CN104698844B  Uncertainty compensatory slidingmode control method of hydraulic position servo system  Google Patents
Uncertainty compensatory slidingmode control method of hydraulic position servo system Download PDFInfo
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 CN104698844B CN104698844B CN201510066478.9A CN201510066478A CN104698844B CN 104698844 B CN104698844 B CN 104698844B CN 201510066478 A CN201510066478 A CN 201510066478A CN 104698844 B CN104698844 B CN 104698844B
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 238000006073 displacement reactions Methods 0.000 claims description 9
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Abstract
The invention discloses an uncertainty compensatory slidingmode control method of a hydraulic position servo system. The uncertainty compensatory slidingmode control method comprises the steps of firstly, establishing a mathematic model of the hydraulic position servo system, then respectively designing a mismatching disturbance observer and a matching disturbance observer, designing a slidingmode controller based on the mismatching disturbance observer and the matching disturbance observer, and finally proving the global asymptotic stability of the system according to a Lyapunov stability principle. By means of the uncertainty compensatory slidingmode control method, the gain of discontinuous terms of a sliding mode is remarkably reduced, and meanwhile accelerated speed information of the system is not used, so that matching uncertainty nonlinearity and mismatching uncertainty nonlinearity simultaneously exist in the system, asymptotic tracking steadystate performance is obtained, the capacity of resisting to matching and mismatching uncertainty and nonlinearity of the uncertainty compensatory slidingmode control method applied in the hydraulic position servo system is improved, and good tracking performance is obtained.
Description
Technical field
The invention belongs to electrohydraulic servo control technical field, the uncertain benefit of particularly a kind of Hydraulic Position Servo
The slidingmode control repaid.
Background technology
Hydrauservo System has that power to weight ratio is big, response is fast and the rigid outstanding advantages such as strong of antiloading, in numerous important necks
Find broad application in domain.Electrohydraulic servo system is a typical nonlinear system, comprising many nonlinear characteristics and modeling
It is uncertain.Nonlinear characteristic has servo valve flow pressure nonlinear, nonlinear in tribology etc..Modeling is uncertain to include parameter not
Certainty and uncertainty is nonlinear, and wherein parameter uncertainty mainly has load quality, the viscosity friction coefficient of executor, lets out
The coefficient of leakage, servo valve flow gam, hydraulic oil elastic modelling quantity etc., it is uncertain it is nonlinear mainly have do not model friction dynamic,
System highorder dynamic, outer interference and do not model leakage etc..When electrohydraulic servo system is to high accuracy, high frequency sound development, system is presented
Impact of the nonlinear characteristic to systematic function it is more notable, and model probabilistic presence and can make to set with system nominal plant model
The controller of meter is unstable or depression of order, therefore electrohydraulic servo system nonlinear characteristic and modeling uncertainty are to limit systematic function
The key factor of lifting.With industry and the continuous progress of national defence technical merit, conventional linear Design Theory was based in the past
Controller can not gradually meet the high performance demands of system, it is therefore necessary to for the nonlinear characteristic in electrohydraulic servo system
The more advanced nonlinear control strategy of research.
Matching and mismatched uncertainty and nonlinear Control problem for electrohydraulic servo system, many methods quilt in succession
Propose.In the design of Hydraulic Position Servo controller, for electrohydraulic servo system exist matching and it is unmatched not
Definitiveness, the basic thought of back stepping control design is by accurately being compensated nonlinear function so that error in the controller
Dynamical linearization.Although can obtain perfect asymptotic tracking performance in theory, the model of real system is impossible essence
Really known, always presence modeling is uncertain, therefore can deteriorate the tracking performance of theory analysis acquisition.Selfadaptation control method
Although can the probabilistic problem of processing parameter, be could to obtain gradually in the case where hypothesis system does not have outer interference
The steadystate behaviour of close tracking.Due to there is mismatched uncertainty in system, the basic ideas of traditional slidingmode control are
Mismatched with matching uncertainties so as to reach slidingmode surface to overcome by the robustness for increasing controller, but, even if reaching
After slidingmode surface, systematically tracking error cannot be still zero under the interference of mismatching uncertain, can only obtain one and not
With a related uniformly bounded steady track error of uncertain supremum.Also, by increasing discontinuous term gain
Method is likely to activating system high frequency dynamic in practice, makes system unstability increasing the robustness of controller.Thus pass
The slidingmode control of system has very big engineering limitations.
The content of the invention
It is an object of the invention to provide a kind of sliding formwork control side of the uncertain compensation of liquid Hydraulic Position Servo
Method.
The technical solution for realizing the object of the invention is：A kind of cunning of the uncertain compensation of Hydraulic Position Servo
Mould control method, comprises the following steps：
Step 1, the mathematical model for setting up Hydraulic Position Servo；
Step 2, separately design mismatch and match interference observer；
Step 3, design are based on the sliding mode controller for mismatching and matching interference observer；
Step 4, according to Liapunov stability principle proof system asymptotically stable in the large.
Compared with prior art, its remarkable advantage is the present invention：(1) dexterously design terminal sliding formwork disturbanceobserver of the invention
The matching of device observation Hydraulic Position Servo and mismatched uncertainty, and will matching and not in design sliding mode controller
Fall with uncertain compensation, significantly cut down sliding formwork discontinuous term gain；(2) present invention does not use system acceleration information,
So that system exists concurrently with matching and the nonlinear performance for obtaining asymptotic tracking of mismatched uncertainty, sliding formwork control is enhanced
Approach application resists matching and mismatched uncertainty and nonlinear ability in Hydraulic Position Servo；(3) present invention
Solve the problems, such as that slidingmode control tracking error in the case where system has mismatched uncertainty cannot converge to zero,
And obtain the tracking performance that steady track error is zero.
Description of the drawings
Fig. 1 is the slidingmode control flow chart of the uncertain compensation of the Hydraulic Position Servo of the present invention.
Fig. 2 is the schematic diagram of the Hydraulic Position Servo of the present invention.
Fig. 3 is the slidingmode control principle schematic of the uncertain compensation of the Hydraulic Position Servo of the present invention.
Fig. 4 is the lower system output of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation to expecting
The tracking process of instruction.
Fig. 5 is the position tracking of the lower system of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation
The time dependent curve of error.
Fig. 6 be the mismatch of the lower system of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation not
Definitiveness observation curve.
Fig. 7 be the mismatch of the lower system of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation not
Definitiveness observation error changes over curve.
Fig. 8 is that the matching of the lower system of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation is not true
Qualitative observation curve.
Fig. 9 is that the matching of the lower system of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation is not true
Qualitative observation error changes over curve.
Figure 10 is that the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation is lower and without mismatching not
Position tracking error under the sliding mode controller effect of definitiveness compensation changes over curve.
Figure 11 is that the control of the lower system of the sliding mode controller effect of the matching of the present invention and mismatched uncertainty compensation is defeated
Enter time dependent curve.
Figure 12 be the lower system of sliding mode controller effect without mismatched uncertainty compensation of the present invention control input with
The curve of time change.
Specific embodiment
Below in conjunction with the accompanying drawings and specific embodiment is described in further detail to the present invention.
With reference to Fig. 1～3, the slidingmode control of the uncertain compensation of the Hydraulic Position Servo of the present invention, including
Following steps：
Step 1, the mathematical model for setting up Hydraulic Position Servo；
Step 11, Hydraulic Position Servo are the system of the fluid motordriven inertia load by servo valve control；
According to Newton's second law, the equation of motion of inertia load is：
In formula (1), m is inertia load parameter；P_{L}For two chamber pressure reduction of hydraulic motor；Discharge capacities of the A for hydraulic motor；B is viscosity
Coefficient of friction；For modeling error, including m, P_{L}, B nominal value and actual value between deviation and outer load it is dry
Disturb；Displacements of the y for inertia load；For the speed of inertia load,For the acceleration of inertia load；T is time variable；
Ignore the external leakage of hydraulic motor, then the Pressure behaviour equation in two chamber of hydraulic motor is：
P in formula (2)_{1}And P_{2}The respectively pressure in two chamber of hydraulic motor,WithRespectively P_{1}And P_{2}Derivative；V_{1}=V_{01}+
Ay,V_{2}=V_{02} Ay, V_{1}And V_{2}The control volume in two chamber of hydraulic motor is represented respectively；V_{01}And V_{02}Respectively hydraulic motor two chamber
Original volume；β_{e}For effective fluid elastic modelling quantity；C_{t}For internal leakage coefficient；q_{1}(t) and q_{2}T () is respectively P_{1}And P_{2}Dynamical equation
Modeling error；Q_{1}And Q_{2}The respectively oil suction chamber flow and oil back chamber flow of hydraulic motor；Q_{1}And Q_{2}With servo valve displacement x_{v}Pass
It is to be：
In formula (3)s(x_{v}) definition be：
Wherein, k_{q}For flow gain, C_{d}Discharge coefficient；ω is valve element area gradient；ρ is fluid density；P_{s}It is to supply oil pressure
Power, P_{r}For return pressure；Two cavity pressure of hydraulic motor meets 0 ＜ P_{r}＜ P_{1}＜ P_{s}, 0 ＜ P_{r}＜ P_{2}＜ P_{s},P_{L} ＜ ＜ P_{S}；
Due to considering that servo valve dynamic needs to install extra displacement transducer to obtain the displacement of valve core of servo valve, and
For tracking performance only has small lifting；Therefore the dynamic of servo valve is all ignored in a large amount of related researchs, it is assumed that use
The servo valve of high response, spool displacement are approximately proportional component i.e. x with control input_{v}=k_{i}U, therefore formula (3) can be write as
K in formula (5)_{t}=k_{q}k_{i}Represent total flow gain, k_{i}For servo valve gain, u is that Hydraulic Position Servo is defeated
Enter,
Step 12, definition status variable：Then the state equation of system is：
System physical parameter m, B, β in formula (6)_{e}、k_{t}、V_{01}、V_{02}And C_{t}It is name in the design of observer and controller
Value, its deviation between actual value are concentrated and are placed in nonmodeled terms, be d (x, t), be q in third channel in leading to second
(t)；Wherein, d (x, t) is the mismatched uncertainty of system, including outer load disturbance, does not model friction and Unmarried pregnancy；q
T () is the uncertainty of the modeling error of Pressure behaviour, i.e. system matches；Wherein：
Due to hydraulic system parameters m, B, β_{e},k_{t}And C_{t}Affected to change by various factors (such as temperature, component wear degree etc.)
It is very big, therefore for simplified system state equation, definition:
d_{1}(x, t)=d (x, t)
Because  P_{L} ＜ ＜ P_{S}, so as to g (x) ≠ 0；Second channel mismatched uncertainty d_{1}(x, t) and third channel are matched
Uncertain d_{2}(x, t) is all bounded, i.e.,：
d_{1}(x,t)≤D_{1},d_{2}(x,t)≤D_{2}
D in formula_{1}、D_{2}Respectively  d_{1}(x, t)  and  d_{2}(x, t)  the upper bound, is all known positive number, and d_{1}(x, t) single order is led
Number is present；Then Hydraulic Position Servo model is
Step 2, separately designs mismatch and matches interference observer, and step is as follows：
Step 21, design mismatch interference observer：
Definition mismatches interference observer slidingmode surface s_{1}For：
s_{1}=z_{1}x_{2} (10)
Wherein, z_{1}To mismatch dynamic in interference observer；
In formula (11), k_{1}、β_{1}、ε_{1}、p_{1}And q_{1}It is mismatch interference observer coefficient；p_{1}＜ q_{1}, and positive odd number is, k_{1}、
β_{1}、ε_{1}It is positive number, β_{1}≥D_{1}；
Then d_{1}The estimation of (x, t)For：
Had by formula (10), (11)：
Definition mismatches interference observer Lyapunov Equation：
Again because of β_{1}≥D_{1}, then：
If there is a positive definite integral form V_{0}T () is met with lower inequality：
Then, V_{0}T () is in time t_{s}Equilibrium point is converged to inside, wherein
Wherein, 0,0 ＜ γ ＜ 1 of α ＞ 0, λ ＞；
Therefore, V_{1}T () will be in Finitetime convergence to equilibrium point, i.e. s_{1}To be zero in finite time, nowTo also receive
Zero is held back, and because of d_{1}(x, t) estimation difference
Then probabilistic estimation differenceAlso will be 0 in finite time；I.e. after finite time
Obtain mismatching interference observer：
Step 22, design matching interference observer：
Definition matching interference observer slidingmode surface s_{2}For：
s_{2}=z_{2}x_{3} (20)
Wherein, z_{2}To match dynamic in interference observer；
In formula (21), k_{2}、β_{2}、ε_{2}、p_{2}And q_{2}It is matching interference observer coefficient；Wherein p_{2}＜ q_{2}, and positive odd number is,
k_{2}、β_{2}、ε_{2}It is positive number, β_{2}≥D_{2}；Then d_{2}The estimation of (x, t)For：
Had by formula (21), (22)：
Definition matching interference observer Lyapunov Equation：
Again because of β_{2}＞ D_{2}, then have,
Therefore, V_{2}T () will be zero in finite time, i.e. s_{2}To be zero in finite time, nowZero will also be converged to again
Because of d_{2}(x, t) estimation difference
The estimation difference then disturbedAlso will be zero in finite time, i.e., after finite time
Obtain matching interference observer：
Step 3, design are based on the sliding mode controller for mismatching and matching interference observer, specific as follows：
Define Hydrauservo System position tracking error e_{0}, speed Tracking error e_{1}, acceleration tracking error e_{2}, plus accelerate
Degree tracking error e_{3}：
e_{0}(t)=x_{1}x_{d}(t) (27)
Wherein, x_{d}T () is system reference signal, x_{d}T () is that three ranks are continuous, and system reference position signalling x_{d}(t), it is
System reference speed signalSystem reference acceleration signalAnd system reference acceleration signalAll it is bounded；
Define sliding mode controller slidingmode surface s:
Wherein c_{1}、c_{2}、c_{3}Sliding mode controller parameter is, and is all higher than zero, and cause expression formula
It is Hurwitz, then has：
Obtaining sliding mode controller u is：
Wherein k is sign (s) gains, and k ＞ 0.
Step 4, stability is carried out with Lyapunov stability theory prove, obtain the globally asymptotically stable of system
As a result；It is specific as follows：
Step 41, by formula (33) substitute into formula (32) have：
Define sliding mode controller Lyapunov Equation：
Then have：
Then sliding mode controller slidingmode surface s will be zero in finite time；Now have：
Again because of s_{1}、s_{2}And finite time in be 0, if t_{1}For the moment that s is zero, t_{2}For s_{1}It is zero moment, t_{3}For s_{2}For
Zero moment, then there is t_{4}=max { t_{1},t_{2},t_{3}, through t_{4}Have after moment：
And because:
Then：
e_{2}(t)+c_{1}e_{1}(t)+c_{2}e_{0}(t)+c_{3}∫e_{0}(t) dt=d_{1}(t) (40)
I.e.：
Step 42, whenWhen：
Then have, when t → ∞ has：
Therefore e_{0}(t)=x_{1}x_{d}(t) the time tend to it is infinite under conditions of go to zero；
WhenWhen δ is a certain normal number：
Then have, when t → ∞ has：
Therefore e_{0}(t)=x_{1}x_{d}(t) the time tend to it is infinite under conditions of converge in Uniformly stable circle.
In summary, for Hydraulic Position Servo design matching and the sliding formwork control of mismatched uncertainty compensation
Device can make system obtain globally asymptotically stable result.Adjust observer coefficient k_{1}、β_{1}、ε_{1}、p_{1}、q_{1}、k_{2}、β_{2}、ε_{2}、p_{2}、q_{2}Can
So that the tracking error of observer goes to zero in finite time, gain c is adjusted_{1}、c_{2}、c_{3}, k can make the tracking error of system
The time tend to it is infinite under conditions of go to zero.The sliding formwork control that Hydraulic Position Servo is matched and mismatched uncertainty is compensated
Device principle schematic processed is as shown in Figure 3.
With reference to specific embodiment, the present invention will be further described.
Embodiment 1
With reference to Fig. 1～Fig. 3, it is the designed controller performance of examination, takes following parameter in simulations and electrohydraulic position is watched
Dress system is modeled：
Load rotating inertia m=40kgm^{2}, motor displacement A=2 × 10^{4}m^{3}/ rad, viscosity friction coefficient B=80Nm
S/rad, charge oil pressure P_{s}=7MP_{a}, return pressure P_{r}=0, fluid elastic modelling quantity β_{e}=2 × 10^{8}P_{a}, two chamber original volume V of motor_{01}
=V_{02}=1 × 10^{3}m^{3}, leadage coefficient C_{t}=9 × 10^{12}m^{3}/s/P_{a}, overall throughput gainPressure
Power dynamic modeling error q_{1}(t)=q_{2}(t)=6 × 10^{6}m^{3}Rad/s, outer load disturbance f (t)=200 [1exp ( 0.1t^{3})]
(N·m)。
The expectation instruction of given system is x_{1d}=sin (t) [1exp ( 0.01t^{3})](rad)。
Take following controller to compare：
Matching and the sliding mode controller of mismatched uncertainty compensation：Take mismatch interference observer parameter k_{1}=1000, β_{1}
=0.002, ε_{1}=0.05, p_{1}=3, q_{1}=5, match interference observer parameter k_{2}=1000, β_{2}=0.006, ε_{2}=0.05, p_{2}=
5, q_{2}=7, controller parameter c_{1}=24, c_{2}=192, c_{3}=512, k=2.
The sliding mode controller of matching uncertainties compensation：Matching interference observer parameter k_{2}=1000, β_{2}=0.006, ε_{2}=
0.05, p_{2}=5, q_{2}=7, controller parameter c_{1}=24, c_{2}=192, c_{3}=512, k=200.
The lower system of sliding mode controller effect of matching and mismatched uncertainty compensation exports tracking, device to expectation instruction
Tracking error is as shown in Figure 4, Figure 5；In Fig. 4, expectation instruction is almost overlapped with system curve of output；From Fig. 4 and Fig. 5,
With under the sliding mode controller effect compensated with mismatched uncertainty, the position of Hydrauservo System exports the tracking essence to instructing
Degree is very high, the amplitude about 1 × 10 of steady track error^{6}(rad)。
Fig. 6, Fig. 7 are the mismatching uncertains of the lower system of the sliding mode controller effect of matching and mismatched uncertainty compensation
Property observation curve and observation error change over curve, and in Fig. 6, mismatched uncertainty estimated value is truly mismatched with system
Uncertain curve is essentially coincided；Designed terminal sliding mode interference observer be can be seen that from Fig. 6, Fig. 7 to watch hydraulic position
The mismatched uncertainty of dress system estimates that very accurately the observation error of mismatched uncertainty is after the very short time
Converge to rapidly zero；
Fig. 8, Fig. 9 are the matching uncertainties of the lower system of the sliding mode controller effect of matching and mismatched uncertainty compensation
Observation curve and observation error change over curve, and in Fig. 8, matching uncertainties estimated value is not known with system true match
Linearity curve is essentially coincided；As can be seen that designed terminal sliding mode interference observer is to hydraulic position servo system from Fig. 8, Fig. 9
The matching uncertainties of system estimate that very accurately the observation error of matching uncertainties is received also rapid after the very short time
Hold back zero；
Figure 10, Figure 11 are the sliding mode controller of matching and mismatched uncertainty compensation and compensate without mismatched uncertainty
The tracking error of sliding mode controller change over curve and control input changes over curve；From fig. 10 it can be seen that
The tracking accuracy of the sliding mode controller with mismatching uncertain compensation is very high, steadystate error about 1 × 10^{6}(rad), and
Under sliding mode controller effect without mismatched uncertainty compensation, steady track error about 3 × 10^{5}(rad), meanwhile, by scheming
Understand, the transient state tracking error of the lower system of sliding mode controller effect without mismatched uncertainty compensation is also mismatched not than having
Definitiveness compensating controller it is big.
From Figure 11, Figure 12, the discontinuous term ratio of gains of the sliding mode controller with mismatching uncertain compensation is invariably
The sliding mode controller of matching uncertainties compensation is much smaller, and with less steadystate error.Therefore understand, with mismatch
The sliding mode controller of uncertain compensation largely reducing the shake of controller, and ensure that more accurate tracking accuracy.
The present invention has merged the thought of disturbanceobserver and compensation based on traditional sliding Mode Robust Control (SMC) method, for
Hydraulic Position Servo designs the sliding formwork control of the matching based on terminal sliding mode interference observer and mismatched uncertainty compensation
Method processed；The method dexterously observe the matching of Hydraulic Position Servo and mismatch not by design terminal sliding formwork interference observer
Definitiveness, and matching and mismatched uncertainty compensation are fallen in design sliding mode controller, significantly cut down sliding formwork and do not connect
Continuous item gain, while not using system acceleration information so that system exists concurrently with matching and mismatched uncertainty nonthread
Property obtain the steadystate behaviour of asymptotic tracking, enhance slidingmode control be used in Hydraulic Position Servo opposing matching and
Mismatched uncertainty and nonlinear ability, and obtain good tracking performance.
