CN105549395B - Ensure the mechanical arm servo-drive system dead time compensation control method of mapping - Google Patents
Ensure the mechanical arm servo-drive system dead time compensation control method of mapping Download PDFInfo
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Abstract
A kind of mechanical arm servo-drive system dead time compensation control method for ensureing mapping, including：Establish the dynamic model of mechanical arm servo-drive system, initialization system mode, sampling time and control parameter；According to Order Derivatives in Differential Mid-Value Theorem, it is a simple time-varying system by the non-linear input dead zone linear approximation in system, derives the mechanical arm servo system models with unknown dead zone；Introduce the bound function for limiting tracking error transient response；By error conversion method, a transformed error variable is defined；Using the Lyapunov method, the virtual controlling amount of design system；Unknown virtual controlling amount is estimated using neural network；And be the problems such as avoiding inverting complexity degree f explosion, add firstorder filter.The present invention provide one kind can the input of effective compensation unknown dead zone to systematic influence, the complexity explosion issues that the method for inversion is avoided to bring improve the tenacious tracking control that system transients tracking performance simultaneously ensures position signal.
Description
Technical field
The present invention relates to it is a kind of ensure mapping mechanical arm servo-drive system dead time compensation control method, particular with
The flexible mechanical arm servo system self-adaptive control method in non-linear input dead zone.
Background technology
Mechanical arm servo-drive system is widely used in the high performance system such as robot, aviation aircraft how
Realize that the quick accurate control of mechanical arm servo-drive system has become a hot issue.Wherein, flexible mechanical arm due to
Material is few, and light-weight, the low advantage that consumes energy more and more is paid attention to.However, unknown dead-time voltage link is widely present in
In mechanical arm servo-drive system, the efficiency reduction that frequently can lead to control system is even failed.Therefore, to improve control performance,
Compensation and control method for nonlinear dead-zone is essential.The method of traditional solution dead-time voltage is usually to establish extremely
The inversion model in area or approximate inversion model, and pass through the bound parameter designing adaptive controller for estimating dead zone, with deadband eliminating
Nonlinear influence.However, in the nonlinear systems such as mechanical arm servo-drive system, the inversion model in dead zone is often not easy accurately to obtain
.For dead-time voltage input unknown present in system, linearized based on Order Derivatives in Differential Mid-Value Theorem through row, become one
Simple linear time varying system, avoids ancillary relief, so as to approach unknown function and not with a simple neural network
Know parameter.
For the control problem of mechanical arm servo-drive system, there are many control methods, such as PID control, self adaptive control,
Sliding formwork control etc..Sliding formwork control is considered as an effective robust control in terms of systematic uncertainty and external disturbance is solved
Method.However, the discontinuous switching characteristic of sliding formwork control in itself will cause the buffeting of system, become sliding formwork control and exist
The obstacle applied in real system.Someone is combined the method for inversion with sliding formwork control, but the method can only also realize the stable state of system
Control can not carry out system quick, complete tracking.Therefore, it is proposed to a kind of mechanical arm servo system for ensureing mapping
System dead time compensation control method, introduces the bound function for limiting tracking error transient response, passes through error conversion method, defines one
The guarantee transient response problem of tracking error is converted into the bounded sex chromosome mosaicism of the error variance by transformed error variable.Using Lee
Ya Punuofu methods, the virtual controlling amount of design system, and be the problems such as avoiding inverting complexity degree f explosion, add first-order filtering
Device so as to ensure the boundedness of transformed error variable and uniform convergence, obtains system output in the complete quick of entire section
Tracking performance.
