CN110456646A - Jumbolter drill boom pivot angle adaptive sliding-mode observer design method based on EKF - Google Patents
Jumbolter drill boom pivot angle adaptive sliding-mode observer design method based on EKF Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B15/00—Supports for the drilling machine, e.g. derricks or masts
- E21B15/003—Supports for the drilling machine, e.g. derricks or masts adapted to be moved on their substructure, e.g. with skidding means; adapted to drill a plurality of wells
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- E—FIXED CONSTRUCTIONS
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- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B44/00—Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
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- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract
The present invention is directed to valve control jumbolter drill boom electrohydraulic system, it is proposed a kind of jumbolter drill boom pivot angle adaptive sliding-mode observer design method based on EKF, for solving many influence factors present in electrohydraulic servo system, such as valve dead-time voltage, Parameter uncertainties, and unknown load disturbance, and accurately track drill boom setting position.By introducing smooth dead zone inversion model, dead zone advance compensator is designed, to weaken adverse effect of the dead zone to control performance.Suitable sliding formwork adaptive law is designed, is influenced with estimating unknown deadzone parameter and eliminating load disturbance.In addition, introducing EKF estimating system noise, and drill boom position is predicted, to reduce sliding formwork buffeting.Based on AMESim and MATLAB associative simulation the result shows that: designed controller can effective compensation dead time effect, and eliminate load disturbance influence, while system can be made accurately to track drill boom pivot angle setting position, demonstrate the validity of proposed control strategy.
Description
Technical field
The present invention relates to a liquid servo techniques fields, and in particular to a kind of jumbolter drill boom pivot angle based on EKF is adaptive
Answer System with Sliding Mode Controller design method.
Background technique
Quickly, implementing tunnelling safe and efficiently is to influence the important link of coal mining efficiency and production safety.It is logical
Often, full-mechanized roadway is in coal seam or half coal seam, and roadway surrounding rock primary stress is higher, and vulnerable to adjacent tunnel mining induced stress etc.
Disturbing influence may cause tunnel collapsing, reduce if anchor pole/cable bolting timely and effectively cannot be carried out to tunnel sky top
Drivage efficiency, or even there is casualties.The Anchor Care network that anchor pole/cable bolting validity depends on tunnel design initial stage is whole
The accurate positioning and accurate drilling control of the design of body structure and jumbolter to designed anchor bar/anchor cable optimal location.For
Meet the anchor bar/anchor cable installation requirements of different location, the drilling control of jumbolter includes the horizontal position along drift section direction
Move control, drill boom swinging angle control and drilling depth control.Only the drilling movement under above three freedom degree, ability are completed in collaboration
Realize effective Anchor Care to entire drift section.Wherein, the rapidity and accuracy of jumbolter drill boom swinging angle control, directly certainly
Determine two to help and shoulder nest anchor pole/cable bolting stability and validity.Traditional jumbolter drill boom swinging angle control, completely according to
Rely in rig personnel, rotates angle according to its experience estimation drill boom, realization is positioned manually, and is easy to produce biggish positioning and misses
Difference, positioning accuracy are low.Therefore, advanced, effective controller is designed, for realizing valve control hydraulic jumbolter drill boom rotation system
The automatic control of hydraulic jumbolter drill boom pivot angle is very necessary in system.
In view of hydraulic jumbolter motion control is to be realized by electro-hydraulic proportional valve as power mechanism driving drill boom deflection
, so drill boom rotary system substantially belongs to electrohydraulic servo system.In addition, it is capable of providing biggish torque capability, so that
Related research result based on electrohydraulic servo system has been widely used in the fields such as robot, aerospace, engineering machinery.
However, electrohydraulic servo system in the prevalence of intrinsic nonlinearity characteristic, Parameter uncertainties and unknown load disturbance at
To influence an important factor for high-precision quasi-moving of hydraulic actuator controls.Therefore, it is existing for eliminating or improving these challenges to become
The research emphasis in stage.
Nonlinear characteristic existing for electrohydraulic servo system is mainly reflected on valve dead zone, this is because in electro-hydraulic proportional valve
Often there is biggish amount of lap in middle position, to generate zero-bit dead zone.It, can shadow in position closed loop if dead zone is excessive
The dynamic response and steady-state performance for ringing control system can also generate apparent lag in practical operation.In order to obtain preferably
Control performance is had important practical significance using reasonable dead-time Compensation Technology.In addition, deadzone parameter is usually unknown, and difficult
With detection, this uncertainty increases dead area compensation difficulty.