Claims (4)
1. the slidingmode control that a kind of uncertainty of Hydraulic Position Servo is compensated, it is characterised in that including following step
Suddenly：
Step 1, the mathematical model for setting up Hydraulic Position Servo；
Step 2, separately design mismatch and match interference observer；
Step 3, design are based on the sliding mode controller for mismatching and matching interference observer；
Step 4, according to Liapunov stability principle proof system asymptotically stable in the large；
Wherein, the mathematical model for setting up Hydraulic Position Servo described in step 1, specific as follows：
Step 11, Hydraulic Position Servo are the system of the fluid motordriven inertia load by servo valve control；According to
Newton's second law, the equation of motion of inertia load is：
In formula (1), m is inertia load parameter；P_{L}For two chamber pressure reduction of hydraulic motor；Discharge capacities of the A for hydraulic motor；B is viscous friction
Coefficient；For modeling error, including m, P_{L}, B nominal value and actual value between deviation and outer load disturbance；Y is
The displacement of inertia load；For the speed of inertia load,For the acceleration of inertia load；T is time variable；
Ignore the external leakage of hydraulic motor, the Pressure behaviour equation in two chamber of hydraulic motor is：
P in formula (2)_{1}And P_{2}The respectively pressure in two chamber of hydraulic motor,WithRespectively P_{1}And P_{2}Derivative；V_{1}=V_{01}+Ay,V_{2}
=V_{02} Ay, V_{1}And V_{2}The control volume in two chamber of hydraulic motor is represented respectively；V_{01}And V_{02}The respectively initial appearance in two chamber of hydraulic motor
Product；β_{e}For effective fluid elastic modelling quantity；C_{t}For internal leakage coefficient；q_{1}(t) and q_{2}T () is respectively P_{1}And P_{2}The modeling of dynamical equation is missed
Difference；Q_{1}And Q_{2}The respectively oil suction chamber flow and oil back chamber flow of hydraulic motor；Q_{1}And Q_{2}With servo valve displacement x_{v}Relation be：
In formula (3)s(x_{v}) definition be：
Wherein, k_{q}For flow gain, C_{d}Discharge coefficient；ω is valve element area gradient；ρ is fluid density；P_{s}For charge oil pressure, P_{r}For
Return pressure；Two cavity pressure of hydraulic motor meets 0 ＜ P_{r}＜ P_{1}＜ P_{s}, 0 ＜ P_{r}＜ P_{2}＜ P_{s},P_{L} ＜ ＜ P_{S}；
Servo valve of the Hydraulic Position Servo using altofrequency response, spool displacement are approximately proportional component i.e. with control input
x_{v}=k_{i}U, therefore formula (3) can be write as
K in formula (5)_{t}=k_{q}k_{i}Represent total flow gain, k_{i}For servo valve gain, u is Hydraulic Position Servo input,
Step 12, definition status variable：Then the state equation of system is：
System physical parameter m, B, β in formula (6)_{e}、k_{t}、V_{01}、V_{02}And C_{t}It is nominal value in the design of observer and controller, its
Deviation between actual value is concentrated and is placed in nonmodeled terms, is d (x, t) in the second channel, is q in third channel
(t)；Wherein, d (x, t) is the mismatched uncertainty of system, including outer load disturbance, does not model friction and Unmarried pregnancy；q
T () is the uncertainty of the modeling error of Pressure behaviour, i.e. system matches；Wherein：
For simplified system state equation, definition：
Because  P_{L} ＜ ＜ P_{S}, then g (x) ≠ 0；Second channel mismatched uncertainty d_{1}The matching of (x, t) and third channel is not true
Qualitative d_{2}(x, t) is all bounded, i.e.,：
d_{1}(x,t)≤D_{1},d_{2}(x,t)≤D_{2}
D in formula_{1}、D_{2}Respectively  d_{1}(x, t)  and  d_{2}(x, t)  the upper bound, is all known positive number, and d_{1}(x, t) first derivative is deposited
；Then Hydraulic Position Servo model is
2. the slidingmode control that the uncertainty of Hydraulic Position Servo according to claim 1 is compensated, its feature
It is that mismatch is separately designed described in step 2 and interference observer is matched, step is as follows：
Step 21, design mismatch interference observer：