Invention content
In order to overcome the dead-time voltage of existing mechanical arm servo-drive system, model parameter uncertainty and the method for inversion
The deficiency of the complexity explosion brought etc., the present invention propose a kind of mechanical arm servo-drive system dead area compensation for ensureing mapping
Control method simplifies the design structure of controller, realizes the mechanical arm system Position Tracking Control inputted with unknown dead zone,
Guarantee system stablizes fast transient tracking.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows：
A kind of mechanical arm servo-drive system dead time compensation control method for ensureing mapping, the control method include following
Step：
Step 1, the dynamic model of mechanical arm servo-drive system, initialization system mode, sampling time and control ginseng are established
Number, process are as follows：
The dynamic model expression-form of 1.1 mechanical arm servo-drive systems is
Wherein, q and θ is respectively the angle of robot linkage and motor；I is the inertia of connecting rod；J is the inertia of motor；K is
Spring rate；M and L is the quality and length of connecting rod respectively；U is control signal；V (u) is dead zone, is expressed as：
Wherein gl(u), gr(u) it is unknown nonlinear function；blAnd brFor the unknown width parameter in dead zone, meet bl＜ 0, br＞
0；
Define x1=q,x3=θ,Formula (1) is rewritten as
Wherein, y is system output trajectory；
Step 2, according to Order Derivatives in Differential Mid-Value Theorem, by the non-linear input dead zone linear approximation in system for one it is simple when
Change system derives the mechanical arm servo system models with unknown dead zone, including following process；
2.1 pairs of non-linear unknown dead zones carry out linear process
Wherein | ω (u) |≤ωN, ωNIt is that unknown positive number meets ωN=(g 'r+g′l)max{br,blAnd
2.2 according to Order Derivatives in Differential Mid-Value Theorem, then
Then
Formula (4) by formula (6) and formula (9), is rewritten as following equivalents by 2.3：
Step 3, uncertainty is approached with neural network, process is as follows：
Defining continuous function is：
H (X)=W*Tφ(X)+ε (11)
Wherein W*T∈Rn1×n2It is ideal weight matrix, φ (X) ∈ Rn1×n2It is the function of ideal neural network, ε is
The evaluated error of neural network meets | ε |≤εN, φ (X) functional form is：
Wherein, a, b, c, d are suitable constant；
Step 4, computing system transient control performance function and error conversion, process are as follows：
In the control of 4.1 system transients, controller input signal is：
U (t)=ρ (Fφ(t),ψ(t),||e(t)||)×e(t) (13)
Wherein, e (t)=y-yd, ydIt is ideal pursuit path, e (t) is tracking error, and ψ (t) is zoom factor, Fφ(t)
It is the boundary of error variance, | | e (t) | | it is euclideam norm, in order to ensure that e (t) is developed in boundary, time-varying gain ρ ()
For：
The boundary of 4.2 design error variables is：
Wherein,It is a continuous positive function,To t >=0, haveThen
Fφ(t)=δ0exp(-a0t)+δ∞ (16)
Wherein δ0≥δ∞＞ 0,And | e (0) | ＜ Fφ(0)；
4.3, which define transient control error variance, is：
Step 5, system transients Properties Control dummy variable in the method for inversion is calculated, dynamic sliding surface and differential, process are as follows：
5.1 define transient control dummy variable and its differential：
Define error variance：
E=y-yd (18)
Wherein, ydIt is the ideal movements track of the system, y is real system output；
Then, formula (15) derivation is obtained：
Wherein, φF=1/ (Fφ-||e||)2；
5.2 define Liapunov function:
To V1Derivation obtains：
5.3 design virtual controlling amounts
Wherein, k1For constant, and k1＞ 0；
5.4 define a new variable α1, allow virtual controlling amountIt is τ by time constant1Firstorder filter：
5.5 define filtering errorThen
5.6 are estimated with neural network
Step 6, for formula (4), virtual controlling amount is designed；
6.1 define error variance
si=zi-αi-1, i=2,3 (26)
The first differential of formula (15) is：
6.2 design virtual controlling amounts
Wherein, k2For constant and k2＞ 0,It is the estimated value of ε,It is W1Estimated value；
6.3 design virtual controlling amounts
Wherein, k3For constant and k3＞ 0,It is the estimated value of ε,It is W2Estimated value；
6.4 define a new variable αi, allow virtual controlling amountIt is τ by time constantiFirstorder filter：
6.6 are estimated with neural network
Step 7, the input of design controller, process are as follows：
7.1 define error variance
s4=z4-α3 (34)
The first differential of calculating formula (20) is：
7.2 design controller input u：
Wherein,For ideal weight W3Estimated value, k5≥1/n,It is ε3Estimated value；
7.3 design adaptive rates：
Wherein, KjIt is adaptive matrix, vμ ＞ 0；
Step 8, liapunov function is designed, process is as follows：
Wherein,W*It is ideal value；
Derivation is carried out to formula (26) to obtain：
IfThen decision-making system is stable.
The present invention is considering unknown input dead zone, designs a kind of flexible mechanical arm servo system for ensureing mapping
System dead time compensation control method, it realizes that the stabilization of system quickly tracks, ensures tracking error in finite time convergence control.