Compensating Control based on adaptive law estimation deadzone parameter is the effective ways that deadband eliminating influences, especially
For complicated nonlinear system.Document (Hu C, Yao B, Wang Q.Performance-oriented adaptive
robust control of a class of nonlinear systems preceded by unknown dead-zone
with comparative experimental results[J].IEEE/ASME Transactions on
Mechatronics, 2013,18 (1): 178-189) a kind of nonlinear autoregressive method is proposed, not by online updating
Dead zone reverse link parameter is known to compensate dead time effect, obtains preferable control effect.Document (Deng H, Luo J, Duan X, et
al.Adaptive inverse control for gripper rotating system in heavy-duty
manipulators with unknown dead-zones[J].IEEE Transactions on Industrial
Electronics, 2017,64 (10): 7952-7961) a kind of linear controller based on dead zone inversion model is designed, eliminate weight
The dead zone of type manipulator paw rotary system influences.But using linear control method may cause system output with actually it is defeated
There are deviations between out.It is worth noting that, the dead zone inversion model established in both of the aforesaid document be all it is discontinuous, in reality
In application process, these discontinuous dead zone inversion models will lead to system control input and generate buffeting, for precise flange
For, it is unstable to even result in system.In order to solve this discontinuous problem, document (Zhou J, Wen C, Zhang
Y.Adaptive output control of nonlinear systems with uncertain dead-zone
Nonlinearity [J] .IEEE Transactions on Automatic Control, 2006,51 (3): 504-511) structure
A kind of smooth dead zone inversion model is made, while being the adaptive controller of the Nonlinear System Design with unknown dead zone, this method
Not only solve the influence of dead zone generation, and the buffeting problem for effectively avoiding system from being likely to occur.
Other than Parameter uncertainties and non-linear factor mentioned above, this chapter also contemplates the presence of drill boom rotary system
The influence factors such as unknown load disturbance.These disturbance factors make drill boom swinging angle control system more complicated, control product
Matter is severely impacted, and is difficult to set up its effective mathematical model.Therefore, jumbolter is extremely difficult to using Traditional control strategy
The accurate positioning of drill boom, which controls, to be required.Sliding formwork control because it is of less demanding to model accuracy, to Parameter Perturbation and external disturbance not
Sensitivity, and have many advantages, such as that system response is fast, simple without on-line identification and physics realization, it is widely used to a variety of fields
It closes.Document (Kang H S, Lee Y, Hyun C H, et al.Design of sliding-mode control based on
fuzzy disturbance observer for minimization of switching gain and chattering
[J] .Soft Computing, 2015,19 (4): 851-858) propose a kind of sliding-mode control with interference observer, effectively
Influence of the interference to system is reduced, while weakening sliding formwork buffeting.Document (Yuan X, Chen Z, Yuan Y, et a1.Design
of fuzzy sliding mode controller for hydraulic turbine regulating system via
Input state feedback linearization method [J] .Energy, 2015,93 (1): 173-187) design one
Kind Fuzzy Sliding Model Controller controls the controller application in Adaptive System of Water-Turbine Engine, to internal system disturbance and external noise
With higher robustness.Document (Cerman O,PAdaptive fuzzy sliding mode control for
Electro-hydraulic servo mechanism [J] .Expert Systems with Applications, 2012,39
(11): 10269-10277) for a kind of Continuous Nonlinear Systems with unknown dynamic and Bounded Perturbations, one kind is proposed certainly
Modified fuzzy sliding mode controlling method, effective compensation interference are adapted to, and significantly reduces the buffeting problem of classical sliding formwork control.Document (Palli
G, Strano S, Terzo M.Sliding-mode observers for state and disturbance
Estimation in electro-hydraulic systems [J] .Control Engineering Practice, 2018,
74 (5): 58-70) a kind of sliding mode observer is designed, outer interference and influence of the noise to electrohydraulic system are substantially reduced, is improved simultaneously
Dynamic/static properties of control system.
In addition, in the controls, the process noise (random disturbances in input signal) and measurement noise being often accompanied by (are surveyed
The error generated during amount) it also will affect the dynamic property of control system, and aggravate system chatter, give Accurate Position Control band
Difficulty is carried out.In order to overcome these unfavorable factors, position prediction is a kind of effective ways.Kalman filtering is pre- as a kind of position
The linear filtering algorithm of survey can observe unknown quantity using known measurements in particular time range, and to the shape of unknown quantity
State makes optimal estimation, and system is made to have accurate tracking performance.For the filtering problem of nonlinear system, EKF filter is generallyd use
Wave technology linearizes nonlinear system model, in turn, completes filter tracking using Kalman filtering algorithm.
Summary of the invention
Goal of the invention: the purpose of the present invention is to provide a kind of jumbolter drill boom pivot angle adaptive sliding mode based on EKF
Control System Design method, it is intended to it is not true in the prevalence of intrinsic nonlinearity characteristic, parameter to solve electrohydraulic servo system
The technical issues of influence factors such as fixed and unknown load disturbance, make system that there is accurate tracking performance and higher robustness.
To realize above-mentioned target, the technical solution adopted by the present invention is that:
Jumbolter drill boom pivot angle adaptive sliding-mode observer design method based on EKF, comprising steps of
(1) whole mathematical model of valve control hydraulic jumbolter drill boom rotary system is constructed:
Wherein,θLIndicate that hydraulic jumbolter drill boom rotates angle,Indicate that drilling machine bores
The rotation speed of arm, PLIndicate the load pressure of bearing shaft；DmFor hydraulic motor displacement, JtFor equivalent turn of hydraulic motor axis always
Dynamic inertia, BtFor the total equivalent viscous damping coefficient of hydraulic motor axis, GtFor the total equivalent stiffness of hydraulic motor axis, TtFor bearing shaft folding
Calculate the equivalent outer loading moment of hydraulic motor axis, ΔfIndicate the internal disturbance as caused by Parameter uncertainties and unmodeled friction etc.
The uncertain factor of composition, CtmFor total leadage coefficient of hydraulic motor, VmIt indicates comprising connecting pipe, hydraulic motor and electro-hydraulic
Including proportioning valve into/controllable the total measurement (volume) of oil back chamber, βeFor the oil liquid effective volume elasticity modulus of hydraulic system, n is transmission ratio,
CdFor the discharge coefficient of electro-hydraulic proportional valve valve port, ω is the area gradient of electro-hydraulic proportional valve, xv, it is the spool position of electro-hydraulic proportional valve
It moves, ρ is oil liquid density, PSExpression system charge oil pressure, u are the input control voltage of electro-hydraulic proportional valve, and m represents valve dead zone two sides
Gradient, sign () be sign function, is defined as:
The expression formula of δ (u) are as follows:
Wherein, δlAnd δrThe respectively threshold value of electro-hydraulic proportional valve dead zone two sides breakpoint, δlAnd δrFor determining that dead zone is wide
Degree；
(2) for the mathematical model of step (1) building, with the input control voltage and jumbolter drill boom of electro-hydraulic proportional valve
Pivot angle is quantity of state, designs extended Kalman filter to predict the jumbolter drill boom pivot angle of subsequent timeIt is rightWith work as
Preceding target pivot angle θdIt asks poor, obtains jumbolter drill boom pivot angle error:
(3) the spreading kalman filter that the mathematical model for step (1) building and extended Kalman filter predict
Wave device constructs adaptive sliding mold and dead-zone compensator；
The sliding formwork control ratio of adaptive sliding mold are as follows:
Adaptive law are as follows:
Wherein, uasmcFor the output signal of adaptive sliding mold, k1、k2For coefficient, k1∈R+, k2∈R+,For e's
Single order, second dervative,For θdThree order derivatives；G (x)=θ4R (x),θ1、θ2、θ3、θ4
For coefficient, The Reaching Law parameter that K is positive, s are switching
Function, μ indicate handoff factor, γ1, γ2It is controller intrinsic parameter to be designed and is positive number；sμFor saturation function；φ=
[φ(xv), 1- φ (xv)]T,χ () is unit jump function,MeetFor deadzone parameter vector,For the estimated value of deadzone parameter vector,ForOne
Order derivative；
The output signal of dead-zone compensator are as follows:Respectively δrWith
δlEstimated value；
(4) by the output signal u of adaptive sliding moldasmcWith the output signal u of dead-zone compensatorcompAddition obtains electro-hydraulic
The input control voltage u of proportioning valve.
Further, the specific steps of the whole mathematical model of the building valve control hydraulic jumbolter drill boom rotary system
Are as follows:
Step (2-1) converts the various loads on bearing shaft onto motor drive shaft, the inertia load torque after building is equivalent
Equilibrium equation:
Wherein, load pressure PL=P1-P2, P1、P2Respectively motor is into, back oil cavity pressure.
The flow continuity equation of step (2-2) building Electro-hydraulic Proportional Control hydraulic motor:
Wherein, the load of electro-hydraulic proportional valve controls flow QL=(Q1+Q2)/2, Q1、Q2Respectively indicate hydraulic motor into, return
Oil stream amount；
The load that step (2-3) constructs electro-hydraulic proportional valve controls flow QL, load control pressure PLWith electric-hydraulic proportion valve core
Displacement xvRelational expression between three:
Construct the spool displacement mathematical model of the Dead Zone containing electro-hydraulic proportional valve:
Then spool displacement mathematical model is modified as follow form:
xv=N (u)=m (u- δ (u))
Step (2-4) definition status variableIntegrate inertia load torque balance side
Journey, the flow continuity equation of liquid proportional Valve-control hydraulic motor and spool displacement mathematical model obtain the rotation of valve control jumbolter drill boom
Transfer from one department to another the mathematical model of system:
Further, the extended Kalman filter design method comprising steps of
Step (3-1) constructs the state equation of the valve control hydraulic jumbolter drill boom rotary system mathematical model:
In formula, f (x (t)) is systematic observation matrix, and B (t) is control matrix, and G (t) is disturbance, and h (x (t)) is output square
Battle array；Wherein,
H (x (t))=[x1, 0,0]T
Step (3-2) provides the discrete time of the state equation in the case where considering process noise and measurement noise
State space equation:
In formula, w (k), v (k) are incoherent zero mean Gaussian white noise each other, the covariance matrix of process noise w (k)
For Q, the covariance matrix for measuring noise v (k) is R, and meets E (w (k))=0, E (v (k))=0；
Step (3-3) is obtained after discrete-time state-space equation local linearization:
In formula, H (k) is observing matrix,A (k) is state-transition matrix, A (k)
Expression formula are as follows:
A (k)=I+FkTs
Wherein, I is unit matrix, TsFor the sampling time, F (k) is gradient matrix:
Step (3-4) provides the time update equation and state renewal equation of discrete extended Kalman filter；Wherein,
Time update equation includes:
Prior state estimation:
Prior estimate error covariance matrix: P (k | k-1)=A (k | k-1) P (k-1) AT(k|k-1)+G(k-1)Q(k-1)
GT(k-1)
State renewal equation includes:
Kalman gain: K (k)=P (k | k-1) HT(k)(H(k)P(k|k-1)HT(k)+R(k))-1
T (k) moment optimal estimation:
Evaluated error covariance matrix after update: P (k)=(I-K (k) H (k)) P (k | k-1)
Wherein,For the posteriority state estimation at t (k-1) moment, P (k-1) is t (k-1) moment posteriority state mistake
Poor covariance matrix；
The initialization condition of system are as follows:
In formula,For the estimated value of t (0) moment system mode, P (0) is that the evaluated error of t (0) moment system mode is assisted
Variance matrix.
Further, it constructs adaptive sliding mold and the specific steps of dead-zone compensator includes:
Step (4-1) introduces smooth dead zone inverse function in control input signal u, to avoid the buffeting of u bring: enabling N1
() is expressed as smooth dead zone inverse function, then:
Wherein,For smooth continuous indicator function, ε is greater than zero constant；The effect of φ ()
It is the chattering phenomenon in order to avoid being likely to occur in the control of drill boom rotary system；
Deadzone parameter vector is expressed as by step (4-2)It enablesIndicate δrEstimated value and estimation miss
Difference enablesIndicate deadzone parameter δlEstimated value and evaluated error, then the estimated value table of deadzone parameter vector is shown asThe expression formula of u is rewritten into:
In formula, dead-zone compensator output signal is designed to:
Wherein, φ=[φ (xv), 1- φ (xv)]T；
Step (4-3) enablesEvaluated error beObtain the output signal and reality of adaptive sliding mode controller
Relational expression between the displacement of border proportional valve spool, it may be assumed that
In formula,
Wherein,
Wherein, χ () is unit jump function,Meet
Step (4-4) provides the dynamic characteristic of valve control hydraulic jumbolter drill boom rotary system by Third-order differential equations:
According to system pivot angle error e, switching function is designed:
In order to limit the variation of s, the concept in boundary layer is introduced, i.e., s is defined using saturation functionμ:
sμ=s- μ sat (s/ μ)
In formula,
Sliding formwork control ratio is designed as following form by the Reaching Law parameter for enabling K be positive:
Adaptive law is designed are as follows:
The utility model has the advantages that unreliable, Anchor Care low efficiency and valve control drill boom rotary system are deposited for current tunnel Anchor Care mode
In many adverse effect factors, a kind of Adaptive Sliding Mode Position control method based on EKF is proposed.Based on AMESim and MATLAB
Associative simulation the experimental results showed that, designed controller can effective compensation dead time effect, and eliminate load disturbance influence, together
When can accurately track drill boom pivot angle setting position.For this research contents, also it is other types drill boom swinging angle control, provides
New control strategy and research method has far reaching significance to the intelligent development of drill control.
Detailed description of the invention
Fig. 1 is valve control hydraulic jumbolter drill boom rotating mechanism schematic diagram；
Fig. 2 is valve control hydraulic jumbolter drill boom swinging angle control block diagram；
Fig. 3 is the system combined analogous diagram of valve control hydraulic jumbolter drill boom swinging angle control；
Fig. 4 is different controller response curves under step signal
Fig. 5 is different controller tracking error curves under step signal
Wherein: 1, asynchronous machine；2, constant displacement pump；3, fuel tank；4, safety valve；5, oil filter；6, electro-hydraulic proportion reversing valve；7,
Hydraulic motor；8, turbine and worm decelerator.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
It is as shown in Figure 1 valve control hydraulic jumbolter drill boom rotary system, mainly by asynchronous machine 1, constant displacement pump 2, fuel tank
3, safety valve 4, oil filter 5, electro-hydraulic proportion reversing valve 6, hydraulic motor 7 and turbine and worm decelerator 8 form.Asynchronous machine 1
It drives constant displacement pump 2 to rotate, exports the high pressure oil of certain flow, through electro-hydraulic proportion reversing valve 6, drive 7 positive/negative turns of hydraulic motor,
And turbine and worm decelerator 8 is driven to move, it is final to realize drill boom deflection.It is big by the opening for changing electro-hydraulic proportion reversing valve 6
It is small, revolving speed is exported to control hydraulic motor 7, and then control the output revolving speed of turbine and worm decelerator 8, makes drill boom in worm gear snail
Under the action of bar deceleration mechanism 8, anchor bar/anchor cable pre-installed position is accurately swung to.
The technical solution adopted by the present invention is that: a kind of jumbolter drill boom pivot angle adaptive sliding-mode observer side based on EKF
Method, comprising the following steps:
Step 1: establishing valve control hydraulic jumbolter drill boom rotary system.
Step 2: the valve control hydraulic jumbolter drill boom rotary system established in conjunction with step 1 is based on valve control hydraulic anchor
Drilling machine drill boom rotary system working principle and restriction modeling conditions, construct the mathematical model of each key link, and integrate and obtain valve
Control the whole mathematical model of hydraulic jumbolter drill boom rotary system.Firstly, being bored according to the valve control hydraulic jumbolter established
Arm rotary system is based on valve control hydraulic jumbolter drill boom rotary system working principle, and it is as follows to limit modeling conditions:
(1) ignore the pressure loss in piping between electro-hydraulic proportion reversing valve and hydraulic motor；
(2) the leakage fluidised form for assuming electro-hydraulic proportion reversing valve and hydraulic motor is laminar flow, ignores pipeline leakage loss；
(3) assume that oil liquid bulk modulus and oil liquid density are constant, and be constant；
(4) assume hydraulic motor into pressure is equal everywhere in/oil back chamber.
Secondly, the whole mathematical model of building valve control hydraulic jumbolter drill boom rotary system.
Step 2-1, D is enabledmFor hydraulic motor displacement, JtFor the total equivalent moment of inertia of hydraulic motor axis, BtFor hydraulic motor
The total equivalent viscous damping coefficient of axis, GtFor the total equivalent stiffness of hydraulic motor axis, TtIt is equivalent outer to hydraulic motor axis for bearing shaft conversion
Loading moment, ΔfIndicate the uncertain factor that the internal disturbance caused by Parameter uncertainties and unmodeled friction etc. form.It will
Various loads conversion on bearing shaft on hydraulic motor axis, then it is equivalent after inertia load torque balance equation can be expressed as
Wherein, TmIt is that various load conversions turn to the equivalent inertia load of hydraulic motor axis on hydraulic motor axis on bearing shaft
Square；Load pressure PL=P1-P2, wherein P1, P2Respectively motor is into, back oil cavity pressure, θLIndicate the rotation of hydraulic jumbolter drill boom
Gyration,WithRespectively indicate the rotation speed and rotary acceleration of drilling machine drill boom.
Step 2-2, C is enabledtmFor total leadage coefficient of hydraulic motor, VmIt indicates to exist comprising connecting pipe, hydraulic motor and valve
It is interior into the/controllable total measurement (volume) of oil back chamber, βeFor the oil liquid effective volume elasticity modulus of hydraulic system, n is transmission ratio, then proportioning valve
The flow continuity equation of draining pressure motor it can be said that
Wherein, the load of proportioning valve controls flow QL=(Q1+Q2)/2。
Step 2-3, C is enableddFor the discharge coefficient of valve port, ω is the area gradient of proportioning valve, xvFor the spool position of proportioning valve
It moves, ρ is oil liquid density, then the load of valve controls flow QL, load control pressure PLWith spool displacement xvRelationship between three,
It can be described as follows:
Wherein, PSExpression system charge oil pressure, sign () are sign function, be may be defined as:
The input control voltage for enabling electro-hydraulic proportional valve is u, then the spool displacement mathematical model of the Dead Zone containing valve can indicate
Are as follows:
Formula (5) can be rewritten into following form:
xv=N (u)=m (u- δ (u)) (6)
In formula,
Wherein, N () represents valve dead-time voltage function, and m represents the gradient of valve dead zone two sides, and δ (u) represents dead zone ginseng
Numerical value, δlAnd δrThe size of the respectively threshold value of proportioning valve dead zone two sides breakpoint, value determines skip distance.Under normal conditions,
Parameter δl, δrValue be unknown and bounded, have δlmin≤δl≤δlmax0,0 < δ of <rmin≤δr≤δrmax。
Step 2-4, definition status variableIntegration obtains valve control jumbolter drill boom
The mathematical model of rotary system is as follows:
Step 3: according to the whole mathematical model of valve control hydraulic jumbolter drill boom rotary system and swinging angle control requirement, if
Count a kind of hydraulic jumbolter drill boom pivot angle adaptive sliding mode controller based on EKF.Specific design process is as follows:
Step 3-1, using dead zone inverse transformation, control input signal u bring is effectively avoided to buffet.Enable N1() is expressed as
Smooth dead zone inverse function, then:
Wherein,For smooth continuous indicator function, ε is greater than zero constant.The effect of φ ()
It is the chattering phenomenon in order to avoid being likely to occur in the control of drill boom rotary system.
To be analyzed convenient for Dead Zone, deadzone parameter vector can be expressed asDue toIt is unknown, so, extremely
Zone properties can only be expressed by parameter Estimation.It enablesWithRespectively represent deadzone parameter δr, δlEstimated value and estimation miss
Difference, then the estimated value table of deadzone parameter vector is shown asTherefore formula (6) can be rewritten into:
In formula, dead-zone compensator output signal is designed to:
Wherein, φ=[φ (xv), 1- φ (xv)]T。
It enablesEvaluated error beConvolution (5)~formula (11), available adaptive sliding mode controller
Relational expression between output signal and actual ratio spool displacement, it may be assumed that
In formula,
Wherein,
Wherein, χ () is unit jump function, againMeetTherefore, it is easy to get | sat (uasmc)|≤1。
Step 3-2, the dynamic characteristic for the hydraulic jumbolter drill boom rotary system that convolution (8) and formula (12) are derived by
Third-order differential equations indicate:
In formula,G (x)=θ4R(x).Wherein, coefficient Bearing shaft conversion is represented to hydraulic motor axis
It is integrally disturbed caused by equivalent outer loading moment and unmodeled friction and the unknown, and F has upper rank.
Note pivot angle given value is θd, define system pivot angle error are as follows:
Then design switching function:
In formula, k1∈R+, k2∈R+。
In order to limit the variation of s, the concept in boundary layer is introduced, i.e., s is defined using saturation functionμ:
su=s- μ sat (s/ μ) (19)
In formula,
Sliding formwork control ratio is designed as following form by the Reaching Law parameter for enabling K be positive:
Adaptive law is designed are as follows:
Theorem: for the drill boom rotary system (8) with sliding-mode surface, given control law (21) and adaptive law (22),
(23), met by the system tracking error e that (17) defineIt proves:
suTime differential can be write as:
The sliding formwork control ratio formula (21) of design is substituted into formula (25), thenIt can turn to:
Choose liapunov function:
In formula, γ1, γ2It is controller intrinsic parameter to be designed and is positive number.
Assuming that whole disturbance term variation is slowly, takeAfter V derivation,Expression formula:
It is obtained after formula (22) and (23) are substituted into formula (28):
Above-mentioned sliding formwork control is shown with existence and accessibility, it was demonstrated that system can be realized sliding formwork movement,
It can guarantee the stability of swash angle position control.
Step 3-3, noise can be not only filtered using EKF, current state and position can also be estimated, and
The position and state of subsequent time are predicted.
For formula (8), drill boom rotates nonlinear system, and general equation of state is writeable are as follows:
In formula, f (x (t)) is systematic observation matrix, and B (t) is control matrix, and G (t) is disturbance, and h (x (t)) is output square
Battle array.Wherein,
H (x (t))=[x1, 0,0]T(34) since extended Kalman filter is linear based on Kind of Nonlinear Dynamical System
Discretization.In the case where considering process noise and measurement noise, drill boom rotates Nonlinear Systems ' Discrete time state space
Equation is writeable are as follows:
In formula, w (k), v (k) are incoherent zero mean Gaussian white noise each other, the covariance matrix of process noise w (k)
For Q, the covariance matrix for measuring noise v (k) is R, and meets E (w (k))=0, E (v (k))=0.
After formula (35) local linearization,
In formula, state-transition matrix A (k)=I+F (k) Ts, I is unit matrix, TsFor sampling time, the gradient square of system
Battle arrayWherein coefficient
Observing matrix
The position exported is rotated in order to which drill boom is effectively estimated, is needed using following two step:
(1) time update equation of discrete extended Kalman filter are as follows:
Prior state estimation:
Prior estimate error covariance matrix: P (k | k-1)=A (k | k-1) P (k-1) AT(k|k-1)+G(k-1)Q(k-1)
GT(k-1)
(2) the state renewal equation of discrete extended Kalman filter are as follows:
Kalman gain: K (k)=P (k | k-1) HT(k)(H(k)P(k|k-1)HT(k)+R(k))-1
T (k) moment optimal estimation:
Evaluated error covariance matrix after update: P (k)=(I-K (k) H (k)) P (k | k-1)
Wherein,For the posteriority state estimation at t (k-1) moment, P (k-1) is t (k-1) moment posteriority state mistake
Poor covariance matrix.
The optimal estimation value of etching system when going out t (k) for recursion, needs the initialization condition of given system:
In formula,For the estimated value of t (0) moment system mode, P (0) is that the evaluated error of t (0) moment system mode is assisted
Variance matrix.
Step 4: for valve control hydraulic jumbolter drill boom rotary system shown in Fig. 1, the connection based on AMESim and MATLAB
It closes Simulation Experimental Platform and realizes designed controller, verify dynamic/static cost control performance of designed controller.
Embodiment
Hydraulic jumbolter drill boom pivot angle Sliding Mode Adaptive Control system block diagram based on EKF filter, as shown in Figure 2.
Associative simulation experiment porch based on AMESim and MATLAB realizes designed controller, wherein controller is in Matlab2012a
In realized by s function；In addition, building the physics mould for completing valve control jumbolter drill boom electrohydraulic system in AMESim R13
Type；And realized by the simulink_cosim interface in AMESim R13 and transmitted with the signal of controller, as shown in Figure 3.Valve
Device core parameter value in drilling machine drill boom rotary system is controlled, as shown in table 1.
