CN108233781A - A kind of DC brushless motor adaptive backstepping sliding mode control method based on Nonlinear Disturbance Observer - Google Patents

A kind of DC brushless motor adaptive backstepping sliding mode control method based on Nonlinear Disturbance Observer Download PDF

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Publication number
CN108233781A
CN108233781A CN201810048153.1A CN201810048153A CN108233781A CN 108233781 A CN108233781 A CN 108233781A CN 201810048153 A CN201810048153 A CN 201810048153A CN 108233781 A CN108233781 A CN 108233781A
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observer
brushless motor
disturbance
sliding mode
error
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CN108233781B (en
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庄浩
张登峰
王聪
李军
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P23/0009—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Feedback Control In General (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a kind of DC brushless motor adaptive backstepping sliding mode control methods based on Nonlinear Disturbance Observer, and Unmarried pregnancy and the external loading interference of DC brushless motor are observed and compensated using Nonlinear Disturbance Observer.To the electric system after interference compensation, controller is designed using adaptive inverting slip-form, ensures that entire DC brushless motor system is stablized.The present invention with back-stepping sliding mode control solve the disadvantage that back stepping control need controlled device Accurate Model information and can not disturbance cancelling, improve the robustness of system.The Unmarried pregnancy of DC brushless motor is observed and compensated with external loading interference with Nonlinear Disturbance Observer, reduces the buffeting level of back-stepping sliding mode control and improves control accuracy.Adaptive law is designed to disturbance-observer upper error, estimates the upper bound of disturbance-observer error, using the estimated value of disturbance-observer upper error as sliding formwork handoff gain, ensures that entire DC brushless motor system is stablized.

Description

A kind of adaptive inverting sliding formwork of DC brushless motor based on Nonlinear Disturbance Observer Control method
Technical field
The invention belongs to technical field of motor servo control, and in particular to a kind of direct current based on Nonlinear Disturbance Observer Brushless motor adaptive backstepping sliding mode control method.
Background technology
DC brushless motor has the advantages that Traditional DC motor, such as good mechanical property and governor control characteristics, plays turn Square is big, overload capability is strong, easy to adjust, dynamic characteristic is good etc., but with ac motor structure it is simple, it is reliable, safeguard A series of features such as facilitate, therefore very extensive application obtained in many high-tech areas, such as Laser Processing, robot and Numerically-controlled machine tool etc..Classical PID tricyclics (position ring, speed ring and electric current loop) control method is the master of DC brushless motor at present Want control method.However, there are Unmarried pregnancies and the influence of external loading interference for DC brushless motor, these are uncertain dry Control performance will be deteriorated or even make control system unstable by disturbing.Therefore traditional three close-loop control based on PID cannot meet height Performance control needs need the more advanced control method of research.
Currently for the control method of DC brushless motor, there are PID control, back stepping control, fuzzy control and sliding formwork control The control methods such as system.As a multivariable, nonlinear control system, motor model cannot obtain accurately DC brushless motor Measure, traditional PID control method cannot obtain ideal control effect when wide speed regulating range and load disturbance are frequently mutated Fruit.Complicated nonlinear system is resolved into the subsystem no more than systematic education by back-stepping design, then designs each subsystem Lyapunov functions and intermediate virtual controlled quentity controlled variable, however traditional back stepping control needs the accurate modeling information of motor and can not Disturbance cancelling.Experience of the realization of fuzzy control dependent on operator, application range are restricted.Sliding mode variable structure control There is rapidity, strong robustness and realize simple.In conventional sliding formwork control, very big handoff gain is generally required Eliminate additional interference and indeterminate, very big handoff gain will cause serious buffeting problem, deteriorate control effect.
In summary, the shortcoming of the control technology of existing DC brushless motor mainly has the following：
1st, shadow of the interference to Brush-Less DC motor control of DC brushless motor Unmarried pregnancy and external loading is had ignored It rings.
2nd, traditional back stepping control method needs the accurate modeling information of DC brushless motor and can not disturbance cancelling.
3rd, traditional sliding formwork control generally requires very big handoff gain to eliminate additional interference and indeterminate, very greatly Handoff gain will cause serious buffeting problem, deteriorate control effect.
4th, pid control algorithm robustness is poor, it is impossible to meet the control requirement of Dynamic High-accuracy performance applications occasion.
Invention content
For solve the disadvantage that traditional back stepping control need the accurate modeling information of motor and can not disturbance cancelling, the present invention will Back stepping control is combined with sliding formwork control so that back-stepping sliding mode control has robust to motor Unmarried pregnancy and external loading interference Property.Simultaneously in order to reduce the handoff gain of traditional back-stepping sliding mode control, the buffeting for reducing traditional back-stepping sliding mode control is horizontal, improves Brush-Less DC motor control precision estimates motor Unmarried pregnancy and external loading interference using Nonlinear Disturbance Observer Meter, and interference is compensated, conservative handoff gain F is replaced by the upper bound β of smaller handoff gain, that is, disturbance-observer error.Needle The upper bound β of disturbance-observer error is difficult to determine, the adaptive law of disturbance-observer upper error is designed, in disturbance-observer error Boundary β estimated, by handoff gain of the estimated value of disturbance-observer upper error as DC brushless motor back-stepping sliding mode control, Ensure that entire DC brushless motor system is stablized, further reduce the level of buffeting.It is a kind of based on non-present invention aims at proposing The brush DC electricity adaptive backstepping sliding mode control method of linear disturbance observer.
To reach above-mentioned purpose, the technical solution adopted in the present invention is as follows：
A kind of DC brushless motor adaptive backstepping sliding mode control method based on Nonlinear Disturbance Observer, feature exist In including the following steps：
Step 1, the mathematical model for establishing DC brushless motor.
Step 2, in the case where considering that DC brushless motor Unmarried pregnancy and external loading interfere, using based on inverting Sliding-mode control is into the design of line control unit.
Step 3, configuration Nonlinear Disturbance Observer carry out DC brushless motor Unmarried pregnancy and external loading interference Observation, and compensate.
Step 4, the DC brushless motor system to introducing Nonlinear Disturbance Observer, design disturbance-observer upper error Adaptive law estimates the upper bound of disturbance-observer error, by the estimated value of disturbance-observer upper error as inverting sliding formwork The handoff gain of control ensures that entire DC brushless motor system is stablized.
Step 1, the mathematical model for establishing DC brushless motor
The mechanical motion equation of DC brushless motor is：
In formula：TeFor electromagnetic torque, Te=ktI (t), ktFor moment coefficient, TLFor load torque, J is motor rotary inertia, B is joint damping coefficient, and w (t) is motor angular velocity, and I (t) is bus current.
The voltage equation of DC brushless motor：
In formula：R' is armature winding resistance, and R'=2r, r are phase resistance, and L' is armature winding inductance, L'=2 (L-M), L For every phase winding self-induction, M mutual inductances between every two phase winding, keFor winding back emf coefficient.
By formula (1) and formula (2) the dynamic systems equation of DC brushless motor is：
Choose state variable x1(t)=θ (t), x2(t)=w (t),The then state side of DC brushless motor Journey is represented by：
In formula：
Step 2, in the case where considering that DC brushless motor Unmarried pregnancy and external loading interfere, using inverting sliding formwork Control method is into the design of line control unit.
1) in the case of considering DC brushless motor Unmarried pregnancy and external loading interference, the state equation of motor is：
It is F (t)=Δ a to enable total interference1*x3(t)+Δa2*x2（T)+Δ b*u+d (t), then state equation be：
Wherein Always to interfere the upper bound, Δ a1*x3(t)+Δa2*x2(t)+Δ b*u be Unmarried pregnancy, d (t) it is interfered for external loading.
2) design of back-stepping sliding mode control device
The error of definition system：
Wherein：δ1With δ2For the virtual controlling amount of design, xdFor given position signal.
Step1:First error subsystem：e1=x1(t)-xd
Define first Lyapunov function:
Design first virtual controlling amount δ1：
It is obtained by formula (11) and formula (10)：
If e2=0, thenv1Asymptotic Stability, it is therefore desirable to carry out next step design, introduce virtual controlling amount δ2, make e2It goes to zero.
Step2:Second error subsystem：e2=x2(t)-δ1
Define second Lyapunov function:
Design second virtual controlling amount δ2：
It is obtained by formula (13) and formula (16)：
It is obtained by formula (15) and formula (17)：
If e3=0, thenv2Asymptotic Stability, it is therefore desirable to carry out next step design, make e3It goes to zero.