The present invention technical concept be：It can not be surveyed for state, and with the mechanical arm servo system of unknown dead zone input
System optimizes dead space arrangements using Order Derivatives in Differential Mid-Value Theorem, becomes a simple linear time varying system.In conjunction with nerve net
The mapping control of network, inverting dynamic surface sliding formwork control and transformed error variable, designs a kind of mechanical arm servo-drive system
Dead time compensation control method.By Order Derivatives in Differential Mid-Value Theorem, make dead zone continuously differentiable, using error transform, obtain new error and become
Amount, then be combined by the method for inversion and sliding formwork to design virtual controlling variable, for complexity caused by the method for inversion is avoided to explode
Problem adds in firstorder filter, and the derivative of virtual controlling amount is estimated using neural network, realizes the position transient state of system
Tracing control.The present invention provides a kind of complexity explosion issues that the method for inversion can effectively be avoided to bring and dead zone input to system
Dysgenic compensating control method, realize the tenacious tracking of system and improve mapping.
Beneficial effects of the present invention are：The complexity explosion that dead zone inversion calculation operates and the method for inversion is intrinsic is avoided to ask
Topic, simplify control device structure improve system transients tracking performance and ensure the tenacious tracking control of position signal.
Description of the drawings
Fig. 1 is the schematic diagram of the nonlinear dead-zone of the present invention；
Fig. 2 is the schematic diagram of the tracking effect of the present invention；
Fig. 3 is the schematic diagram of the tracking error of the present invention；
Fig. 4 is the schematic diagram of the controller input of the present invention；
Fig. 5 is the control flow chart of the present invention.
Specific embodiment
The present invention will be further described below in conjunction with the accompanying drawings.
With reference to Fig. 1-Fig. 5, a kind of mechanical arm servo-drive system dead time compensation control method for ensureing mapping, including following
Step：
Step 1, the dynamic model of mechanical arm servo-drive system, initialization system mode, sampling time and control ginseng are established
Number, process are as follows：
The dynamic model expression-form of 1.1 mechanical arm servo-drive systems is
Wherein, q and θ is respectively the angle of robot linkage and motor；I is the inertia of connecting rod；J is the inertia of motor；K is
Spring rate；M and L is the quality and length of connecting rod respectively；U is control signal；V (u) is dead zone, is expressed as：
Wherein gl(u), gr(u) it is unknown nonlinear function；blAnd brFor the unknown width parameter in dead zone, meet bl＜ 0, br＞
0；
Define x1=q,x3=θ,Formula (1) is rewritten as
Wherein, y is system output trajectory；
Step 2, according to Order Derivatives in Differential Mid-Value Theorem, by the non-linear input dead zone linear approximation in system for one it is simple when
Change system derives the mechanical arm servo system models with unknown dead zone, including following process；
2.1 pairs of non-linear unknown dead zones carry out linear process
Wherein | ω (u) |≤ωN, ωNIt is that unknown positive number meets ωN=(g 'r+g′l)max{br,blAnd
2.2 according to Order Derivatives in Differential Mid-Value Theorem, then
Then
Formula (4) by formula (6) and formula (9), is rewritten as following equivalents by 2.3：
Step 3, uncertainty is approached with neural network, process is as follows：
Defining continuous function is：
H (X)=W*Tφ(X)+ε (11)
Wherein W*T∈Rn1×n2It is ideal weight matrix, φ (X) ∈ Rn1×n2It is the function of ideal neural network, ε is
The evaluated error of neural network meets | ε |≤εN, φ (X) functional form is：
Wherein, a, b, c, d are suitable constant；
Step 4, computing system transient control performance function and error conversion, process are as follows：
In the control of 4.1 system transients, controller input signal is：
U (t)=ρ (Fφ(t),ψ(t),||e(t)||)×e(t) (13)
Wherein, e (t)=y-yd, ydIt is ideal pursuit path, e (t) is tracking error, and ψ (t) is zoom factor, Fφ(t)
It is the boundary of error variance, | | e (t) | | it is euclideam norm, in order to ensure that e (t) is developed in boundary, time-varying gain ρ ()
For：
The boundary of 4.2 design error variables is：
Wherein,It is a continuous positive function,To t >=0, haveThen
Fφ(t)=δ0exp(-a0t)+δ∞ (16)
Wherein δ0≥δ∞＞ 0,And | e (0) | ＜ Fφ(0)；
4.3, which define transient control error variance, is：
Step 5, system transients Properties Control dummy variable in the method for inversion is calculated, dynamic sliding surface and differential, process are as follows：
5.1 define transient control dummy variable and its differential,
Define error variance：
E=y-yd (18)
Wherein, ydIt is the ideal movements track of the system, y is real system output；
Then, formula (15) derivation is obtained：
Wherein, φF=1/ (Fφ-||e||)2；
5.2 define Liapunov function:
To V1Derivation obtains：
5.3 design virtual controlling amounts
Wherein, k1For constant, and k1＞ 0；
5.4 define a new variable α1, allow virtual controlling amountIt is τ by time constant1Firstorder filter：
5.5 define filtering errorThen
5.6 are estimated with neural network
Step 6, for formula (4), virtual controlling amount is designed, process is as follows：
6.1 define error variance
si=zi-αi-1, i=2,3 (26)
The first differential of formula (15) is：
6.2 design virtual controlling amounts
Wherein, k2For constant and k2＞ 0,It is the estimated value of ε,It is W1Estimated value；
6.3 design virtual controlling amounts
Wherein, k3For constant and k3＞ 0,It is the estimated value of ε,It is W2Estimated value；
6.4 define a new variable αi, allow virtual controlling amountIt is τ by time constantiFirstorder filter：
6.6 are estimated with neural network
Step 7, the input of design controller, process are as follows：
7.1 define error variance
s4=z4-α3 (34)
The first differential of calculating formula (20) is：
7.2 design controller input u：
Wherein,For ideal weight W3Estimated value, k5≥1/n,It is ε3Estimated value；
7.3 design adaptive rates：
Wherein, KjIt is adaptive matrix, vμ ＞ 0；
Step 8, liapunov function is designed
Wherein,W*It is ideal value；
Derivation is carried out to formula (26) to obtain：
IfThen decision-making system is stable.
For the validity of verification institute extracting method, The present invention gives the mechanical arm servo-drive system dead zone benefits for ensureing mapping
Repay the tracking performance of control method and the figure of tracking error.The parameter of system initialization is：x1(0)=0, x2(0)=0, nerve net
The parameter of network is：K=0.1, a=2, b=10, c=1, d=-1, the boundary function parameter to mapping control are：δ0=1,
δ∞=0.2, a0=0.3, the parameter of virtual controlling amount is：k1=1, k2=20, k3=20, k4=5, k5=1, firstorder filter
Time constant parameter is t2=t3=t4=0.02；System model parameter is Mgl=5, I=1, J=1, K=40, I=1；And
Dead zone is：
Track ydThe signal of=0.5 (sin (t)+sin (0.5t)), as seen from Figure 2, ensures the machinery of mapping
Arm servo-drive system dead time compensation control method can be very good to track movement locus；From figure 3, it can be seen that the tracking of this method
Error very little, it is almost nil.From fig. 4, it can be seen that in the case that with dead zone input controller, nonlinear dead-zone limitation compared with
Greatly, the tenacious tracking of realization system is remained to.Therefore, the present invention provide one kind can the unknown dead zone of effective compensation, avoid the method for inversion
The complexity explosion issues brought have demonstrate,proved system transients Properties Control method, realize that the stabilization of system quickly tracks.
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
Above-described embodiment is limited to, without departing from essence spirit of the present invention and the premise without departing from 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 mechanical arm servo-drive system dead time compensation control method for ensureing mapping, it is characterised in that：The controlling party
Method includes the following steps：
Step 1, the dynamic model of mechanical arm servo-drive system, initialization system mode, sampling time and control parameter, mistake are established
Journey is as follows：
The dynamic model expression-form of 1.1 mechanical arm servo-drive systems is
Wherein, q and θ is respectively the angle of robot linkage and motor；I is the inertia of connecting rod；J is the inertia of motor；K is spring
Stiffness coefficient；M and L is the quality and length of connecting rod respectively；U is control signal；V (u) is dead zone, is expressed as：
Wherein gl(u), gr(u) it is unknown nonlinear function；blAnd brFor the unknown width parameter in dead zone, meet bl＜ 0, br＞ 0；
Define x1=q,x3=θ,Formula (1) is rewritten as
Wherein, y is system output trajectory；
1.2 defined variable z1=x1, z2=x2,
Then formula (3) is rewritten into
Wherein,
Step 2, it is a simple time-varying system by the non-linear input dead zone linear approximation in system according to Order Derivatives in Differential Mid-Value Theorem
System, derives the mechanical arm servo system models with unknown dead zone, including following process；
2.1 pairs of non-linear unknown dead zones carry out linear process
Wherein | ω (u) |≤ω N, ω N are that unknown positive number meets ω N=(g 'r+g′l)max{br,blAnd
2.2 according to Order Derivatives in Differential Mid-Value Theorem, then
Whereinξr∈[br,+∞)；
Whereinξl∈(-∞,bl]；
Then
Formula (4) by formula (6) and formula (9), is rewritten as following equivalents by 2.3：
Wherein,
Step 3, uncertainty is approached with neural network, process is as follows：
Defining continuous function is：
H (X)=W*Tφ(X)+ε (11)
Wherein, n1,n2＞ 0, W*T∈Rn1×n2It is ideal weight matrix, φ (X) ∈ Rn1×n2It is the letter of ideal neural network
Number, ε is the evaluated error of neural network, is met | ε |≤εN, φ (X) functional form is：
Wherein, a, b, c, d are suitable constant；
