CN108155833A - Consider the motor servo system Asymptotic Stability control method of electrical characteristic - Google Patents
Consider the motor servo system Asymptotic Stability control method of electrical characteristic Download PDFInfo
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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
- H02P6/08—Arrangements for controlling the speed or torque of a single motor
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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
- H02P6/34—Modelling or simulation for control purposes
Abstract
The invention discloses a kind of motor servo system Asymptotic Stability control methods for considering electrical characteristic, are related to electromechanical servo field, method includes：Establish the mathematical model of DC brushless motor servo-drive system；Design makes the self-adaptive robust controller of electric system asymptotically stability；Stability analysis is carried out with Lyapunov stability theory.The present invention establishes relatively complete true electromechanical servo system model, and high state equation is established in unified mechanically and electrically part；Backstepping design method design system controller is used based on self adaptive control thought, inhibit unknown BOUNDED DISTURBANCES by designing Continuous Nonlinear robust feedback term, it designs robust parameter adaptive law and carries out parameter identification, so that system obtains good tracking performance in the case of having Parameter uncertainties and Uncertain nonlinear at the same time, reach system tracking error to go to zero, controlled quentity controlled variable is continuous, the good control purpose of parameter identification ability.
Description
Technical field
The present invention relates to direct current generator SERVO CONTROL fields, relate generally to a kind of motor servo system for considering electrical characteristic
Asymptotic Stability control method.
Background technology
Permanent-magnet brushless DC electric machine is since its own is with fast response time, simple in structure, reliable, small, matter
Measure it is small, loss less, efficient and motor shape and size can it is versatile and flexible wait remarkable advantages, application range is extremely
Extensively, almost throughout aerospace, national defence, industrial and agricultural production and the every field of daily life.With the development of industrial technology,
High-precision motion control has become the main direction of development of modern electromechanical equipment.Electromechanical servo system is one typical non-thread
Sexual system is easily influenced by parameter uncertainty and disturbance.Therefore, the PID controller based on linear control theory cannot expire
The high performance demand of foot, needs to study advanced Design of non-linear controllers.
For the control problem of electromechanical servo system, many methods are by extensive discussions.In motor servo system, due to work
Make the limitation in situation difference and some structures, system can not possibly accurately reflect real system dynamic in modeling completely completely
Characteristic.In fact, the model typically set up is a kind of approximation of system dynamic characteristic, it describes system key property and ignores
Some secondary characteristics, these parts i.e. commonly called uncertain dynamic characteristic.Obviously feedback linearization method can not be used
Direct compensation, this is just needed when designing controller, is taken suitable strategy compensation or is inhibited these uncertain dynamic characteristics,
Otherwise, they are it is possible that the control performance of meeting severe exacerbation controller, so as to cause low precision, limit cycle concussion even causes
The unstability of system.
For nonlinear problem present in electric system, many control methods are suggested in succession.Wherein self adaptive control
Method for that can not be for accurately in the process of running slowly varying Mechatronic Systems may occur for measurement parameter or parameter
A kind of very effective control strategy can obtain the control effect of progressive tracking.But adaptive controller is based on system
It is designed there is no outer load disturbance with the hypothesis for ignoring other secondary non-modeling structure errors, can theoretically ensure to work as
Systematic parameter can converge to true value and obtain progressive tracking performance when system meets persistent excitation condition.Studies have shown that work as
Even if the external interference of very little can make systematic parameter estimation generation is elegant in turn result in system when persistent excitation condition is unsatisfactory for
It is unstable.Also, even if when meeting persistent excitation condition, larger external interference can also be such that system tracking error gradually increases
Until unstability.In real electrical machinery system, Uncertain nonlinear is inevitable, therefore simple self-adaptive controlled in practice
System can not obtain high-precision control performance.To overcome the classical sliding formwork control that Uncertain nonlinear influence proposes as one
Kind of robust control method, it is simple in structure, can effectively inhibit any bounded unmodelled dynamics and external interference simultaneously
Obtain the steady-state behaviour of progressive tracking.But as a kind of discontinuous control method, sliding formwork control needs constantly to carry out logic
Switching, moves so that system is maintained on " sliding mode ".Such case easily causes sliding-mode surface and buffets problem, it, which will be destroyed, is
The superperformance of system, while be easy to the high frequency characteristics that do not model in activating system and make system unstability.
Invention content
The purpose of the present invention is to provide a kind of motor servo system Asymptotic Stability control methods for considering electrical characteristic.
Realize the object of the invention technical solution be：A kind of motor servo system Asymptotic Stability control for considering electrical characteristic
Method includes the following steps：
Step 1, the mathematical model for establishing DC brushless motor servo-drive system；
Step 2, design make the self-adaptive robust controller of electric system asymptotically stability；
Step 3 carries out stability analysis with Lyapunov stability theory.
Compared with prior art, the present invention its remarkable advantage is：(1) electrical characteristic and machinery of the invention by Mechatronic Systems
Characteristic unified Modeling more towards actual conditions, designs the tricyclic feedback controller based on position and speed electric current；For parameter not
It determines design discontinuous mapping type adaptive law, enhances parameter identification robustness；For Uncertain nonlinear design is inhibited to be based on
The Continuous Nonlinear feedback robust item of sliding-mode structure, avoids the buffeting problem brought in practical application by standard signum function；(2)
By theory analysis and simulating, verifying, designed self-adaptive robust controller can obtain good tracking effect and parameter is distinguished
Knowledge ability ensures that system realizes Globally asymptotic.
Description of the drawings
Fig. 1 is motor servo system control strategy figure.
Fig. 2 is motor servo system schematic diagram.
Fig. 3 is tracking process schematic of the lower system output of ARC controllers control to given reference signal.
Fig. 4 is the tracking error time history plot of system under ARC controller actions.
Fig. 5 is ARC and the tracking accuracy comparison diagram of PID controller.
Fig. 6 is the curve graphs of the control signal u of ARC controllers at any time.
Fig. 7 is the parameter adaptive curve graph under ARC controls.
Specific embodiment
Below in conjunction with the accompanying drawings and specific embodiment is described in further detail the present invention.
With reference to Fig. 1, Fig. 2, a kind of motor servo system Asymptotic Stability control method for considering electrical characteristic, including following step
Suddenly：
Step 1, the Complete mathematic model for establishing motor servo system, including mechanical property and electrical characteristic；
Step 1.1, according to mechanically and electrically characteristic, establishing the DC brushless motor system equation of motion is：
In formula (1), J be inertia load equivalent rotary inertia, kiFor Motor torque constant, i is armature supply,For armature electricity
The derivative of stream, B are viscosity friction coefficient, dnUnknown constant value disturbance is represented,Other uncertain dynamic characteristics are represented, than
If time-varying disturbs, high frequency dynamic etc. is not modeled, and L represents armature inductance, and u represents armature both end voltage and practical control to be designed
Amount input processed, R represent armature internal resistance, kbArmature damped coefficient is represented, t is time variable,Respectively motor angular displacement, angle
Speed and angular acceleration.
Step 1.2, definition status variable：Take state vector x=[x1,x2,x3]T, then formula (1)
The equation of motion is converted into state equation：
Defined parameters collection vector θ=[θ1,θ2,θ3]T, wherein θ1=J/ki, θ2=B/ki, θ3=dn/ki。Equivalent unmodelled dynamics after being converted in expression system.
The design object of system controller is：For given position reference x1d(t), the control of a bounded is designed
System input u makes system export x1The reference signal of system is kept up with as much as possible.
In addition, due to system mechanics partial parameters J, ki, B, dnIt cannot accurately learn or be considered slow time-varying, phase
For this, it is believed that electric part parameter L, R, kbIt is to stablize known parameters.Although mechanical part parameter cannot be known,
Its general information is knowable.In addition, system does not know dynamic characteristicCan not accurate modeling, but system do not model it is non-
Linear and time-varying such as interferes at the always bounded.To sum up, it is assumed hereinafter that always set up.
Assuming that 1：System reference signal x1dIt is Second Order Continuous, and the instruction of system desired locations, speed command acceleration refer to
Order is all bounded；
System does not know dynamic characteristicMagnitude range it is known that i.e.
δ in formulafFor known constant.
Assuming that 2：The magnitude range of parameter uncertainty θ is it is known that i.e.
θ in formulamin=[θ1min,θ2min,θ3min]T, θmax=[θ1max,θ2max,θ3max]TKnown bound for vectorial θ.
