evaluated error of θ (t),It is the estimation of θ (t),It isEstimation,It isEvaluated error,It is the evaluated error of p (t, r),It is the estimation of p (t, r)；It allows
And the estimation of B (t)ByIt provides, this causes
Meaning be B (t) evaluated error；It is limited by above-mentioned in view of system and lag model it is assumed that and noticing (4)
In d [v] (t) and Fr[v] (t) be it is integrated, propose following control law：
kdFor the coefficient of saturation function, work as kd> 0,
When, parameterAnd functionIt will be updated by following adjustment procedure
Wherein, parameter γ, η and q is the normal number of determining adaptation rate, and Proj () is a projection operator, is defined as follows：
Projection operator needs parameter θ,With the upper and lower bound of p (t, r)；But these parameters are only used for specified projection operator
Parameter variation range；As long as estimation parameter has boundary, these ranges would not be restricted；
vh(t) the compensation component of representative function d [v] (t)；It is assumed that d [v] (t) is constant function or known function, d [v] (t) is product
Divide equation, its boundedness is not assumed；Density function p (r) is not the function of time, therefore this can be considered as lag model
Parameter, and thus formulate one estimation law；
ForCalculating simply can replace integrating with R, i.e., using numerical technique
By R divided by size closely-spaced, that wherein determination is spaced by N；The selection of the size of space depends on required precision；(6), (15) and
(18) stability of closed-loop system described in-(20) is identified below；
System for being provided in equation (3), be by PI model (4) propose hysteresis non-linearity, it is assumed that for 1-4 with
IfWithThen equation (15) and (18)-(20) are specified
Robust adaptive controller ensure that all closed signals are all bounded, as t → ∞, the error of state vector and desired rail
MarkIt converges to
4. a kind of supersonic motor servo-control system sliding-mode control according to claim 1, which is characterized in that institute
Stating shaft coupling is yielding coupling.
5. a kind of supersonic motor servo-control system sliding-mode control according to claim 1, which is characterized in that institute
Supersonic motor, photoelectric encoder, torque sensor are stated respectively through the fixed bracket of supersonic motor, the fixed branch of photoelectric encoder
The fixed bracket of frame, torque sensor is fixed on the pedestal.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811067088.3A CN108832836B (en) | 2018-09-13 | 2018-09-13 | A kind of supersonic motor servo-control system sliding-mode control |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811067088.3A CN108832836B (en) | 2018-09-13 | 2018-09-13 | A kind of supersonic motor servo-control system sliding-mode control |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108832836A true CN108832836A (en) | 2018-11-16 |
| CN108832836B CN108832836B (en) | 2019-06-04 |
Family
ID=64149789
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811067088.3A Active CN108832836B (en) | 2018-09-13 | 2018-09-13 | A kind of supersonic motor servo-control system sliding-mode control |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108832836B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111865169A (en) * | 2020-07-21 | 2020-10-30 | 南京航空航天大学 | Model-free integral sliding mode control method of ultrasonic motor servo system |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN203775078U (en) * | 2014-04-11 | 2014-08-13 | 衢州职业技术学院 | Ultrasonic motor speed position controller based on ARM and DDS |
| CN104660098A (en) * | 2015-03-23 | 2015-05-27 | 安徽理工大学 | Low-frequency PWM and single neuron self-adaption-based ultrasonic motor control system |
| CN106208807A (en) * | 2016-09-19 | 2016-12-07 | 闽江学院 | Supersonic motor servo-control system hysteresis compensating control method based on observer |
-
2018
- 2018-09-13 CN CN201811067088.3A patent/CN108832836B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN203775078U (en) * | 2014-04-11 | 2014-08-13 | 衢州职业技术学院 | Ultrasonic motor speed position controller based on ARM and DDS |
| CN104660098A (en) * | 2015-03-23 | 2015-05-27 | 安徽理工大学 | Low-frequency PWM and single neuron self-adaption-based ultrasonic motor control system |
| CN106208807A (en) * | 2016-09-19 | 2016-12-07 | 闽江学院 | Supersonic motor servo-control system hysteresis compensating control method based on observer |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111865169A (en) * | 2020-07-21 | 2020-10-30 | 南京航空航天大学 | Model-free integral sliding mode control method of ultrasonic motor servo system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108832836B (en) | 2019-06-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110784149B (en) | Mechanical resonance suppression method and system for alternating current servo system | |
| WO2006134702A1 (en) | Machine position control device | |
| CN104993766B (en) | A kind of two quality system resonance suppressing methods | |
| CN114142781B (en) | Method for adjusting PI parameters of current loop of pre-filter permanent magnet synchronous motor | |
| CN106208807A (en) | Supersonic motor servo-control system hysteresis compensating control method based on observer | |
| CN106877774B (en) | Input supersonic motor servo adaptive control system and method under saturation conditions | |
| Ellis et al. | Cures for low-frequency mechanical resonance in industrial servo systems | |
| CN108832836B (en) | A kind of supersonic motor servo-control system sliding-mode control | |
| CN110647105B (en) | Limited control set model prediction contour control method suitable for double-shaft or three-shaft feed driving system | |
| CN113890424B (en) | Parameter identification-based tuning method for PI controller of speed ring of permanent magnet synchronous motor | |
| CN110609470A (en) | Anti-integral saturation design method based on transition process | |
| CN109407511A (en) | Duplex path feedback Coupled Rigid-flexible platform courses method | |
| RU2368934C2 (en) | Adaptive control system | |
| CN106026832A (en) | Improved ADRC control algorithm-based permanent magnet synchronous linear motor control method | |
| CN108227479A (en) | The PID control method and PID control system of a kind of articulated robot | |
| Wang et al. | A high performance permanent magnet synchronous motor servo system using predictive functional control and Kalman filter | |
| CN107807532A (en) | A kind of adaptive inversion vibration isolation control method for ultra-magnetic telescopic vibration-isolating platform | |
| CN106842957A (en) | A kind of supersonic motor method of servo-controlling based on output feedback controller | |
| CN109067271B (en) | DC motor servo control method based on robust disturbance compensation scheme | |
| CN109150004B (en) | A kind of supersonic motor servo-control system neural network control method | |
| Lee et al. | A controller design method for constructing a robust track-following system | |
| Li et al. | Modeling and fuzzy sliding decoupling control of looper multivariable system | |
| CN107257212B (en) | A kind of output feedback piezo motor control method based on contragradience and inverse dead-zone model | |
| Zhu et al. | Double vibration suppression of PMSM servo system based on strong tracking of reference trajectory | |
| CN115951364B (en) | Method for improving positioning accuracy of piezoelectric type rapid steering mirror platform |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |