CN105697463B - A kind of Hydraulic Position Servo exports feedback adaptive control method - Google Patents

A kind of Hydraulic Position Servo exports feedback adaptive control method Download PDF

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CN105697463B
CN105697463B CN201610164099.8A CN201610164099A CN105697463B CN 105697463 B CN105697463 B CN 105697463B CN 201610164099 A CN201610164099 A CN 201610164099A CN 105697463 B CN105697463 B CN 105697463B
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CN105697463A (en
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任海鹏
龚佩芬
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Xian University of Technology
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F15FLUID-PRESSURE ACTUATORS; HYDRAULICS OR PNEUMATICS IN GENERAL
    • F15BSYSTEMS ACTING BY MEANS OF FLUIDS IN GENERAL; FLUID-PRESSURE ACTUATORS, e.g. SERVOMOTORS; DETAILS OF FLUID-PRESSURE SYSTEMS, NOT OTHERWISE PROVIDED FOR
    • F15B21/00Common features of fluid actuator systems; Fluid-pressure actuator systems or details thereof, not covered by any other group of this subclass
    • F15B21/02Servomotor systems with programme control derived from a store or timing device; Control devices therefor
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/30Circuit design
    • G06F30/36Circuit design at the analogue level
    • G06F30/367Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

Feedback adaptive control method is exported the invention discloses a kind of Hydraulic Position Servo, step includes:1) model of controlled Hydraulic Position Servo is set up, detection is obtained each above-mentioned variable parameter in real time by respective detecting instrument respectively;Negligible friction, obtains three rank linear models of hydraulic system, and control targe is to make the desired output required by Model output tracking;2) the output Feedback Adaptive Controller model of Hydraulic Position Servo is set up;3) Hydraulic Position Servo unknown parameters ' value is estimated, it will estimate that obtained numerical value inputs computer, the parameter of Feedback Adaptive Controller model exported for real-time update, computer controls the signal output of amplifier, the displacement of real-time regulating piston,.The inventive method need not increase pressure detecting hardware or algorithm, result in more preferable tracking effect and Geng Gao control accuracy.

Description

A kind of Hydraulic Position Servo exports feedback adaptive control method
Technical field
The invention belongs to hydraulic system high precision position tracking control technology field, it is related to a kind of Hydraulic Position Servo Export feedback adaptive control method.
Background technology
Hydraulic system (i.e. Hydraulic Position Servo) be using liquid as working media, its have power to volume ratio it is big, The advantages of bearing capacity is strong, fast response time, control accuracy are high, inertia is small, speed governing is convenient and safe, hydraulic technique is Through being widely used in every field.
But it is due to rubbing between Complex Flows characteristic, hydraulic cylinder and the sliding block that the internal leakage of liquid, liquid pass through valve port Wiping power is relatively large, and these factors cause the high precision tracking of Hydraulic Position Servo is controlled very difficult.
The content of the invention
Feedback adaptive control method is exported it is an object of the invention to provide a kind of Hydraulic Position Servo, is solved The problem of prior art is not high enough to the tracing control precision of Hydraulic Position Servo.