Step3:Third error subsystem：e3=x3(t)-δ2
Define sliding formwork diverter surface：
S=ce2+e3, (c ＞ 0) (20)
Then
Define third Lyapunov functions:
Design control law is：
Back-stepping sliding mode control device stability analysis：
Control law (23) is substituted intoIn expression formula (22):
Therefore entire electric system is stablized.
Step 3, configuration Nonlinear Disturbance Observer always interfere F (t) to estimate DC brushless motor, and mended It repays.
(23) are restrained according to the back-stepping sliding mode control in step 2, handoff gainSelection dependent on the upper of total interference F (t) Boundary according to conservative approach, selects sufficiently large handoff gainTo ensure the stability of system, but serious tremble can be brought It is dynamic.Therefore, it is necessary to always F (t) being interfered to estimate, and to always F (t) being interfered to compensate, reduce the influence of interference.
According to the state equation of the DC brushless motor in the case where considering motor Unmarried pregnancy and external loading interference (6), Nonlinear Disturbance Observer is configured.
The disturbance-observer error is enabled to be：
WhereinFor the observation error of interference,Observation for interference.
Defining Nonlinear Disturbance Observer is：
In formula：P (x)=L1x3(t), L1＞ 0.
Then the dynamical equation of disturbance-observer error is：
Because L1＞ 0, then disturbance-observer error is by exponential convergence.
Order compensates control lawBack-stepping sliding mode control device output control law is u1, master control rule is u=u1+ u2, then after introducing interference observer compensating action, the state equation (6) of motor becomes：
After introducing Nonlinear Disturbance Observer,Expression formula changes：
According to the control law (23) of back-stepping sliding mode control device, the electric system for introducing Nonlinear Disturbance Observer is designed new Control law u1：
Wherein β is disturbance-observer errorThe upper bound.
After introducing Nonlinear Disturbance Observer, back-stepping sliding mode control device stability analysis：
Control law (29) is substituted intoIn expression formula (28)
Therefore after introducing nonlinear disturbance observer, entire electric system is stablized.
Step 4, the DC brushless motor system to introducing Nonlinear Disturbance Observer, design disturbance-observer upper error Adaptive law estimates the upper bound of disturbance-observer error, by the estimated value of disturbance-observer upper error as inverting sliding formwork The handoff gain of control ensures that entire DC brushless motor system is stablized.
DefinitionEstimated value for disturbance-observer upper error β：
Evaluated errorFor：
DefinitionParameter update law be：
Then Estimation of Upper-Bound error dynamics equation is
It enables
After introducing nonlinear disturbance observer, DC brushless motor adaptive backstepping sliding mode control system stability analysis：
Define Lyapunov functions:
Therefore the DC brushless motor adaptive backstepping sliding mode control system based on nonlinear disturbance observer is stablized.
To sum up：The final adaptive backstepping sliding mode control device output control law u of the present invention1For：
Compensating control law is： Therefore the final master control rule of the present invention is u=u1+u2,
A kind of DC brushless motor adaptive backstepping sliding mode control method based on Nonlinear Disturbance Observer of the present invention, instead The basic thought for drilling design method is that complicated nonlinear system is resolved into subsystem no more than systematic education, is then every A subsystem separately designs liapunov function and intermediate virtual controlled quentity controlled variable, backs to whole system always, whole until completing The design of a control law.For DC brushless motor, back stepping control method with sliding mode variable structure control method is combined, then may be used To expand the use scope of back stepping control method so that DC brushless motor has Unmarried pregnancy and external loading interference certain Robustness.Simultaneously using Nonlinear Disturbance Observer to always F (t) being interfered to estimate, and with total interference estimate to always doing It disturbs F (t) to compensate, reduces the influence of interference, conservative cut is replaced by the upper bound β of smaller handoff gain, that is, disturbance-observer error Change gainSo as to reduce the handoff gain of traditional back-stepping sliding mode control, the buffeting for reducing traditional back-stepping sliding mode control is horizontal.Most It is difficult to determine for disturbance-observer upper error β afterwards, the adaptive law of design disturbance-observer upper error β is missed by disturbance-observer Handoff gain of the estimated value in the poor upper bound as DC brushless motor back-stepping sliding mode control after interference compensation, ensure entire direct current without Brush motor system is stablized, and further reduces handoff gain and buffet level.
