CN105739311B - Electromechanical servo system constrained control method based on default echo state network - Google Patents
Electromechanical servo system constrained control method based on default echo state network Download PDFInfo
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
A kind of electromechanical servo system constrained control method based on default echo state network, including：Establish the dynamic model of electromechanical servo system, initialization system mode, sampling time and control parameter；According to Order Derivatives in Differential Mid-Value Theorem, the non-linear input in system is saturated limited linearization process, derives the electromechanical servo system model with unknown saturation；Based on default echo state network control method, calculating control system tracking error, sliding-mode surface, and tracking error is converted according to default capabilities function, obtains new error variance to design virtual controlling amount；By virtual controlling amount by higher differentiation device, and design control input.The present invention provide one kind can effective compensation input, output it is limited, improve the high-order dynamic face sliding-mode control of neural network approximation capability, realize that the stabilization of system quickly tracks, guarantee that there is good transient state steady-state performance.
Description
Technical field
The invention belongs to the control method of electromechanical servo system, it is related to a kind of electromechanics based on default echo state network and watches
Dress system constrained control method, particular with the control method of the limited electromechanical servo system of input-bound and output.
Background technique
With the fast development and motor system of power electronic technique, computer science, modern control theory, material technology
Stepping up for technological level is made, is set in precise numerical control machine, industrial robot, electronics processing and detection device, laser processing
The industrial control fields such as standby, printing machinery, package packing machine, tailoring machinery, production automation, non-linear electromechanical servo system
It is widely applied.Non-linear electromechanical servo system is with mechanical parameters such as displacement, angle, power, torque, velocity and accelerations
For the automatic control system of control object.However, limited link, including input-bound and output are limited, it is widely present in electromechanics
In servo-system, the transient state steady-state performance decline of control system, even unstability frequently can lead to.Therefore, in controller design
In the process, it is necessary to consider that limited link bring is negatively affected and compensated, how realize the quick accurate control of electromechanical servo system
System has become a hot issue.
Default capabilities control method is in output constrained system using relatively broad.In control process, one is proposed
Rate of convergence, the default capabilities function of maximum overshoot and steady-state error are described, and is used to conversion output error.This method
Key problem in technology is how to select default capabilities function that primal system is converted to error converting system, to guarantee the transient state of system
Steady-state performance.It is inputted for unknown saturation present in system, traditional saturation compensation method is usually to establish the inverse mould of saturation
Type or approximate inversion model, and by the bound parameter designing adaptive controller of estimation saturation, to compensate the influence of saturation.So
And in the nonlinear systems such as electromechanical servo system, the inversion model of saturation is often not easy accurately to obtain.To based in differential
It is worth theorem to linearize through row, becomes a simple time-varying system, avoid ancillary relief.
Neural network is often used to estimation, approximate unknown function due to its good approximation capability., but BP Neural Network
Network is essentially static network, can only realize static non linear mapping relations, is not suitable for the real-time identification of dynamical system.
Recurrent neural network is a kind of dynamic network, can be well reflected system dynamic characteristic, but due to its training method complexity, seldom
Applied to practical due to the simplicity and rapidity of echo state network training, becomes and solve the problems, such as many important ways
Diameter.The maximum feature of echo state network is intrinsic nerve tuple of the hidden layer by a large amount of (several hundred to thousands of) partially connecteds
At referred to as state reserve pool.Thus the network has extremely strong short term memory capacity and training algorithm is simple.But it is led in control
On domain, the application of echo state network is few, needs to develop and study.
Summary of the invention
In order to overcome existing electromechanical servo system can not effective compensation input-bound, do not consider transient performance, and
The bad equal deficiency of static neural network Approximation effect, the present invention provide a kind of electromechanical servo based on default echo state network
System constrained control method, it is contemplated that the presence of input and output limitation problem approaches unknown function using echo state network,
Limited electromechanical servo system tracing control is realized, ensure that system has good transient state steady-state performance.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows：
A kind of electromechanical servo system constrained control method based on default echo state network, includes the following steps：
Step 1, the dynamic model of electromechanical servo system is established, process is as follows：
The dynamic model expression-form of 1.1 electromechanical servo systems is
Wherein, x is position；M is inertia；k0It is force constant；It is state variable；It is frictional force；
Be model caused by a BOUNDED DISTURBANCES, from coupled characteristic, measurement noise, electronic interferences and other it is uncertain because
Element；U is the control input voltage of motor；V (u) is saturation, is expressed as：
Wherein sgn (u) is unknown nonlinear function；vmaxFor unknown parameter of saturation, meet vmax> 0；
1.2 define x1=x,Formula (1) is rewritten as
Wherein, y is system output trajectory；
Step 2, according to Order Derivatives in Differential Mid-Value Theorem, the non-linear input saturation in system is subjected to linearization process, is derived
Electromechanical servo system model with unknown saturation, comprises the following processes；
2.1 pairs of saturated models carry out smooth treatment
Then
V (u)=sat (u)=g (u)+dsat (u) (5)
Wherein, dsat (u) indicates existing error between smooth function and saturated model；
2.2 according to Order Derivatives in Differential Mid-Value Theorem, and there are δ ∈ (0,1) to make
Whereinu0∈(0,u)；
Select u0=0, formula (6) is rewritten as
2.3 are rewritten as following equivalents by formula (5) and formula (7), by formula (3)：
Wherein
Step 3, calculating control system tracking error, sliding-mode surface and transformed error, process are as follows：
3.1 define the tracking error of control system, and sliding-mode surface is
Wherein, ydDesired trajectory can be led for second order, and λ is constant, and λ > 0；
3.2 obtain new transformed error ε according to sliding-mode surface1；
Wherein ρ1(t) expression formula is
ρ1(t)=(ρ0-ρ∞)e-lt+ρ∞ (11)
Parameter ρ0> ρ∞> 0 and l > 0；Withα(t) derivative expressions are
ParameterSize and initially need to design；Function S () expression formula is
Wherein, ε is transformed error variable；
3.3 pairs of formula (10) derivations obtain：
Wherein
3.4 design virtual controlling amounts
Wherein, k1For constant, and k1> 0；Function Q () be Nussbaum function, select expression formula for
WhereinAdaptive law be designed as
3.5 allow virtual controlling amountPass through high order sliding mode differentiator
Wherein parameter μ1,1> 0, μ2,1> 0, β1,1It is virtual controlling amountThe filtered variable obtained by differentiator；
Step 4, the input of design controller, process are as follows：
4.1 define error variance
s2=x2-β1,1 (19)
4.2 obtain transformed error ε according to the error variance of definition2
Wherein ρ2(t) expression formula is
ρ2(t)=(ρ0-ρ∞)e-lt+ρ∞ (21)
Parameter ρ0> ρ∞> 0 and l > 0；Withα(t) derivative expressions are as shown in formula (12)；Function S () expression formula is such as
Shown in formula (13)；
Formula (20) derivation is obtained：
Wherein
4.3 approach the Nonlinear uncertainty being not directly availableDefine following neural network
Wherein, W*For ideal weight, η*For neural network perfect error value, meet | η*|≤ηN,Expression formula is：
Wherein Win, Wd, WfbFor random value；U is controller input；For height
This function, expression formula are
WhereinIt is the output of i-th of node of hidden layer；χiIt is the center vector of i-th of node Gaussian function, i.e. χi=
[χi1,χi2,…χil]T；liIt is the width of i-th of node Gaussian function；Y is neural network output, and expression formula is
Selection of Function G=1；
4.4 design controllers input u：
Wherein,For ideal weight W*Estimated value,For evaluated error η*Estimated value.
4.5 design adaptive rates：
Wherein,Γ is adaptive gain matrix, and σ, k, γ is constant,
And σ > 0, κ > 0, γ > 0.
The present invention is based on echo state network, default capabilities control methods, it is contemplated that there is a situation where that input, output are limited
Under, the constrained control method of electromechanical servo system is designed, realizes the fast and stable tracking of system, and guarantees the transient state of control performance
Steady-state performance.