The technical solution adopted by the present invention is that a kind of Hydraulic Position Servo exports feedback adaptive control method, should Method is embodied according to following steps:
Step 1, the model for setting up Hydraulic Position Servo
The mathematical modeling of the Hydraulic Position Servo such as following formula (1):
Wherein, PaAnd PbRespectively hydraulic cylinder rodless cavity A and rod chamber B pressure,WithRespectively PaAnd PbSingle order Derivative, PsAnd PrRespectively charge oil pressure and return pressure, QaAnd QbRespectively flow into rodless cavity A and outflow rod chamber B stream Amount, AaAnd AbIt is piston in rodless cavity A and rod chamber B effective active area, VaAnd VbFor hydraulic cylinder rodless cavity A and rod chamber B Volume, CdFor discharge coefficient, CtFor internal leakage coefficient, w is proportioning valve area gradient, xvFor proportioning valve spool displacement, kvFor than Example valve proportionality coefficient, u is control signal, and ρ is fluid density, βeFor bulk modulus, M is load quality, BpFor viscous damping Coefficient, k is spring loaded coefficient, and y is the displacement of hydraulic cylinder piston, and y is obtained by the detection of displacement detecting instrument,WithRespectively y First derivative and second dervative, FLFor outer load force,
Introduce load flow QLWith load pressure PLDefinition:
Ignore outer load force FLAnd the nonlinear load such as Coulomb friction, linearization process is carried out to nonlinear function, obtained Mechanism model to the Hydraulic Position Servo is:
Wherein, KxaAnd KpaFlow gain and flow pressure coefficient after respectively linearizing, AmRepresent being averaged for hydraulic cylinder Effective area,
The state variable for defining the Hydraulic Position Servo is:Wherein Subscript T refer to vector transposition,
Then the state equation of the Hydraulic Position Servo is:
The approximate three rank linear models for obtaining the Hydraulic Position Servo near matching point are as follows:
WhereinX is corresponded to respectively1、x2、x3First derivative, a0、a1、a2, b be unknown model parameters, For y three order derivatives, control targe is the desired output y for making piston displacement y tracking requiredm
Step 2, the output Feedback Adaptive Controller model for setting up Hydraulic Position Servo
An output Feedback Adaptive Controller, its model such as following formula (6) are built to formula (5):
U '=θTω, (6)
Wherein, the control signal before u' is amplitude limit;θTIt is 4 dimensional vectors, θ with ωTIt is θ transposed vector, θ=[k θ1 θ2 θ0]T, ω=[ym ω1 ω2 y]T, ω1And ω2Respectively by input signal ymObtained with output signal y filtering, i.e., such as Shown in formula (7):
Wherein,WithRespectively ω1And ω2First derivative, Λ, h be design parameter,
VariableDerivative asked for by Euler's formula, concrete form such as following formula (8):
Wherein,It is x (t) first derivative,RepresentIn the value of k sampling instant, when Δ T is sampling Between,
Amplitude limit, concrete form such as following formula (9) are carried out to control signal u:
Wherein, UmaxFor control signal u amplitude limit value;
Step 3, the estimate for calculating output Feedback Adaptive Controller model parameter
Actual hydraulic pressure positional servosystem uses the transmission function W of formula (5)p(s) such as following formula:
It is assumed that transmission function Wm(s) reference model such as following formula:
Wherein, bm、a2m、a1m、a0mFor the parameter of reference model;
The estimate rule of auto-adaptive parameter is determined, with reference to following formula (12):
Wherein, θ=[k θ1 θ2 θ0]T,It is θ first derivative;γ is regulation parameter;
Sgn (b) is the sign function on b, as b > 0, sgn (b)=1;As b=0, sgn (b)=0;As b < 0 When, sgn (b)=- 1;
It is W by transmission function to represent signal vector ωm(s) the output signal corresponding to module,It isTransposed vector;
ε=e+ α η are augmented error, e=y-ymFor tracking error, ymIt is input signal, y is output signal,It is the one of α Order derivative, η=θTWm(ω)-WmTIt is ω) auxiliary error, WmTω) it is signal vector θTω is by it is expected that transmission function is Wm (s) the signal after module, θTIt is θ transposed vector,
Tracking error e is first calculated, then calculates auxiliary error η, and then ε is tried to achieve using the α values of last moment, ε is substituted into public The θ values at current time are tried to achieve in the first equation in formula (12), during by trying to achieve current in the second equation in ε substitution formula (12) The α values at quarter,
The vectorial θ that estimation is obtained, i.e. k, θ1、θ2And θ0Numerical value be used for real-time update export Feedback Adaptive Controller The parameter of modular form (6), the position of signal output, the in real time piston of regulation asymmetrical cylinder that computer passes through D/A converter Shifting amount.
The beneficial effect of the inventive method is to design the output feedback adaptive control based on Hydraulic Position Servo Device, and the Experimental comparison of three kinds of different curves is tracked from existing PID controller, experimental result shows the inventive method Tracking accuracy is higher, specifically includes:1) speed, acceleration and pressure sensor hardware are not needed, system simplifies, and controls cost It is low;2) accurate parameters of object are not needed, just can implement effectively control;3) compared with existing PID control method, result in Higher control accuracy.