Definition mismatches interference observer slidingmode surface s_{1}For：
s_{1}=z_{1}x_{2} (10)
Wherein, z_{1}To mismatch dynamic in interference observer；
In formula (11), k_{1}、β_{1}、ε_{1}、p_{1}And q_{1}It is mismatch interference observer coefficient；p_{1}＜ q_{1}, and positive odd number is, k_{1}、β_{1}、
ε_{1}It is positive number, β_{1}≥D_{1}；
Then d_{1}The estimation of (x, t)For：
Had by formula (10), (11)：
Definition mismatches interference observer Lyapunov Equation：
Again because of β_{1}≥D_{1}, then：
If there is a positive definite integral form V_{0}T () is met with lower inequality：
Then, V_{0}T () is in time t_{s}Equilibrium point is converged to inside, wherein
Wherein, 0,0 ＜ γ ＜ 1 of α ＞ 0, λ ＞；
Therefore, V_{1}T () will be in Finitetime convergence to equilibrium point, i.e. s_{1}To be zero in finite time, nowAlso will convergence
To zero, and because of d_{1}(x, t) estimation difference
Then probabilistic estimation differenceAlso will be 0 in finite time；I.e. after finite time
Obtain mismatching interference observer：
Step 22, design matching interference observer：
Definition matching interference observer slidingmode surface s_{2}For：
s_{2}=z_{2}x_{3} (20)
Wherein, z_{2}To match dynamic in interference observer；
In formula (21), k_{2}、β_{2}、ε_{2}、p_{2}And q_{2}It is matching interference observer coefficient；Wherein p_{2}＜ q_{2}, and positive odd number is, k_{2}、
β_{2}、ε_{2}It is positive number, β_{2}≥D_{2}；Then d_{2}The estimation of (x, t)For：
Had by formula (21), (22)：
Definition matching interference observer Lyapunov Equation：
Again because of β_{2}＞ D_{2}, then have,
Therefore, V_{2}T () will be zero in finite time, i.e. s_{2}To be zero in finite time, nowZero will also be converged to again because of d_{2}
(x, t) estimation difference
The estimation difference then disturbedAlso will be zero in finite time, i.e., after finite time
Obtain matching interference observer：
3. the slidingmode control that the uncertainty of Hydraulic Position Servo according to claim 2 is compensated, its feature
It is that the design described in step 3 is based on the sliding mode controller for mismatching and matching interference observer, specific as follows：
Define Hydrauservo System position tracking error e_{0}, speed Tracking error e_{1}, acceleration tracking error e_{2}, acceleration with
Track error e_{3}：
e_{0}(t)=x_{1}x_{d}(t) (27)
Wherein, x_{d}T () is system reference signal, x_{d}T () is that three ranks are continuous, and system reference position signalling x_{d}T (), system are joined
Examine rate signalSystem reference acceleration signalAnd system reference acceleration signalAll it is bounded；
Define sliding mode controller slidingmode surface s:
Wherein c_{1}、c_{2}、c_{3}Sliding mode controller parameter is, and is all higher than zero, and cause expression formulaIt is
Hurwitz's, then have：
Obtaining sliding mode controller u is：
Wherein k is sign (s) gains, and k ＞ 0.
4. the slidingmode control that the uncertainty of Hydraulic Position Servo according to claim 3 is compensated, its feature
It is, it is according to Liapunov stability principle proof system asymptotically stable in the large described in step 4, specific as follows：
Step 41, by formula (33) substitute into formula (32) have：
Define sliding mode controller Lyapunov Equation：
Then have：
Then sliding mode controller slidingmode surface s will be zero in finite time；Now have：
Again because of s_{1}、s_{2}And finite time in be 0, if t_{1}For the moment that s is zero, t_{2}For s_{1}It is zero moment, t_{3}For s_{2}It is zero
Moment, then there is t_{4}=max { t_{1},t_{2},t_{3}, through t_{4}Have after moment：
And because：
Then：
e_{2}(t)+c_{1}e_{1}(t)+c_{2}e_{0}(t)+c_{3}∫e_{0}(t) dt=d_{1}(t) (40)
I.e.：
Step 42, whenWhen：
Then have, when t → ∞ has：
Therefore e_{0}(t)=x_{1}x_{d}(t) the time tend to it is infinite under conditions of go to zero；
WhenWhen δ is positive number：
Then have, when t → ∞ has：
Therefore e_{0}(t)=x_{1}x_{d}(t) the time tend to it is infinite under conditions of converge in Uniformly stable circle.
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