Technical concept of the invention is：It can not be surveyed for state, and the electromechanical servo system limited with input, output
System optimizes saturated structures using Order Derivatives in Differential Mid-Value Theorem, proposes the electromechanical servo system based on saturated model.In conjunction with echo state
Network, default capabilities control and high-order dynamic face sliding formwork control, design a kind of constrained control method of electromechanical servo system.It is logical
Order Derivatives in Differential Mid-Value Theorem is crossed, makes to be saturated continuously differentiable, then approach unknown function by echo state network, eliminates tradition saturation
Ancillary relief.Also, default capabilities control method transformed error variable is utilized, designs virtual controlling amount further according to transformed error.
Empty control amount is obtained into filtered variable and its derivative by higher differentiation device, improves conventional dynamic face stability vulnerable to parameter shadow
The deficiencies of ringing, realizes the tenacious tracking of system.The present invention provide one kind can effective compensation input, output it is limited, improve mind
High-order dynamic face sliding-mode control through network approximation capability, realizes that the stabilization of system quickly tracks, and guarantees to have good
Transient state steady-state performance.
Advantages of the present invention is：The limited influence to system tracing control performance of input, output is avoided, dynamic neural is utilized
Network approaches Unknown Model indeterminate, realizes the tenacious tracking of system, reaches good transient state steady-state performance.
Detailed description of the invention
Fig. 1 is the schematic diagram of non-linear saturation of the invention；
Fig. 2 is the schematic diagram of tracking effect of the invention；
Fig. 3 is the schematic diagram of tracking error of the invention；
Fig. 4 is the schematic diagram that controller of the invention inputs；
Fig. 5 is the schematic diagram of estimation effect of the invention；
Fig. 6 is control flow chart of the invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
- Fig. 6 referring to Fig.1, the electromechanical servo system constrained control method based on default echo state network, including following step
Suddenly：
Step 1, the dynamic model of electromechanical servo system is established, process is as follows：
The dynamic model expression-form of 1.1 electromechanical servo systems is
Wherein, x is position；M is inertia；k0It is force constant；It is state variable；It is frictional force；
Be model caused by a BOUNDED DISTURBANCES, from coupled characteristic, measurement noise, electronic interferences and other it is uncertain because
Element；U is the control input voltage of motor；V (u) is saturation, is expressed as：
Wherein sgn (u) is unknown nonlinear function；vmaxFor unknown parameter of saturation, meet vmax> 0；
1.2 define x1=x,Formula (1) is rewritten as
Wherein, y is system output trajectory；
Step 2, according to Order Derivatives in Differential Mid-Value Theorem, the non-linear input saturation in system is subjected to linearization process, is derived
Electromechanical servo system model with unknown saturation, comprises the following processes；
2.1 pairs of saturated models carry out smooth treatment
Then
V (u)=sat (u)=g (u)+dsat (u) (5)
Wherein, dsat (u) indicates existing error between smooth function and saturated model；
2.2 according to Order Derivatives in Differential Mid-Value Theorem, and there are δ ∈ (0,1) to make
Whereinu0∈(0,u)；
Select u0=0, formula (6) is rewritten as
2.3 are rewritten as following equivalents by formula (5) and formula (7), by formula (3)：
Wherein
Step 3, calculating control system tracking error, sliding-mode surface and transformed error, process are as follows：
3.1 define the tracking error of control system, and sliding-mode surface is
Wherein, ydDesired trajectory can be led for second order, and λ is constant, and λ > 0；
3.2 obtain new transformed error according to sliding-mode surface