Compared with prior art, the present invention its advantage is：
(1) DC brushless motor is decomposed into three subsystems, simplifies setting for controller by the present invention with the method for inversion Meter.
(2) back stepping control method and sliding formwork control are combined by the present invention, are solved traditional back stepping control needs and are accurately built Mould information and can not disturbance cancelling the shortcomings that, improve the robustness of system.
(3) present invention uses Nonlinear Disturbance Observer to always F (t) being interfered to estimate, and with interference estimate to total Disturbance F (t) is compensated, and reduces the influence of interference, is replaced by the upper bound β of smaller handoff gain, that is, disturbance-observer error conservative Handoff gainSo as to reduce the handoff gain of traditional back-stepping sliding mode control, the buffeting for reducing traditional back-stepping sliding mode control is horizontal, Improve control accuracy.
(4) present invention is difficult to determine for the upper bound β of disturbance-observer error, designs the adaptive of disturbance-observer upper error Rule is increased by the estimated value of disturbance-observer upper error as the switching of DC brushless motor back-stepping sliding mode control after interference compensation Benefit ensures that entire DC brushless motor system is stablized, and further reduces handoff gain and buffet level.
(5) therefore, the adaptive inverting sliding formwork of a kind of DC brushless motor based on Nonlinear Disturbance Observer of the invention Control method can be applied to motor field.
It is characterized in that：First using with the method for inversion, Brushless DC Motor Position control system is decomposed into three subsystems System, simplifies the design of controller；Then back stepping control method and sliding formwork control are combined, solving traditional back stepping control needs Want motor Accurate Model information and can not disturbance cancelling the shortcomings that, improve the robustness of system；Then Nonlinear perturbations are used Observer estimates, and mended with interference estimate to always disturbing total interference of Brushless DC Motor Position control system It repays, reduces the influence of interference, conservative handoff gain is replaced by the upper bound of smaller handoff gain, that is, disturbance-observer error, so as to subtract The handoff gain of little tradition back-stepping sliding mode control, the buffeting for reducing traditional back-stepping sliding mode control is horizontal, improves control accuracy；Finally It is difficult to determine for the upper bound of disturbance-observer error, the adaptive law of disturbance-observer upper error is designed, by disturbance-observer error Handoff gain of the estimated value in the upper bound as DC brushless motor back-stepping sliding mode control after interference compensation, ensures entire brush DC Electric system is stablized, and further reduces handoff gain and buffet level.
Description of the drawings
Fig. 1 is the control system for non-brush direct currunt electromotors structure diagram.
Fig. 2 is the tracking error curve based on Nonlinear Disturbance Observer DC brushless motor adaptive backstepping sliding mode control Figure.
Fig. 3 is the DC brushless motor tracking error curve figure of traditional back-stepping sliding mode control.
Fig. 4 is the tracking error curve figure based on Nonlinear Disturbance Observer DC brushless motor back-stepping sliding mode control.
Fig. 5 is the control voltage curve based on Nonlinear Disturbance Observer DC brushless motor adaptive backstepping sliding mode control Figure.
Fig. 6 is the Brush-Less DC motor control voltage curve of traditional back-stepping sliding mode control.
Fig. 7 is the control voltage curve based on Nonlinear Disturbance Observer DC brushless motor back-stepping sliding mode control.
Specific embodiment
The present invention is further described below in conjunction with the accompanying drawings.
A kind of DC brushless motor adaptive backstepping sliding mode control system based on Nonlinear Disturbance Observer, such as Fig. 1 institutes Show, Nonlinear Disturbance Observer is estimated total interference of DC brushless motor according to the state of motor and control voltage and right Total interference compensates.Last combining adaptive back-stepping sliding mode control device obtains the control voltage of motor, control brush DC electricity Machine tracing positional Setting signal xd。
Above-mentioned technical proposal, specific implementation include the following steps：
Step 1, the mathematical model for establishing DC brushless motor
The mechanical motion equation of DC brushless motor is：
In formula：TeFor electromagnetic torque, Te=ktI (t), ktFor moment coefficient, TLFor load torque, J is motor rotary inertia, B is joint damping coefficient, and w (t) is motor angular velocity, and I (t) is bus current.
The voltage equation of DC brushless motor：
In formula：R' is armature winding resistance, and R'=2r, r are phase resistance, and L' is armature winding inductance, L'=2 (L-M), L For every phase winding self-induction, M mutual inductances between every two phase winding, keFor winding back emf coefficient.
By formula (1) and formula (2) the dynamic systems equation of DC brushless motor is：
Choose state variable x1(t)=θ (t), x2(t)=w (t),The then state side of DC brushless motor Journey is represented by：
In formula：
Step 2, in the case where considering that DC brushless motor Unmarried pregnancy and external loading interfere, using inverting sliding formwork Control method is into the design of line control unit.
1) in the case of considering DC brushless motor Unmarried pregnancy and external loading interference, the state equation of motor is：
It is F (t)=Δ a to enable total interference1*x3(t)+Δa2*x2(t)+Δ b*u+d (t), then state equation be：
Wherein Always to interfere the upper bound, Δ a1*x3(t)+Δa2*x2(t)+Δ b*u be Unmarried pregnancy, d (t) it is interfered for external loading.
2) design of back-stepping sliding mode control device
The error of definition system：
Wherein：δ1With δ2For the virtual controlling amount of design, xdFor given position signal.
Step1:First error subsystem：e1=x1(t)-xd
Define first Lyapunov function:
Design first virtual controlling amount δ1：
It is obtained by formula (11) and formula (10)：
If e2=0, thenv1Asymptotic Stability, it is therefore desirable to carry out next step design, introduce virtual controlling amount δ2, make e2 It goes to zero.
Step2:Second error subsystem：e2=x2(t)-δ1
Define second Lyapunov function:
Design second virtual controlling amount δ2：
It is obtained by formula (13) and formula (16)：
It is obtained by formula (15) and formula (17)：
If e3=0, thenv2Asymptotic Stability, it is therefore desirable to carry out next step design, make e3It goes to zero.
Step3:Third error subsystem：e3=x3(t)-δ2
Define sliding formwork diverter surface：
S=ce2+e3, (c ＞ 0) (20)
Then
Define third Lyapunov functions:
Design control law is：
Back-stepping sliding mode control device stability analysis：
Control law (23) is substituted intoIn expression formula (22):
Therefore entire electric system is stablized.
Step 3, configuration Nonlinear Disturbance Observer always interfere F (t) to estimate DC brushless motor, and mended It repays.
(23) are restrained according to the back-stepping sliding mode control in step 2, handoff gainSelection dependent on the upper of total interference F (t) Boundary according to conservative approach, selects sufficiently large handoff gainTo ensure the stability of system, but serious tremble can be brought It is dynamic.Therefore, it is necessary to always F (t) being interfered to estimate, and to always F (t) being interfered to compensate, reduce the influence of interference.
According to the state equation of the DC brushless motor in the case where considering motor Unmarried pregnancy and external loading interference (6), Nonlinear Disturbance Observer is configured.
The disturbance-observer error is enabled to be：
WhereinFor the observation error of interference,Observation for interference.
Defining Nonlinear Disturbance Observer is：
In formula：P (x)=L1x3(t), L1＞ 0.
Then the dynamical equation of disturbance-observer error is：
Because L1＞ 0, then disturbance-observer error is by exponential convergence.
Order compensates control lawBack-stepping sliding mode control device output control law is u1, master control rule is u=u1+ u2, then after introducing interference observer compensating action, the state equation (6) of motor becomes：
After introducing Nonlinear Disturbance Observer,Expression formula changes：
According to the control law (23) of back-stepping sliding mode control device, the electric system for introducing Nonlinear Disturbance Observer is designed new Control law u1：
Wherein β is disturbance-observer errorThe upper bound.
After introducing Nonlinear Disturbance Observer, back-stepping sliding mode control device stability analysis：
Control law (29) is substituted intoIn expression formula (28):
Therefore after introducing nonlinear disturbance observer, entire electric system is stablized.
Step 4, the DC brushless motor system to introducing Nonlinear Disturbance Observer, design disturbance-observer upper error Adaptive law estimates the upper bound of disturbance-observer error, by the estimated value of disturbance-observer upper error as inverting sliding formwork The handoff gain of control ensures that entire DC brushless motor system is stablized.
DefinitionEstimated value for disturbance-observer upper error β：
Evaluated errorFor：
DefinitionParameter update law be：
Then Estimation of Upper-Bound error dynamics equation is
It enables
After introducing nonlinear disturbance observer, DC brushless motor adaptive backstepping sliding mode control system stability analysis：
Define Lyapunov functions:
Therefore the DC brushless motor adaptive backstepping sliding mode control system based on nonlinear disturbance observer is stablized.
To sum up：The final adaptive backstepping sliding mode control device output control law u of the present invention1For：
Compensate control law For：Therefore the final master control rule of the present invention is u=u1+u2,
It is imitated for the DC brushless motor adaptive backstepping sliding mode control method based on Nonlinear Disturbance Observer True verification.
The parameter of DC brushless motor is：Rated voltage 24v, rated current 11.4A, rotary inertia J=1.98e-4kg/ m2, joint damping coefficient B=0N.m.s, per phase winding self-induction L=35uH, per phase winding mutual inductance M=0, moment coefficient kt= 0.058Nm/A, back emf coefficient ke=6.07v/krpm, per phase winding resistance r=0.31 Ω, number of pole-pairs p=4, loading moment TL =0.1N/m, loading moment disturbance are Δ TL=0.05sin (t) N/m, system it is expected that the position command of tracking is curve xd=sin (3t)rad。
Adaptive backstepping sliding mode control device parameter is set as：k1=300, k2=300, c=300, h=300；It is non-linear dry The parameter for disturbing observer is set as：L1=50；
It is emulated, is set for the DC brushless motor back-stepping sliding mode control method based on Nonlinear Disturbance Observer Disturbance-observer upper error
Fig. 3 is the position tracking error of traditional back-stepping sliding mode control, and maximum position tracking error is 5.2*e during stable state- 3rad。
Fig. 4 is the position tracking error of the back-stepping sliding mode control based on Nonlinear Disturbance Observer, and maximum tracks during stable state Error is 1.2*e-5rad.It compares with Fig. 3, after introducing Nonlinear Disturbance Observer to the compensating action of interference, efficiently reduces Position tracking error, improves control accuracy.
Fig. 2 is the position tracking error curve diagram of the present invention, and maximum position tracking error is 2.8*e during stable state-6Rad, with Fig. 4 is compared, and the present invention is on the basis of the back-stepping sliding mode control method based on Nonlinear Disturbance Observer, with adaptive approach Disturbance-observer upper error is estimated, by estimated value the cutting as motor back-stepping sliding mode control of disturbance-observer upper error Gain is changed, the tracking error further reduced further improves control accuracy.
Fig. 6 is the control voltage curve of traditional back-stepping sliding mode control, and control voltage has very big buffeting horizontal, buffets Amplitude reaches 2.4v or even the positive and negative saltus step of control voltage occurs, significantly the fragile brush DC electricity of the control voltage of saltus step Machine can not actually use.
Fig. 7 is the control voltage of the back-stepping sliding mode control based on Nonlinear Disturbance Observer, and the maximum of voltage is controlled to buffet Amplitude is 0.1v, compared with Fig. 6, after introducing Nonlinear Disturbance Observer to the compensating action of interference, efficiently reduces control The buffeting amplitude of voltage.
Fig. 5 is the control voltage curve of the present invention, and the maximum buffeting amplitude for controlling voltage is 0.0045v, with Fig. 7 phases Than the present invention is on the basis of the back-stepping sliding mode control method based on Nonlinear Disturbance Observer, with adaptive approach to dry It disturbs the observation error upper bound to be estimated, be increased by the estimated value of disturbance-observer upper error as the switching of motor back-stepping sliding mode control Benefit, the buffeting that further reduced control voltage are horizontal.
In actual DC brushless motor control system, according to PWM control principles, the voltage at armature winding both ends is put down Mean value u=α Us, UsThe duty ratio of rated voltage 24v, α for PWM for supply voltage, that is, motor, 0 ＜ α ＜ 1.It is according to the present invention The maximum buffeting amplitude 0.0045v of control voltage, buffeting amplitude, ao α=0.01875% of the duty ratio of corresponding PWM, so The buffeting amplitude of the duty ratio of small PWM can be ignored.Therefore the present invention, can use in Practical Project.