Step 4, computing system transient control performance function and error conversion, process are as follows：
In the control of 4.1 system transients, controller input signal is：
U (t)=ρ (Fφ(t),ψ(t),||e(t)||)×e(t) (13)
Wherein, e (t)=y-yd, ydIt is ideal pursuit path, e (t) is tracking error, and ψ (t) is zoom factor, Fφ(t) it is to miss
The boundary of poor variable, | | e (t) | | it is euclideam norm, in order to ensure that e (t) is developed in boundary, time-varying gain ρ () is：
The boundary of 4.2 design error variables is：
Fφ(t)→{e∈Rm|φ(t)×||e(t)||} (15)
Wherein, m ＞ 0, φ (t) are a continuous positive functions, and φ (t) ＞ 0 to t >=0, haveThen
Fφ(t)=δ0exp(-a0t)+δ∞ (16)
Wherein, a0＞ 0, δ0≥δ∞＞ 0,And | e (0) | ＜ Fφ(0)；
4.3, which define transient control error variance, is：
Step 5, system transients Properties Control dummy variable in the method for inversion is calculated, dynamic sliding surface and differential, process are as follows：
5.1 define transient control dummy variable and its differential：
Define error variance：
E (t)=y-yd (18)
Wherein, ydIt is the ideal movements track of the system, y is real system output；
Then, formula (15) derivation is obtained：
Wherein, φF=1/ (Fφ-||e||)2；
5.2 define Liapunov function:
To V1Derivation obtains：
5.3 design virtual controlling amounts
Wherein, k1For constant, and k1＞ 0；
5.4 define a new variable α1, allow virtual controlling amountIt is τ by time constant1Firstorder filter：
5.5 define filtering errorThen
5.6 are estimated with neural network
Wherein
Step 6, for formula (4), virtual controlling amount is designed；
6.1 define error variance
si=zi-αi-1, i=2,3 (26)
The first differential of formula (15) is：
6.2 design virtual controlling amounts
Wherein, k2For constant and k2＞ 0,It is the estimated value of ε,It is W1Estimated value；
6.3 design virtual controlling amounts
Wherein, k3For constant and k3＞ 0,It is the estimated value of ε,It is W2Estimated value；
6.4 define a new variable αi, allow virtual controlling amountIt is τ by time constantiFirstorder filter：
6.5 definitionThen
6.6 are estimated with neural network
Wherein,For ideal weight WiEstimated value,In；
Step 7, the input of design controller, process are as follows：
7.1 define error variance
s4=z4-α3 (34)
The first differential of calculating formula (20) is：
7.2 design controller input u：
Wherein,For ideal weight W3Estimated value, k5>=1/n,It is ε3Estimated value；
7.3 design adaptive rates：
Wherein, KjIt is adaptive matrix, vμ ＞ 0；
Step 8, liapunov function is designed, process is as follows：
Wherein,W*It is ideal value；
Derivation is carried out to formula (26) to obtain：
IfThen decision-making system is stable.
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| CN106113046B (en) * | 2016-07-13 | 2018-09-21 | 浙江工业大学 | Mechanical arm servo system dynamic surface transient control method based on dead zone and friction compensation |
| CN106802569B (en) * | 2017-03-24 | 2019-12-03 | 哈尔滨理工大学 | A kind of adaptive state feedback control method compensating executing agency's dead-time voltage |
| CN109465825B (en) * | 2018-11-09 | 2021-12-10 | 广东工业大学 | RBF neural network self-adaptive dynamic surface control method for flexible joint of mechanical arm |
| CN109581873A (en) * | 2018-12-26 | 2019-04-05 | 河海大学 | The finite time specified performance control algolithm of unknown actuator dead zone switching system |
| CN109884890B (en) * | 2019-02-15 | 2021-12-07 | 浙江工业大学 | Time-varying constraint inversion control method for servo system of electric drive mechanical arm |
| CN110750050B (en) * | 2019-10-11 | 2022-10-28 | 浙江工业大学 | Neural network-based mechanical arm system preset performance control method |
| CN110687787B (en) * | 2019-10-11 | 2022-11-25 | 宁波耀华电气科技有限责任公司 | Self-adaptive control method for mechanical arm system |
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