Step 2, design makes the self-adaptive robust controller of electric system asymptotically stability, and step is as follows：
Step 2.1, e is defined1=x1-x1dFor the position tracking error of system, according to first state equation of (2) formulaChoose x2For virtual controlling amount, to makeIt tends towards stability, enables x2dFor the expectation of virtual controlling amount, x is defined2dWith being
Virtual condition of uniting x2Error be e2=x2-x2d, to e1Derivation obtains：
In formulaFor reference signal x1dDerivative.Design virtual controlling rule x2d：
K in formula1>0 is adjustable gain, and (5) formula of substitution has
Due to e1(s)=G (s) e2(s), G (s)=e in formula1(s)/e2(s)=1/ (s+k1) it is a stable transmission letter
Number, so working as e2When tending to 0, e1Also necessarily tend to 0；So it is next that design controller makes e with regard to target2Tend to 0；
Choose Liapunov candidate functions V1It is as follows：
Then have
Step 2.2, discontinuous parameter mapping used by providing parameter adaptive before design parameter adaptive law：
It enablesRepresent the estimation to unknown parameter θ,For parameter estimating error, to ensure the steady of adaptive control laws
It is qualitative, it is bounded based on systematic parameter, that is, assumes 2, the parameter adaptive discontinuous mapping being defined as follows：
I=1 in formula, 2,3；τ is parameter adaptive function, its specific shape will be provided in subsequent controller design
Formula；Provide following parameter update law：
Gain matrix in formulaFor positive definite diagonal matrix.
For arbitrary auto-adaptive function τ, discontinuous mapping (10) has following property：
The proof of more than property is given below：
For Property P 1, by the definition of discontinuous mapping it is easy to see that therefore not repeating.
For Property P 2, when discontinuous mapping is in the third otherwise ordinary circumstance, have
During for there is the parametric component for meeting discontinuous mapping the first situation in parameter Estimation, only these components need to be considered
Influence whether set up P2.WhenandΓiτiDuring ＞ 0, have
Again
SoThen have
Similarly, whenandΓiτiDuring ＜ 0, have
Again
SoThen have
To sum up, P2 is set up.
Step 2.3, consider second state equation of formula (2), substituted into e2Error dynamics equation in, have
In formula,For e2Derivative,For x2dDerivative.Similarly, x is chosen3For virtual controlling amount, design it and it is expected x3d
For
K in formulan>0, for adjustable non linear robust feedback term gain, k2>0, for positive feedback oscillator, δ (t)>0 is optional letter
Number meetsδn＞ 0, i.e. δ (t) in t ∈ [0, ∞] upper integral bounded,I.e.
For the Continuous Nonlinear robust feedback term of design, for inhibiting external interference and other Unmarried pregnancies.
Definition e3=x3-x3dAnd substitute into (15) formula in (14) formula, then
Choose Liapunov candidate functions V2It is as follows：
Then have
Step 2.4, consider the third state equation of formula (2), substituted into e3Error dynamics equation in, have
In formula,For e3Derivative,For x3dDerivative.According to formula (19), the ADAPTIVE ROBUST control based on model is designed
Device processed is：
K in formula3>0, it is positive feedback oscillator.
(20) are substituted into (19) to obtain
Step 3, the stability of adaptive robust control strategy proves, performance evaluation.
Controller performance：Using the parameter update law of discontinuous mapping, and enable auto-adaptive functionIt chooses big
Small suitable parametrical nonlinearity robust item gain kn, both it had been avoided that reality trembling of bringing of the robust item of sliding formwork switching construction in
It shakes problem, and good tracking accuracy can be obtained.As t → ∞, system obtains the steady result of Globally asymptotic.
Stability analysis：Following Liapunov candidate functions are chosen, with Lyapunov stability theory and fragrant plant
Fragrant plant draws theorem to carry out stability analysis：
It can show that the control method can obtain good tracking performance by analysis, parameter identification ability ensures system
System Globally asymptotic.
It is as follows：
Using discontinuous mapping parameter update law (11), it is derived from fitness function vector
Stability series are analyzed：Choose following Liapunov candidate functions V3, with Lyapunov stability theory into
Row stability analysis.
With the Property P 2 in formula (13), can obtain：
It enablesFormula (24) both sides are integrated
Due toSo V can be obtained3(t) bounded, and then understand e1, e2, e3Equal bounded, then root
According to assume 1 understand system in it is stateful be all bounded.Further, it is all bounded to be easy to get all signals in system
's.Q is congruous continuity according to uniform continuity Distinguishing theorem.
It is obtained by (25)
Then have
It can be obtained according to the Barbara theorem of integrated form
I.e. as t → ∞, Q → 0, then as t → ∞, e1→0.I.e. system tracking error tends to infinite condition in the time
Under go to zero, system Globally asymptotic.
Embodiment
To examine designed controller performance, following parameter is taken to model electric system in simulations：J=
6.9kg·m2, ki=0.05Nm/A, B=0.53Nms/rad, L=1.6H, R=1.56 Ω, kb=19.7Nm/
(r·min-1), dn=-0.01Nm, f (t)=0.07sintNm；Take ARC controller parameters k1=72, k2=16.3, k3=
4.2, kn=1, δf=0.1Nm, θmin=[50,0, -1]T, θmax=[150,20,1]T, Г=diag { 100,15,6 }, δ (t)
=3000/ (t2+1)；Take PID controller proportionality coefficient kp=105, integral coefficient ki=24, differential coefficient kd=0.9.
Given position reference signal is x1d=0.8sin (π t) [1-exp (- 0.01t3)]。
Control action effect attached drawing is as follows：
Fig. 3 is tracking process schematic of the lower system output of ARC controllers control to given reference signal, and Fig. 4 is ARC controls
The tracking error time history plot of the lower system of device effect processed；It can be seen that designed by the present invention from Fig. 3 and Fig. 4
The response of ARC controller systems is fast, and tracking is steady, and tracking error asymptotic convergence is in zero.Fig. 5 is the tracking essence of ARC and PID controller
Comparison diagram is spent, Fig. 6 is the curve graphs of the control signal u of ARC controllers at any time, and Fig. 7 is that the parameter adaptive under ARC controls is bent
Line soil.As can be seen from Figure 5 the tracking accuracy of ARC controllers is apparently higher than conventional PID controllers, and Fig. 6 shows ARC controllers
Signal continuously differentiable is controlled, without big jagged fluctuation, parameter adaptive shown in Fig. 7 works well, and can quickly converge on
True value.
In conclusion controller proposed by the present invention can obtain the good identification to uncertain parameter under simulated environment
Ability and there is good robustness to external interference, compared to traditional PID control, ARC controllers proposed by the invention
System can be greatly improved, and there are the systematic tracking accuracies in the case of Parameter uncertainties and external interference.Simulation results show this
Validity, the superiority of the proposed controller of invention.
Claims (4)
1. a kind of motor servo system Asymptotic Stability control method for considering electrical characteristic, which is characterized in that include the following steps：
Step 1, the mathematical model for establishing DC brushless motor servo-drive system；
Step 2, design make the self-adaptive robust controller of motor servo system asymptotically stability；
Step 3 carries out stability analysis with Lyapunov stability theory.
2. the motor servo system Asymptotic Stability control method according to claim 1 for considering electrical characteristic, feature exist
In step 1 is specially：
Step 1-1, according to mechanically and electrically characteristic, establishing the DC brushless motor system equation of motion is：
In formula (1), J be inertia load equivalent rotary inertia, kiFor Motor torque constant, i is armature supply,For armature supply
Derivative, B are viscosity friction coefficient, dnUnknown constant value disturbance is represented,Other uncertain dynamic characteristics are represented, L represents electricity
Pivot inductance, u represent armature both end voltage, and R represents armature internal resistance, kbRepresenting armature damped coefficient, t is time variable, x,Point
It Wei not motor angular displacement, angular speed and angular acceleration；
Step 1-2, definition status variable：x1=x,x3=i takes state vector x=[x1,x2,x3]T, then the fortune of formula (1)
It is dynamic equations turned for state equation：
Defined parameters collection vector θ=[θ1,θ2,θ3]T, wherein θ1=J/ki, θ2=B/ki,θ3=dn/ki；Table
Show the equivalent unmodelled dynamics after being converted in system；
The design object of system controller is：For given position reference x1d(t), the control for designing a bounded is defeated
Entering u makes system export x1The reference signal of system is kept up with as much as possible；
Have it is assumed hereinafter that setting up：
Assuming that 1：System reference signal x1dIt is Second Order Continuous, and the instruction of system desired locations, the instruction of speed command acceleration are all
It is bounded；
System does not know dynamic characteristicMagnitude range it is known that i.e.
δ in formulafFor known constant；
Assuming that 2：The magnitude range of parameter uncertainty θ is it is known that i.e.
θ in formulamin=[θ1min,θ2min,θ3min]T, θmax=[θ1max,θ2max,θ3max]TKnown bound for vectorial θ.
3. the motor servo system Asymptotic Stability control method according to claim 2 for considering electrical characteristic, feature exist
It is as follows in, the step 2 design self-adaptive robust controller the step of：
Step 2-1 defines e1=x1-x1dFor the position tracking error of system, according to first state equation of (2) formula
Choose x2For virtual controlling amount, to makeIt tends towards stability, enables x2dFor the expectation of virtual controlling amount, x is defined2dWith system reality
State x2Error be e2=x2-x2d, to e1Derivation obtains：
In formulaFor reference signal x1dDerivative, design virtual controlling rule x2d：
K in formula1>0 is adjustable gain, and (5) formula of substitution has
Due to e1(s)=G (s) e2(s), G (s)=e in formula1(s)/e2(s)=1/ (s+k1) it is a stable transmission function, institute
To work as e2When tending to 0, e1Also necessarily tend to 0；
Step 2-2, discontinuous parameter mapping used by providing parameter adaptive before design parameter adaptive law：
It enablesRepresent the estimation to unknown parameter θ,For parameter estimating error, to ensure the stability of adaptive control laws,
It is bounded based on systematic parameter, that is, assumes 2, the parameter adaptive discontinuous mapping being defined as follows：
I=1 in formula, 2,3；τ is parameter adaptive function, provides following parameter update law：
Gain matrix Γ is positive definite diagonal matrix in formula.
For arbitrary auto-adaptive function τ, discontinuous mapping (8) has following property：
P1:
P2:
Step 2-3 considers second state equation of formula (2), is substituted into e2Error dynamics equation in, have
In formula,For e2Derivative,For x2dDerivative, similarly, choose x3For virtual controlling amount, design it and it is expected x3dFor
K in formulan>0 be adjustable non linear robust feedback term gain, k2>0 be positive feedback oscillator, δ (t)>0 is optional function, full
Footδn＞ 0, i.e. δ (t) in t ∈ [0, ∞] upper integral bounded,As set
The Continuous Nonlinear robust feedback term of meter, for inhibiting external interference and other Unmarried pregnancies；
Definitione3=x3-x3d, and (13) formula is substituted into (12) formula, then
Step 2-4 considers the third state equation of formula (2), is substituted into e3Error dynamics equation in, have
In formula,For e3Derivative,For x3dDerivative, according to formula (15), design the self-adaptive robust controller based on model
For：
K in formula3>0, it is positive feedback oscillator.
4. the adaptive robust control method of DC brushless motor servo-drive system according to claim 3, which is characterized in that
Step 3 is as follows：
Using discontinuous mapping parameter update law (9), it is derived from fitness function vector
Choose following Liapunov candidate functions V3, stability analysis is carried out with Lyapunov stability theory：
With the Property P 2 in formula (11), can obtain：
It enablesFormula (19) both sides are integrated
Due toV can be obtained3(t) bounded, and then understand e1, e2, e3Equal bounded, can further according to hypothesis 1
Know in system it is stateful be all bounded, all signals are all bounded in system；It can according to uniform continuity Distinguishing theorem
It is congruous continuity to know Q；
It is obtained by (20)
Then have
It can be obtained according to the Barbara theorem of integrated form
I.e. as t → ∞, Q → 0, then as t → ∞, e1→ 0, i.e. system tracking error becomes under conditions of tending to be infinite in the time
In zero, system Globally asymptotic.
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| CN110703606A (en) * | 2019-10-30 | 2020-01-17 | 曾喆昭 | Novel self-coupling PID cooperative control theory method |
| CN110888320A (en) * | 2019-09-09 | 2020-03-17 | 南京理工大学 | Self-adaptive robust control method based on double-electric-cylinder synchronous motion error modeling |
| CN110928182A (en) * | 2019-11-05 | 2020-03-27 | 南京理工大学 | Robust self-adaptive repetitive control method of hydraulic servo system based on state estimation |
| CN110989357A (en) * | 2019-12-18 | 2020-04-10 | 中国科学院长春光学精密机械与物理研究所 | Identification control method and system for complex electromechanical system |
| CN111830824A (en) * | 2019-12-03 | 2020-10-27 | 南京工大数控科技有限公司 | Direct current motor servo system asymptotic tracking control method considering current loop dynamics |
| CN113852305A (en) * | 2021-09-22 | 2021-12-28 | 广州大学 | Sliding mode control method, system, equipment and medium for direct current motor terminal |
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| CN110888320A (en) * | 2019-09-09 | 2020-03-17 | 南京理工大学 | Self-adaptive robust control method based on double-electric-cylinder synchronous motion error modeling |
| CN110888320B (en) * | 2019-09-09 | 2022-06-28 | 南京理工大学 | Self-adaptive robust control method based on double-electric-cylinder synchronous motion error modeling |
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| CN110989357A (en) * | 2019-12-18 | 2020-04-10 | 中国科学院长春光学精密机械与物理研究所 | Identification control method and system for complex electromechanical system |
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| CN113852305A (en) * | 2021-09-22 | 2021-12-28 | 广州大学 | Sliding mode control method, system, equipment and medium for direct current motor terminal |
| CN113852305B (en) * | 2021-09-22 | 2023-10-27 | 广州大学 | DC motor terminal sliding mode control method, system, equipment and medium |
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