To sum up, back stepping control method is combined by the present invention with sliding mode variable structure control method, expands back stepping control method Use scope so that the present invention to DC brushless motor Unmarried pregnancy and external loading interference have certain robustness.Together Shi Caiyong Nonlinear Disturbance Observers are to always interfering F (t) to estimate, and with total interference estimate to always F (t) being interfered to mend It repays, reduces the influence of interference, conservative handoff gain is replaced by the upper bound β of smaller handoff gain, that is, disturbance-observer errorFrom And it efficiently reduces the control voltage buffeting level of traditional back-stepping sliding mode control and efficiently reduces position tracking error. Finally for disturbance-observer error, the adaptive law of disturbance-observer upper error is designed, by the estimation of disturbance-observer upper error It is worth the handoff gain as motor back-stepping sliding mode control, ensures that entire DC brushless motor system is stablized, further reduced control The buffeting of voltage processed is horizontal and further reduces position tracking error.

Claims (5)

  1. A kind of 1. DC brushless motor adaptive backstepping sliding mode control method based on Nonlinear Disturbance Observer, it is characterised in that Include the following steps：
    Step 1, the mathematical model for establishing DC brushless motor,
    Step 2, consider DC brushless motor Unmarried pregnancy and external loading interfere in the case of, using inverting sliding formwork control Brushless DC Motor Position control system, first using with the method for inversion, is decomposed into three by method processed into the design of line control unit A subsystem, the design of simplify control device；Then back stepping control method and sliding formwork control are combined, are solved with sliding formwork control Traditional back stepping control need motor Accurate Model information and can not disturbance cancelling the shortcomings that,
    Step 3, configuration Nonlinear Disturbance Observer are observed DC brushless motor Unmarried pregnancy and external loading interference, And compensate, the influence of interference is reduced, conservative switching is replaced to increase by the upper bound of smaller handoff gain, that is, disturbance-observer error Benefit reduces the handoff gain of traditional back-stepping sliding mode control,
    Step 4, the DC brushless motor system to introducing Nonlinear Disturbance Observer, design the adaptive of disturbance-observer upper error Ying Lv estimates the upper bound of disturbance-observer error, by the estimated value of disturbance-observer upper error as back-stepping sliding mode control Handoff gain, ensure that entire DC brushless motor system is stablized.
  2. 2. the DC brushless motor adaptive backstepping sliding mode control according to claim 1 based on Nonlinear Disturbance Observer Method, which is characterized in that the step 1 specifically includes：
    The mathematical model of DC brushless motor is established,
    The mechanical motion equation of DC brushless motor is：
    In formula：TeFor electromagnetic torque, Te=ktI (t), ktFor moment coefficient, TLFor load torque, J is motor rotary inertia, and B is Joint damping coefficient, w (t) are motor angular velocity, and I (t) is bus current,
    The voltage equation of DC brushless motor：
    In formula：R ' is armature winding resistance, and R '=2r, r are phase resistance, and L ' is armature winding inductance, and L '=2 (L-M), L is every Phase winding self-induction, M mutual inductances between every two phase winding, keFor winding back emf coefficient,
    By formula (1) and formula (2) the dynamic systems equation of DC brushless motor is：
    Choose state variable x1=θ (t), x2=w (t),Then the state equation of DC brushless motor is represented by：
    In formula：
  3. 3. the DC brushless motor adaptive backstepping sliding mode control according to claim 2 based on Nonlinear Disturbance Observer Method, which is characterized in that the step 2 specifically includes：
    In the case where considering that DC brushless motor Unmarried pregnancy and external loading interfere, using back-stepping sliding mode control method into The design of line control unit,
    1) in the case of considering DC brushless motor Unmarried pregnancy and external loading interference, the state equation of motor is：
    It is F (t)=Δ a to enable total interference1*x3(t)+Δa2*x2(t)+Δ b*u+d (t), then state equation be：
    Wherein For the upper bound always interfered, Δ a1*x3(t)+Δa2*x2(t)+Δ b*u be Unmarried pregnancy, d (t) It is interfered for external loading,
    2) design of back-stepping sliding mode control device
    The error of definition system：
    Wherein：δ1With δ2For the virtual controlling amount of design, xdFor given position signal,
    Step1:First error subsystem：e1=x1(t)-xd
    Define first Lyapunov function:
    Design first virtual controlling amount δ1：
    It is obtained by formula (11) and formula (10)：
    If e2=0, thenv1Asymptotic Stability, it is therefore desirable to carry out next step design, introduce virtual controlling amount δ2, make e2Tend to Zero,
    Step2:Second error subsystem：e2=x2(t)-δ1
    Define second Lyapunov function:
    Design second virtual controlling amount δ2：
    It is obtained by formula (13) and formula (16)：
    It is obtained by formula (15) and formula (17)：
    If e3=0, thenv2Asymptotic Stability, it is therefore desirable to carry out next step design, make e3It goes to zero,
    Step3:Third error subsystem：e3=x3(t)-δ2
    Define sliding formwork diverter surface：
    S=ce2+e3, (c ＞ 0) (20)
    Then
    Define third Lyapunov functions:
    Design control law is：
    Back-stepping sliding mode control device stability analysis：
    Control law (23) is substituted intoIn expression formula (22):
    Therefore entire electric system asymptotic convergence is stablized.