Brief description of the drawings
Fig. 1 is the structural representation of the inventive method control object;
Fig. 2 is the controller architecture schematic diagram of the inventive method;
Fig. 3 is the experimental result that S curve is tracked using the inventive method;
Fig. 4 is the experimental result that sinusoidal signal is tracked using the inventive method;
Fig. 5 is the experimental result that multifrequency sine signal is tracked using the inventive method;
Fig. 6 is the experimental result that S curve is tracked using PID approach;
Fig. 7 is the experimental result that sinusoidal signal is tracked using PID approach;
Fig. 8 is the experimental result that multifrequency sine signal is tracked using PID approach.
In figure, 1. pistons, 2. loads, 3. asymmetrical cylinders, 4. displacement detecting instrument, 5. proportioning valves, 6. computers, 7. subtract Pressure valve, 8. oil pumps, 9. hydraulic pump fuel reserve tanks.
Embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
The Hydraulic Position Servo output feedback adaptive control method of the present invention, is embodied according to following steps:
Step 1, the model for setting up Hydraulic Position Servo
Reference picture 1, the structure of the Hydraulic Position Servo of the inventive method (control object) is, including asymmetrical liquid Cylinder pressure 3, hydraulic cylinder rodless cavity A and rod chamber B effective active area, rodless cavity A effective active area is rod chamber B 1.6 times, the piston 1 in hydraulic cylinder 3 is fixedly connected with load 2, and piston 1 is connected with piston rod, and piston rod (stretches out the portion of cylinder body Point) on be correspondingly arranged on displacement detecting instrument 4, the probe of displacement detecting instrument 4 by with plunger rod contacts, detection obtains piston 1 Displacement information, the signal output part of displacement detecting instrument 4 accesses computer 6 by A/D converter;Proportioning valve 5 selects 3-position 4-way Magnetic valve, the rodless cavity A of hydraulic cylinder 3 can pass through the control of valve and time of the liquid feeding end (P ports) of proportioning valve 5 or proportioning valve 5 Liquid end (T-port) UNICOM, corresponding, the rod chamber B of the hydraulic cylinder 3 accordingly control of passing ratio valve and liquid returning end or liquid feeding end UNICOM;In addition, the liquid feeding end (P ports) of proportioning valve 5 is connected by pressure-reducing valve 7 with oil pump 8, the liquid returning end (T-port) of proportioning valve 5 Connected with hydraulic pump fuel reserve tank 9;The electromagnetic valve core of proportioning valve 5 is connected with by D/A converter with computer 7, when computer 7 is defeated When going out control signal, the control signal controls proportional valve spool to act by D/A converter, realizes liquid flowing control.
Assuming that the Hydraulic Position Servo meets following condition:
1) working media (liquid) that system is used is ideal liquid;
2) flow regime when liquid flows through valve port or other restrictions is constant entropy adiabatic process;
3) fluid pressure and temperature are equal everywhere in same cavity volume;
4) leakage not considered is ignored;
5) during piston movement, the change procedure of two intracavity liquids is adiabatic process;
6) hydraulic power source pressure is constant;
7) compared with system dynamic characteristic, the inertia of proportioning valve can be ignored,
The mathematical modeling such as following formula (1) of the Hydraulic Position Servo is obtained accordingly:
Wherein, PaAnd PbRespectively hydraulic cylinder rodless cavity A and rod chamber B pressure,WithRespectively PaAnd PbSingle order Derivative, PsAnd PrRespectively charge oil pressure and return pressure, QaAnd QbRespectively flow into rodless cavity A and outflow rod chamber B stream Amount, AaAnd AbIt is piston in rodless cavity A and rod chamber B effective active area, VaAnd VbFor hydraulic cylinder rodless cavity A and rod chamber B Volume, CdFor discharge coefficient, CtFor internal leakage coefficient, w is proportioning valve area gradient, xvFor proportioning valve spool displacement, kvFor than Example valve proportionality coefficient, u is control signal, and ρ is fluid density, βeFor bulk modulus, M is load quality, BpFor viscous damping Coefficient, k is spring loaded coefficient, and y is the displacement of hydraulic cylinder piston, and y is obtained by the detection of displacement detecting instrument 4,WithRespectively Y first derivative and second dervative, FLFor outer load force,