1 valve control drill boom rotary system relevant parameter of table and its value
Based on the controller of this patent design, there is related parameter values in control system: δlmin=-1V, δrmax=1V, ε=
0.1, μ=0.05, Ts=0.01s.For dynamic/static cost control performance of access control device, consider to join in dead-time voltage, dead zone
It under unknown and load disturbance the collective effect of number, is tested using step signal as reference value, and flat in associative simulation
ASMC+EKF control on platform designed by comparative analysis PID+EKF control, ASMC+EKF control and this chapter with dead area compensation
Make three kinds of methods.Choose PID controller parameter are as follows: Kp=2.53, Ki=0.08, Kd=0.003；ASMC controller parameter: k1=
4.78 k2=3.81, K=85, γ2=5；ASMC controller parameter with dead area compensation: k1=4.78, k2=3.81, K=85,
γ1=8, γ2=5；EKF controller parameter: Q=10, R=10.Wherein, the ASMC+EKF control of this patent institute belt dead area compensation
Device processed, as shown in Figure 4 under step signal under step signal shown in different controller control response curves and Fig. 5 different controllers with
For track error curve it is found that when load disturbance changes to 52Nm by 2Nm within the 9th second, PID+EKF controller is more quick to disturbing
Sense, and the ASMC+EKF controller of ASMC+EKF controller and no dead-time compensation with dead area compensation can effectively eliminate load and disturb
Dynamic influence, i.e., it is insensitive to shock wave.In addition, other two control method is compared, the ASMC+EKF control with dead area compensation
Device regulating time is shorter, and steady-state error is smaller.Therefore, the drill boom pivot angle Adaptive Sliding Mode Position controller based on EKF can have
Effect overcomes the unfavorable factors such as dead time effect, load disturbance, enables the system to accurately track drill boom setting pivot angle, to realize tunnel
Efficient Anchor Care provides reference method.
The above is only a preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (4)
1. the jumbolter drill boom pivot angle adaptive sliding-mode observer design method based on EKF, which is characterized in that including step
It is rapid:
(1) whole mathematical model of valve control hydraulic jumbolter drill boom rotary system is constructed:
Wherein,θLIndicate jumbolter drill boom pivot angle,Indicate θLFirst derivative, PLIt indicates
The load pressure of bearing shaft；DmFor hydraulic motor displacement, JtFor the total equivalent moment of inertia of hydraulic motor axis, BtFor hydraulic motor
The total equivalent viscous damping coefficient of axis, GtFor the total equivalent stiffness of hydraulic motor axis, TtIt is equivalent outer to hydraulic motor axis for bearing shaft conversion
Loading moment, ΔfIndicate the uncertain factor that the internal disturbance caused by Parameter uncertainties and unmodeled friction etc. form, Ctm
For total leadage coefficient of hydraulic motor, VmIndicate comprising including connecting pipe, hydraulic motor and electro-hydraulic proportional valve into/oil back chamber
Controllable total measurement (volume), βeFor the oil liquid effective volume elasticity modulus of hydraulic system, n is transmission ratio, CdFor the stream of electro-hydraulic proportional valve valve port
Coefficient of discharge, ω are the area gradient of electro-hydraulic proportional valve, xvFor the spool displacement of electro-hydraulic proportional valve, ρ is oil liquid density, PsIndicate system
System charge oil pressure, u are the input control voltage of electro-hydraulic proportional valve, and m represents the gradient of valve dead zone two sides, and sign () is symbol
Function, is defined as:
The expression formula of δ (u) are as follows:
Wherein, δlAnd δrThe respectively threshold value of electro-hydraulic proportional valve dead zone two sides breakpoint, δlAnd δrFor determining skip distance；
(2) for the mathematical model of step (1) building, with the input control voltage of electro-hydraulic proportional valve and jumbolter drill boom pivot angle
For quantity of state, extended Kalman filter is designed to predict the jumbolter drill boom pivot angle of subsequent timeIt is rightWith current mesh
Mark pivot angle θdIt asks poor, obtains jumbolter drill boom pivot angle error:
(3) extended Kalman filter that the mathematical model for step (1) building and extended Kalman filter predict,
Construct adaptive sliding mold and dead-zone compensator；
The sliding formwork control ratio of adaptive sliding mold are as follows:
Adaptive law are as follows:
Wherein, uasmcFor the output signal of adaptive sliding mold, k1、k2For coefficient, k1∈R+, k2∈R+,For e single order,
Second dervative,For θdThree order derivatives；G (x)=θ4R (x),θ1、θ2、θ3、θ4It is to be
Number, The Reaching Law parameter that K is positive, s are switching
Function, μ indicate handoff factor, γ1, γ2It is controller intrinsic parameter to be designed and is positive number；sμFor saturation function；φ=
[φ(xv), 1- φ (xv)]T,χ () is unit jump function,MeetFor deadzone parameter vector,For the estimated value of deadzone parameter vector,ForOne
Order derivative；
The output signal of dead-zone compensator are as follows: Respectively δrAnd δlEstimate
Evaluation；
(4) by the output signal u of adaptive sliding moldasmcWith the output signal u of dead-zone compensatorcompAddition obtains electric-hydraulic proportion
The input control voltage u of valve.