  4. 4. the DC brushless motor adaptive backstepping sliding mode control according to claim 3 based on Nonlinear Disturbance Observer Method, which is characterized in that the step 3 specifically includes：Configuration Nonlinear Disturbance Observer always interferes F to DC brushless motor (t) estimated, and compensated,
    (23) are restrained according to the back-stepping sliding mode control in step 2, handoff gainThe upper bound of the selection dependent on total interference F (t), if Using conservative approach, sufficiently large handoff gain is selectedEnsure the stability of system, can bring serious buffeting, therefore, It needs to always F (t) being interfered to estimate, and to always F (t) being interfered to compensate, reduces the influence of interference,
    According to the state equation (6) of the DC brushless motor in the case where considering that motor Unmarried pregnancy and external loading interfere, Nonlinear Disturbance Observer is configured,
    Assuming that relative to the variation that the dynamic characteristic of nonlinear disturbance observer is always interfered be it is slow, i.e.,
    Enable disturbance-observer error：
    WhereinFor disturbance-observer error,For the observation of interference,
    Defining Nonlinear Disturbance Observer is：
    In formula：P (x)=L1x3(t), L1＞ 0,
    Therefore the dynamical equation of disturbance-observer error is：
    Because L1＞ 0, then disturbance-observer error press exponential convergence,
    Order compensates control lawBack-stepping sliding mode control device output control law is u1, master control rule is u=u1+u2, then draw After entering interference observer compensating action, the state equation (6) of motor becomes：
    After then introducing Nonlinear Disturbance Observer,Expression formula changes：
    According to the control law (23) of back-stepping sliding mode control device, new control is designed to the electric system for introducing Nonlinear Disturbance Observer System rule u1：
    Wherein β is disturbance-observer errorThe upper bound,
    After introducing Nonlinear Disturbance Observer, back-stepping sliding mode control device stability analysis：
    Control law (29) is substituted intoIn expression formula (28):
    Therefore after introducing nonlinear disturbance observer, entire electric system Asymptotic Stability.
  5. 5. the DC brushless motor adaptive backstepping sliding mode control according to claim 4 based on Nonlinear Disturbance Observer Method, which is characterized in that the step 4 specifically includes：To introducing the DC brushless motor system of Nonlinear Disturbance Observer, if The adaptive law of disturbance-observer upper error is counted, the upper bound of disturbance-observer error is estimated, by disturbance-observer upper error Handoff gain of the estimated value as back-stepping sliding mode control, ensure that entire DC brushless motor system is stablized,
    DefinitionFor the estimated value of disturbance-observer upper error β, then evaluated errorFor：
    DefinitionParameter update law be：
    Then Estimation of Upper-Bound error dynamics equation is：
    It enables
    After introducing nonlinear disturbance observer, DC brushless motor adaptive backstepping sliding mode control system stability analysis：
    Define Lyapunov functions:
    Therefore the DC brushless motor adaptive backstepping sliding mode control system based on nonlinear disturbance observer is stablized, to sum up： To final adaptive backstepping sliding mode control device output control law u1For：
    Compensating control law is： Therefore final master control rule is u=u1+u2,
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