Due to asymmetrical cylinder rodless cavity A and rod chamber B effective work area, thus hydraulic cylinder piston exists During forward and reverse motion, flow needed for system, various running parameters are relative to conventional symmetrical structure hydraulic cylinder difference very Greatly, the mathematical modeling of description working oil path is also significantly different,
Therefore, it is specifically incorporated load flow QLWith load pressure PLDefinition:
Ignore outer load force FLAnd the nonlinear load such as Coulomb friction, linearization process is carried out to nonlinear function, obtained Mechanism model to the Hydraulic Position Servo is:
Wherein, KxaAnd KpaFlow gain and flow pressure coefficient after respectively linearizing, AmRepresent being averaged for hydraulic cylinder Effective area,
The state variable for defining the Hydraulic Position Servo is:Wherein Subscript T refer to vector transposition,
Then the state equation of the Hydraulic Position Servo is:
The approximate three rank linear models for obtaining the Hydraulic Position Servo near matching point are as follows:
WhereinX is corresponded to respectively1、x2、x3First derivative, a0、a1、a2, b be unknown model parameters, For y three order derivatives, control targe is the desired output y for making piston displacement y tracking requiredm
Step 2, the output Feedback Adaptive Controller model for setting up Hydraulic Position Servo
It is the Hydraulic Position Servo output Feedback Adaptive Controller that the present invention is designed such as Fig. 2.
An output Feedback Adaptive Controller, its model such as following formula (6) are built to formula (5):
U '=θTω, (6)
Wherein, the control signal before u' is amplitude limit;
θTIt is 4 dimensional vectors, θ with ωTIt is θ transposed vector, θ=[k θ1 θ2 θ0]T,
ω=[ym ω1 ω2 y]T, ω1And ω2Respectively by input signal ymObtained with output signal y filtering, i.e., As shown in formula (7):
Wherein,WithRespectively ω1And ω2First derivative, Λ, h be design parameter,
VariableDerivative asked for by Euler's formula, concrete form such as following formula (8):
Wherein,It is x (t) first derivative,
RepresentIn the value of k sampling instant,
Δ T is the sampling time,
Amplitude limit, concrete form such as following formula (9) are carried out to control signal u:
Wherein, UmaxFor control signal u amplitude limit value;
Step 3, the estimate for calculating output Feedback Adaptive Controller model parameter
Actual hydraulic pressure positional servosystem uses the transmission function W of formula (5)p(s) such as following formula:
It is assumed that transmission function Wm(s) reference model such as following formula:
Wherein, bm、a2m、a1m、a0mFor the parameter of reference model;
The estimate rule of auto-adaptive parameter is determined, with reference to following formula (12):
Wherein, θ=[k θ1 θ2 θ0]T,It is θ first derivative;
γ is regulation parameter;
Sgn (b) is the sign function on b, as b > 0, sgn (b)=1;As b=0, sgn (b)=0;As b < 0 When, sgn (b)=- 1;
It is W by transmission function to represent signal vector ωm(s) the output signal corresponding to module,It isTransposed vector;
ε=e+ α η are augmented error, e=y-ymFor tracking error, ymIt is input signal, y is output signal,It is the one of α Order derivative, η=θTWm(ω)-WmTIt is ω) auxiliary error, WmTω) it is signal vector θTω is by it is expected that transmission function is Wm (s) the signal after module, θTIt is θ transposed vector,
Tracking error e is first calculated, then calculates auxiliary error η, and then ε is tried to achieve using the α values of last moment, ε is substituted into public The θ values at current time are tried to achieve in the first equation in formula (12), during by trying to achieve current in the second equation in ε substitution formula (12) The α values at quarter,
The vectorial θ that estimation is obtained, i.e. k, θ1、θ2And θ0Numerical value be used for real-time update export Feedback Adaptive Controller The parameter of modular form (6), the position of signal output, the in real time piston of regulation asymmetrical cylinder that computer passes through D/A converter Shifting amount,.