2. the jumbolter drill boom pivot angle adaptive sliding-mode observer design method according to claim 1 based on EKF,
It is characterized in that, the specific steps of the whole mathematical model of the building valve control hydraulic jumbolter drill boom rotary system are as follows:
Step (2-1) converts the various loads on bearing shaft onto motor drive shaft, the inertia load torque balance after building is equivalent
Equation:
Wherein, load pressure PL=P1-P2, P1、P2Respectively motor is into, back oil cavity pressure.
The flow continuity equation of step (2-2) building Electro-hydraulic Proportional Control hydraulic motor:
Wherein, the load of electro-hydraulic proportional valve controls flow QL=(Q1+Q2)/2, Q1、Q2Respectively indicate hydraulic motor into, oil return stream
Amount；
The load that step (2-3) constructs electro-hydraulic proportional valve controls flow QL, load control pressure PLWith electro-hydraulic proportional valve spool displacement
xvRelational expression between three:
Construct the spool displacement mathematical model of the Dead Zone containing electro-hydraulic proportional valve:
Then spool displacement mathematical model is modified as follow form:
xv=N (u)=m (u- δ (u))
Step (2-4) definition status variableIntegrate inertia load torque balance equation, liquor ratio
The flow continuity equation and spool displacement mathematical model of example Valve-control hydraulic motor, obtain valve control jumbolter drill boom rotary system
Mathematical model:
3. the jumbolter drill boom pivot angle adaptive sliding-mode observer design method according to claim 2 based on EKF,
It is characterized in that, the design method of the extended Kalman filter comprising steps of
Step (3-1) constructs the state equation of the valve control hydraulic jumbolter drill boom rotary system mathematical model:
In formula, f (x (t)) is systematic observation matrix, and B (t) is control matrix, and G (t) is disturbance, and h (x (t)) is output matrix；Its
In,
H (x (t))=[x1, 0,0]T
Step (3-2) provides the discrete-time state of the state equation in the case where considering process noise and measurement noise
Space equation:
In formula, w (k), v (k) are that incoherent zero mean Gaussian white noise, the covariance matrix of process noise w (k) are Q each other,
The covariance matrix for measuring noise v (k) is R, and meets E (w (k))=0, E (v (k))=0；
Step (3-3) is obtained after discrete-time state-space equation local linearization:
In formula, H (k) is observing matrix,A (k) is state-transition matrix, the expression of A (k)
Formula are as follows:
A (k)=I+F (k) Ts
Wherein, I is unit matrix, TsFor the sampling time, F (k) is gradient matrix:
Step (3-4) provides the time update equation and state renewal equation of discrete extended Kalman filter；Wherein,
Time update equation includes:
Prior state estimation:
Prior estimate error covariance matrix:
P (k | k-1)=A (k | k-1) P (k-1) AT(k|k-1)+G(k-1)Q(k-1)GT(k-1)
State renewal equation includes:
Kalman gain: K (k)=P (k | k-1) HT(k)(H(k)P(k|k-1)HT(k)+R(k))-1
T (k) moment optimal estimation:
Evaluated error covariance matrix after update: P (k)=(I-K (k) H (k)) P (k | k-1)
Wherein,For the posteriority state estimation at t (k-1) moment, P (k-1) is t (k-1) moment posteriority state error association side
Poor matrix；
The initialization condition of system are as follows:
In formula,For the estimated value of t (0) moment system mode, P (0) is the evaluated error covariance of t (0) moment system mode
Matrix.
4. the jumbolter drill boom pivot angle adaptive sliding-mode observer design method according to claim 3 based on EKF,
It is characterized in that, building adaptive sliding mold and the specific steps of dead-zone compensator include:
Step (4-1) introduces smooth dead zone inverse function in control input signal u, to avoid the buffeting of u bring: enabling N-1() table
Be shown as smooth dead zone inverse function, then:
Wherein,For smooth continuous indicator function, ε is greater than zero constant；The effect of φ () be for
Avoid drill boom rotary system control in the chattering phenomenon that is likely to occur；
Deadzone parameter vector is expressed as by step (4-2)It enablesIndicate δrEstimated value and evaluated error,
It enablesIndicate deadzone parameter δlEstimated value and evaluated error, then the estimated value table of deadzone parameter vector is shown asThe expression formula of u is rewritten into:
In formula, dead-zone compensator output signal is designed to:
Wherein, φ=[φ (xv), 1- φ (xv)]T；
Step (4-3) enablesEvaluated error beObtain adaptive sliding mode controller output signal and practical ratio
Relational expression between example spool displacement, it may be assumed that
In formula,
Wherein,
Wherein, χ () is unit jump function,Meet
Step (4-4) provides the dynamic characteristic of valve control hydraulic jumbolter drill boom rotary system by Third-order differential equations:
According to system pivot angle error e, switching function is designed:
In order to limit the variation of s, the concept in boundary layer is introduced, i.e., s is defined using saturation functionμ:
sμ=s- μ sat (s/ μ)
In formula,
Sliding formwork control ratio is designed as following form by the Reaching Law parameter for enabling K be positive:
Adaptive law is designed are as follows:
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