Wherein ρ1(t) expression formula is
ρ1(t)=(ρ0ρρ∞)e-lt+ρ∞ (11)
Parameter ρ0> ρ∞> 0 and l > 0；Withα(t) derivative expressions are
ParameterSize and initially need to design；Function S () expression formula is
3.3 pairs of formula (10) derivations obtain：
Wherein
3.4 design virtual controlling amounts
Wherein, k1For constant, and k1> 0；Function Q () be Nussbaum function, select expression formula for
WhereinAdaptive law be designed as
3.5 allow virtual controlling amountPass through high order sliding mode differentiator
Wherein parameter μ1,1> 0, μ2,1> 0, κ1,1It is virtual controlling amountThe filtered variable obtained by differentiator；
Step 4, the input of design controller, process are as follows：
4.1 define error variance
s2=x2-β1,1 (19)
4.2 obtain transformed error according to the error variance of definition
Wherein ρ2(t) expression formula is
ρ2(t)=(ρ0-ρ∞)e-lt+ρ∞ (21)
Parameter ρ0> ρ∞> 0 and l > 0；Withα(t) derivative expressions are as shown in formula (12)；Function S () expression
Shown in formula such as formula (13)；
Formula (20) derivation is obtained：
Wherein
4.3 in order to approach the Nonlinear uncertainty being not directly availableDefine following neural network
Wherein, W*For ideal weight, η*For neural network perfect error value, meet | η*|≤ηN,Expression formula is：
Wherein Win, Wd, WfbFor a certain range of random value；U is controller input；For Gaussian function, expression formula is
WhereinIt is the output of i-th of node of hidden layer；χiIt is the center vector of i-th of node Gaussian function, i.e. χi=
[χi1,χi2,...χil]T；liIt is the width of i-th of node Gaussian function；Y is neural network output, and expression formula is
Selection of Function G=1；
4.4 design controllers input u：
Wherein,For ideal weight W*Estimated value,For evaluated error η*Estimated value；
4.5 design adaptive rates：
Wherein,Γ=ΓT> 0,Γ is adaptive gain matrix, and σ, κ, γ is constant,
And σ > 0, κ > 0, γ > 0；
For the validity for verifying proposed method, The present invention gives the comparisons of two kinds of control methods：
M1：High-order dynamic sliding-mode surface constrained control method based on default echo state network；
M2：Common common dynamic surface constrained control method based on RBF neural.
In order to more effectively compare, it is [x that all parameter settings, which are all consistent system initialization parameter,1,x2]T=
[0,0]T’k0=1 ' m=1；It is saturated restricted parameters vmax=15；Higher differentiation
Device parameter μ1,1=10 ' μ2,1=5；Default capabilities function parameter ρ0=1 ' ρ∝=0.2, l=0.2, Echo state network parameter Win’Wfb’W0It is all the random value on section [- 1,1],It is distributed in section [- 4,4] × [- 4,4] × [- 4,4] × [- 6,6]；Self adaptive control
The rate parameter controller parameter of κ=10, γ=0.001 k1=41, k2=250；
Track sine wave input, expression formula yd=3sint.From figures 2 and 3, it will be seen that M1 controller compares M2
For controller, there is faster tracking velocity, smaller steady-state error and be more good transient performance (overshoot is small)；From
It is more smooth compared with M2 that Fig. 4 can be seen that M1 control input；From fig. 5, it can be seen that the approximation capability of echo state network is more common
More preferably, evaluated error is smaller for RBF neural, and dynamic estimation performance is better.Therefore, the present invention provides one kind and can effectively mend
It is limited to repay input, output, improves the high-order dynamic face sliding-mode control of neural network approximation capability, realizes that the stabilization of system is fast
Speed tracking, guarantees there is good transient state steady-state performance.
Described above is the excellent effect of optimization that one embodiment that the present invention provides is shown, it is clear that the present invention is not only
It is limited to above-described embodiment, without departing from essence spirit of the present invention and without departing from the premise of range involved by substantive content of the present invention
Under it can be made it is various deformation be implemented.