Embodiment
In the present embodiment, the product type that the critical piece in Hydraulic Position Servo is selected is:
Asymmetrical cylinder uses the model D of FESTO companies:S-HAZ-16-200-LE-SB;
The model that 3-position 4-way proportioning valve is used is D:H-B-43W-RV-NG6-K;
The model that swept resistance formula linear displacement detecting instrument is used is D:S-HAZ-16-200-1-SIBU;
The model that universal data collection card is used is PCI2306;
The model that computer is used be CPU for P2 1.2GHz, the control software of built-in computer is worked out using VB, is passed through The change curve of correlated variables in screen display control process.
The control targe of the present embodiment is respectively set to
Reference signal 1:S curve
ym=-(A/ ω2) sin (ω t)+(A/ ω) t, (13)
The value that A value is 55.825, ω is 0.5 π.
Reference signal 2:Single frequency sinusoidal signal
ym=111.65sin0.5 π t, (14)
Reference signal 3:Multifrequency sine signal
Tested using the output Feedback Adaptive Controller described in formula (7)-formula (12), the ginseng in formula (7)-formula (12) Examine model Wm(s) and filtering parameter Λ, h value by test repeatedly carry out examination gather.
Parameter is set in the present embodiment:Λ=- 20, h=5, Regulation parameter γ=200, control amplitude limit Umax=1.56V,
When it is respectively formula (13)-formula (15) to track expectation target, curve of output is respectively as shown in Fig. 3, Fig. 4, Fig. 5.
The control law of PID controller is as follows:
Actual pid control mode is provided by formula (16), controls the amplitude limit of output identical with the inventive method, wherein PID The parameter of controller obtains K by optimization designP=10, KI=15, KD=0.1.
Such as Fig. 6, Fig. 7, Fig. 8, the control in tracking correspondence desired output using existing PID control method sets forth Effect.
Contrast by Fig. 3-Fig. 8 is visible, and the tracking accuracy of the inventive method is higher.
In order to more intuitively illustrate the control effect of the inventive method, root-mean-square error RMSE is defined as follows
Wherein, N1To compare start time, N2To compare finish time, ek=e (k Δ T).
To avoid the influence of the different initial value of Self Adaptive Control and random disturbances, the tracking of every kind of input signal is carried out many Secondary experiment, following form provides the steady track root-mean-square error of wherein five times experimental results respectively, and its result see the table below 1- Table 3.
The error contrast of table 1, the inventive method and PID control method when tracking S curve signal
The error contrast of table 2, the inventive method and PID control method when tracking sinusoidal signal
The error of table 3, the inventive method with existing control method when tracking multifrequency sine signal is contrasted
From three steady track root-mean-square error average values contrasted in form, in the situation of various expectation targets Under, the average tracking error of the inventive method is both less than existing PID control method.

Claims (3)

1. a kind of Hydraulic Position Servo exports feedback adaptive control method, it is characterised in that this method is according to following step Rapid specific implementation:
Step 1, the model for setting up Hydraulic Position Servo
The mathematical modeling of the Hydraulic Position Servo such as following formula (1):
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Wherein, PaAnd PbRespectively hydraulic cylinder rodless cavity A and rod chamber B pressure,WithRespectively PaAnd PbFirst derivative, PsAnd PrRespectively charge oil pressure and return pressure, QaAnd QbRespectively flow into rodless cavity A and outflow rod chamber B flow, AaWith AbIt is piston in rodless cavity A and rod chamber B effective active area, VaAnd VbFor hydraulic cylinder rodless cavity A and rod chamber B volume, CdFor discharge coefficient, CtFor internal leakage coefficient, w is proportioning valve area gradient, xvFor proportioning valve spool displacement, kvFor proportioning valve ratio Example coefficient, u is control signal, and ρ is fluid density, βeFor bulk modulus, M is load quality, BpFor viscous damping coefficient, keFor spring loaded coefficient, y is the displacement of hydraulic cylinder piston, and y is obtained by displacement detecting instrument (4) detection,WithRespectively y's First derivative and second dervative, FLFor outer load force,
Introduce load flow QLWith load pressure PLDefinition:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <mi>a</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>b</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>L</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>Q</mi> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mi>b</mi> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Ignore outer load force FLAnd the nonlinear load such as Coulomb friction, linearization process is carried out to nonlinear function, the liquid is obtained Pressure positional servosystem mechanism model be:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>L</mi> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>a</mi> </mrow> </msub> <msub> <mi>x</mi> <mi>v</mi> </msub> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mi>p</mi> <mi>a</mi> </mrow> </msub> <msub> <mi>P</mi> <mi>L</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>L</mi> </msub> <mo>=</mo> <msub> <mi>C</mi> <mi>t</mi> </msub> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>+</mo> <mfrac> <mi>V</mi> <mrow> <mn>4</mn> <msub> <mi>&amp;beta;</mi> <mi>e</mi> </msub> </mrow> </mfrac> <msub> <mover> <mi>P</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>L</mi> </msub> <mo>+</mo> <msub> <mi>A</mi> <mi>m</mi> </msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>m</mi> </msub> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>=</mo> <mi>M</mi> <mover> <mi>y</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>B</mi> <mi>p</mi> </msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mi>e</mi> </msub> <mi>y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> 1
Wherein, KxaAnd KpaFlow gain and flow pressure coefficient after respectively linearizing, AmRepresent the average effective of hydraulic cylinder Area,
The state variable for defining the Hydraulic Position Servo is:On therein Mark T refers to the transposition of vector,
Then the state equation of the Hydraulic Position Servo is:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>k</mi> <mi>e</mi> </msub> <mi>m</mi> </mfrac> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <mfrac> <msub> <mi>B</mi> <mi>p</mi> </msub> <mi>m</mi> </mfrac> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <mfrac> <msub> <mi>A</mi> <mi>m</mi> </msub> <mi>m</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>3</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>4</mn> <msub> <mi>&amp;beta;</mi> <mi>e</mi> </msub> </mrow> <mi>V</mi> </mfrac> <msub> <mi>A</mi> <mi>m</mi> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <mfrac> <mrow> <mn>4</mn> <msub> <mi>&amp;beta;</mi> <mi>e</mi> </msub> </mrow> <mi>V</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mrow> <mi>p</mi> <mi>a</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mn>4</mn> <msub> <mi>&amp;beta;</mi> <mi>e</mi> </msub> </mrow> <mi>V</mi> </mfrac> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>a</mi> </mrow> </msub> <msub> <mi>K</mi> <mi>v</mi> </msub> <mi>u</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
The approximate three rank linear models for obtaining the Hydraulic Position Servo near matching point are as follows:
<mrow> <mover> <mi>y</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>0</mn> </msub> <mi>y</mi> <mo>=</mo> <mi>b</mi> <mi>u</mi> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
WhereinX is corresponded to respectively1、x2、x3First derivative, b, α2、α1、α0For unknown model parameters,For y's Three order derivatives, control targe is the desired output y for making piston displacement y tracking requiredm
Step 2, the output Feedback Adaptive Controller model for setting up Hydraulic Position Servo
An output Feedback Adaptive Controller, its model such as following formula (6) are built to formula (5):
U '=θTω, (6)
Wherein, the control signal before u' is amplitude limit;θTIt is 4 dimensional vectors, θ with ωTIt is θ transposed vector, θ=[k1 θ1 θ2 θ0]T, ω=[ym ω1 ω2 y]T, ω1And ω2Respectively by desired output signal ymObtained with piston displacement y filtering, i.e., As shown in formula (7):
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>&amp;Lambda;&amp;omega;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>hy</mi> <mi>m</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>&amp;Lambda;&amp;omega;</mi> <mn>2</mn> </msub> <mo>+</mo> <mi>h</mi> <mi>y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Wherein,WithRespectively ω1And ω2First derivative, Λ, h be design parameter,
VariableDerivative asked for by Euler's formula, concrete form such as following formula (8):
<mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mi>&amp;Delta;</mi> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mi>&amp;Delta;</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&amp;Delta;</mi> <mi>T</mi> </mrow> </mfrac> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Wherein,It is x (t) first derivative,RepresentIn the value of k sampling instant, Δ T is the sampling time,
Amplitude limit, concrete form such as following formula (9) are carried out to control signal u:
<mrow> <mi>u</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>&gt;</mo> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> </mtd> <mtd> <mrow> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <mo>&amp;le;</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>&lt;</mo> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>&lt;</mo> <mo>-</mo> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