Claims (1)
1. a kind of electromechanical servo system constrained control method based on default echo state network, it is characterised in that：Including following
Step：
Step 1, the dynamic model of electromechanical servo system is established, process is as follows：
The dynamic model expression-form of 1.1 electromechanical servo systems is
Wherein, x is position；M is inertia；k0It is force constant；It is state variable；It is frictional force；It is modeling
A generated BOUNDED DISTURBANCES, from coupled characteristic, measurement noise, electronic interferences and other uncertain factors；U is electricity
The control input voltage of machine；V (u) is saturation part, is expressed as：
Wherein sgn (u) is unknown nonlinear function；vmaxFor unknown parameter of saturation, meet vmax> 0；
1.2 define x1=x,Formula (1) is rewritten as
Wherein, y is system output trajectory；
Step 2, according to Order Derivatives in Differential Mid-Value Theorem, the non-linear input saturation in system is subjected to linearization process, derives and has
The electromechanical servo system model of unknown saturation, comprises the following processes；
2.1 pairs of saturated models carry out smooth treatment
Then
V (u)=sat (u)=g (u)+dsat (u) (5)
Wherein, dsat (u) indicates existing error between smooth function and saturated model；
2.2 according to Order Derivatives in Differential Mid-Value Theorem, and there are ξ ∈ (0,1) to make
Whereinuξ=ξ u+ (1- ξ) u0, u0∈(0,u)；
Select u0=0, formula (6) is rewritten as
2.3 are rewritten as following equivalents by formula (5) and formula (7), by formula (3)：
Wherein,
Step 3, calculating control system tracking error, sliding-mode surface and transformed error, process are as follows：
3.1 define the tracking error of control system, and sliding-mode surface is
Wherein, ydDesired trajectory can be led for second order, and λ is constant, and λ > 0；
3.2 obtain new transformed error ε according to sliding-mode surface1；
Wherein ρ1(t) expression formula is
ρ1(t)=(ρ0-ρ∞)e-lt+ρ∞ (11)
Parameter ρ0> ρ∞> 0 and l > 0；Withα(t) derivative expressions are
ParameterSize and initially need to design；Function S () expression formula is
Wherein, ε is transformed error variable；
3.3 pairs of formula (10) derivations obtain：
Wherein
3.4 design virtual controlling amounts
Wherein, k1For constant, and k1> 0；Function Q () be Nussbaum function, select expression formula for
WhereinAdaptive law be designed as
3.5 allow virtual controlling amountPass through high order sliding mode differentiator
Wherein parameter μ1,1> 0, μ2,1> 0, β1,1It is virtual controlling amountThe filtered variable obtained by differentiator；
Step 4, the input of design controller, process are as follows：
4.1 define error variance
s2=x2-β1,1 (19)
4.2 obtain transformed error ε according to the error variance of definition2
Wherein ρ2(t) expression formula is
ρ2(t)=(ρ0-ρ∞)e-lt+ρ∞ (21)
Parameter ρ0> ρ∞> 0 and l > 0；Withα(t) derivative expressions are as shown in formula (12)；Function S () expression formula is such as
Formula (13)
It is shown；
Formula (20) derivation is obtained：
Wherein
4.3 approach the Nonlinear uncertainty being not directly availableDefine following neural network
Wherein, W*For ideal weight, η*For neural network perfect error value, meet | η*|≤ηN,Expression formula is：
Wherein Win, Wd, WfbFor random value；U is controller input；For Gaussian function
Number, expression formula are
WhereinIt is the output of i-th of node of hidden layer；χiIt is the center vector of i-th of node Gaussian function, i.e. χi=[χi1,
χi2,…χil]T；ιiIt is the width of i-th of node Gaussian function；Y is neural network output, and expression formula is
Selection of Function G=1；
4.4 design controllers input u：
Wherein,For ideal weight W*Estimated value,For evaluated error η*Estimated value；
4.5 design adaptive law：
Wherein,Γ=ΓT> 0, Γ are adaptive gain matrixes, σ, κ, and γ is constant, and σ > 0, κ > 0, γ
> 0.
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| CN104950677A (en) * | 2015-06-17 | 2015-09-30 | 浙江工业大学 | Mechanical arm system saturation compensation control method based on back-stepping sliding mode control |
| CN105223808A (en) * | 2015-06-24 | 2016-01-06 | 浙江工业大学 | Based on the mechanical arm system saturation compensation control method that neural network dynamic face sliding formwork controls |
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