Wherein, UmaxFor control signal u amplitude limit value;
Step 3, the estimate for calculating output Feedback Adaptive Controller model parameter
Actual hydraulic pressure positional servosystem uses the transmission function W of formula (5)p(s) such as following formula:
<mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>b</mi> <mrow> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <mi>s</mi> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> 2
Wherein, b, α2、α1、α0For the parameter of object model;
It is assumed that transmission function Wm(s) reference model such as following formula:
<mrow> <msub> <mi>W</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mi>m</mi> </msub> <mrow> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msub> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>1</mn> <mi>m</mi> </mrow> </msub> <mi>s</mi> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>0</mn> <mi>m</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Wherein, bm、α2m、α1m、α0mFor the parameter of reference model;
The estimate rule of auto-adaptive parameter is determined, with reference to following formula (12):
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;theta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mi>s</mi> <mi>g</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>&amp;gamma;</mi> <mi>&amp;epsiv;</mi> <munder> <mi>&amp;omega;</mi> <mo>&amp;OverBar;</mo> </munder> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <munder> <mi>&amp;omega;</mi> <mo>&amp;OverBar;</mo> </munder> <mi>T</mi> </msup> <munder> <mi>&amp;omega;</mi> <mo>&amp;OverBar;</mo> </munder> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mi>&amp;gamma;</mi> <mi>&amp;epsiv;</mi> <mi>&amp;eta;</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <munder> <mi>&amp;omega;</mi> <mo>&amp;OverBar;</mo> </munder> <mi>T</mi> </msup> <munder> <mi>&amp;omega;</mi> <mo>&amp;OverBar;</mo> </munder> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Wherein, θ=[k1 θ1 θ2 θ0]T,It is θ first derivative;γ is regulation parameter;
Sgn (b) is the sign function on b, as b > 0, sgn (b)=1;As b=0, sgn (b)=0;As b < 0, Sgn (b)=- 1;
ω=Wm(ω) represents that signal vector ω is W by transmission functionm(s) the output signal corresponding to module,ω TIt isω Transposed vector;
ε=e+ α η are augmented error, e=y-ymFor tracking error, ymIt is input signal, y is piston displacement,It is that α single order is led Number, η=θTWm(ω)-WmTIt is ω) auxiliary error, WmTω) it is signal vector θTω is by it is expected that transmission function is Wm(s) Module after signal, θTIt is θ transposed vector,
Tracking error e is first calculated, then calculates auxiliary error η, and then ε is tried to achieve using the α values of last moment, ε is substituted into formula (12) the θ values at current time are tried to achieve in the first equation in, ε is substituted into the second equation in formula (12) and tries to achieve current time α values,
The vectorial θ, i.e. k that estimation is obtained1、θ1、θ2And θ0Numerical value be used for real-time update export Feedback Adaptive Controller model The parameter of formula (6), the displacement of signal output, the in real time piston of regulation asymmetrical cylinder that computer passes through D/A converter Amount,.
2. Hydraulic Position Servo according to claim 1 exports feedback adaptive control method, it is characterised in that:Institute In the step 1 stated, the structure of described Hydraulic Position Servo is,
Including asymmetrical hydraulic cylinder (3), hydraulic cylinder rodless cavity A and rod chamber B effective active area, hydraulic cylinder (3) In piston (1) with load (2) be fixedly connected, piston (1), which is connected with piston rod, piston rod, is correspondingly arranged on displacement detecting instrument (4), the signal output part of displacement detecting instrument (4) accesses computer (6) by A/D converter;The rodless cavity A of hydraulic cylinder (3) with The liquid feeding end of proportioning valve (5) or the liquid returning end UNICOM of proportioning valve (5), proportioning valve (5) select three position four-way electromagnetic valve, hydraulic cylinder (3) rod chamber the B accordingly control of passing ratio valve and liquid returning end or liquid feeding end UNICOM;In addition, the P ports of proportioning valve (5) Connected by pressure-reducing valve (7) with oil pump (8), the T-port of proportioning valve (5) is connected with hydraulic pump fuel reserve tank (9);Proportioning valve (5) Electromagnetic valve core is connected with by D/A converter with computer (6).
3. Hydraulic Position Servo according to claim 2 exports feedback adaptive control method, it is characterised in that:Institute Hydraulic cylinder (3) the rodless cavity A stated effective active area is 1.6 times of rod chamber B.
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