CN109839826A - Double drive coordinated movement of various economic factors synchronisation control means - Google Patents

Double drive coordinated movement of various economic factors synchronisation control means Download PDF

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CN109839826A
CN109839826A CN201910161291.5A CN201910161291A CN109839826A CN 109839826 A CN109839826 A CN 109839826A CN 201910161291 A CN201910161291 A CN 201910161291A CN 109839826 A CN109839826 A CN 109839826A
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double drive
fuzzy
formula
economic factors
control
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李枫
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Shenzhen Cui Lu Technology Green Engineering Co Ltd
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Abstract

The invention discloses a kind of double drive coordinated movement of various economic factors synchronisation control means, including establish kinematics model for existing single shaft+The gear deceleration driving method;Design self-adapting fuzzy frictional compensation device compensates the non-linear friction of system;The robustness of system is improved using global synovial membrane control algolithm;Establish the double drive traffic signal coordination controlled based on two shaft position error couplers;Double drive coordinated movement of various economic factors synchronously control is completed using the control algolithm of foundation.The method of the present invention can ensure the location error of kinematic system and the equal asymptotic convergence of synchronous error in zero, simultaneously, control method also possesses good robustness, parameter of electric machine variation bring disturbance caused by external loading variation or interference can be effectively resisted, and can be widely applied in respective double drive kinematic system.

Description

Double drive coordinated movement of various economic factors synchronisation control means
Technical field
Present invention relates particularly to a kind of double drive coordinated movement of various economic factors synchronisation control means.
Background technique
With the development of economic technology, traditional industry has also welcome new opportunity to develop.In traditional industrial machinery In, a motor is usually used to drive production equipment.But with the development of modern industrial technology, modern industry is mechanical Equipment develops towards high-precision, large inertia, varying load, good dynamic response performance direction, therefore is driven again with single motor The requirement of the production work of modern industry is no longer satisfied, but drives loaded work piece jointly using multiple electric motors.Phase It is driven than single motor, multi-motor driving can increase the output power of system, increase the freedom degree of equipment and can provide more Function, be widely used in various heavy duties, varying load, high-precision requirement occasion in.
However, the problem of being related to synchronously control using multi-motor driving, this is the difficult point place of multi-drive system, It is the research hotspot problem of motion control field.But although there are many for double drive coordinated movement of various economic factors synchronously control in recent years Research achievement, but its synchronously control effect is still bad.
Summary of the invention
The purpose of the present invention is to provide a kind of high reliablity, robustness is preferable and the higher double drive of control precision is coordinated Move synchronisation control means.
This double drive coordinated movement of various economic factors synchronisation control means provided by the invention, includes the following steps:
S1. it is directed to existing single shaft+The gear deceleration driving method, establishes kinematics model;
S2. it is directed to single axial movement, design self-adapting fuzzy frictional compensation device compensates the non-linear friction of system;
S3. the robustness of system is improved using global synovial membrane control algolithm;
S4. the double drive traffic signal coordination based on the control of two shaft position error couplers is established;
S5. the double drive traffic signal coordination established using step S4 controls existing single shaft+The gear deceleration driving System, to complete double drive coordinated movement of various economic factors synchronously control.
It is directed to existing single shaft+The gear deceleration driving method described in step S1, establishes kinematics model, specially uses Following steps establish kinematics model:
A. moment of friction suffered by system is equivalent on motor shaft, and the uncertainty of model is equivalent to distracter, To according to following formula founding mathematical models:
J in formulamFor total rotary inertia of motor and transmission mechanism, θmFor motor angular displacement, f (t) is that system is converted to motor Moment of friction on axis, TaFor transmission mechanism output torque, d (t) is system parameter uncertainty item and external interference item, u (t) For motor output torque, TbFor transmission mechanism input torque, θ is load axis angular displacement, and i is reduction ratio, JbThe idling that is negative is dynamic used Amount;
B. the mathematical model obtained according to step A, using following formula to establish with motor torque is input, load shaft angle position Move the dynamic property equation for output:
J=J in formulab/i+iJm
Design self-adapting fuzzy frictional compensation device described in step S2, is specially designed using following steps:
A. the input sample point in input space U is transformed into the fuzzy set A in output SPACE V by fuzzy devicelIn;
B. according to the rule in knowledge base, the fuzzy subset of V can be mapped to fuzzy rule R by inference machinemFuzzy subset In;
C. defuzzifier is again by fuzzy rule RmIn fuzzy set be mapped to discrete point set RnIn;
D. weighted mean method is used, using the output F of following formula computing systemi:
J=1 in formula, 2 ..., M, M are the sum of rule,l =1,2 ..., M,For free parameter and composition vectorFor degree of membership letter Number, xiFor input variable.
Global synovial membrane control algolithm, specifically comprises the following steps: described in step S3
(1) using following formula as global sliding mode function s:
E is tracking error and e=θ-θ in formulad, θ is actual motion track, θdFor ideal motion profile, c is greater than 0 Constant, g (t) are that the function and g (t) designed to reach global sliding mode must satisfy following 3 conditions: condition 1:G (t) → 0 when condition 2:t → ∞;Condition 3:g (t) has first derivative;
(2) using following formula as control law:
In formulaFor the estimated value of J, Δ J isMaximum deviation, D be disturb d (t) maximum value, g be g (t) contracting It writes, KDFor positive control gain, sgn (s) is sign function,For the output valve of self-adapting fuzzy frictional compensation device.
The function expression of the function g (t) designed to reach global sliding mode is g (t)=g (0) e-kt
The double drive traffic signal coordination that foundation described in step S4 is controlled based on two shaft position error couplers, is specially adopted Use formula as the control amount u of double drive coordinated movement of various economic factors synchronously control:
In formulaFor the estimation of inertial matrix J, c=diag { c1,c2It is sliding-mode surface parameter matrix,For the PD feedback control amount of position synchronous error, KD、KEPAnd KEDIt is the parameter square of positive value for element Battle array, c are the constant greater than 0, and sgn (s) is sign function, and G is the gravity compensation on vertical direction, q=[q1,q2]TFor double drive Vector composed by respective freedom degree direction, qdFor the d power of coordinate q, the d power that the second order in formula for q is led, the i.e. seat Put on the d power of acceleration, s be sliding formwork functional vector andE is feed back input amount and E=(I+ α T) e, I is Unit matrix, the synchronous error proportionality coefficient that α is positive,E=[e1 e2]T, e1And e2For the position of twin shaft, KNIncludeThe compensation term of evaluated error and interference upper bound D and meet KN=[KN1,KN2,KN3,KN4]TWith For the adaptive friction compensation item and satisfaction of each axisΘiFor fuzzy system parameter vector and its approach rate It is designed as Θi=-s Γiξi, Γ is Strict Positive Real constant.
This double drive coordinated movement of various economic factors synchronisation control means provided by the invention is a kind of based on adaptive fuzzy friction benefit It repays, the double drive coordinated movement of various economic factors synchronisation control means of total-sliding-mode control and cross-coupling control, is used for double drive mechanical equipment Synchronously control in movement;The method of the present invention can ensure the location error of kinematic system and the equal asymptotic convergence of synchronous error in Zero, meanwhile, control method also possesses good robustness, can effectively resist motor caused by external loading variation or interference The disturbance of Parameters variation bring, and can be widely applied in respective double drive kinematic system, such as H-type goes up and down truss, work Industry robot etc..
Detailed description of the invention
Fig. 1 is the uniaxial transmission mechanism schematic diagram that the method for the present invention is applicable in.
Fig. 2 is the control process schematic diagram of the method for the present invention.
Specific embodiment
This double drive coordinated movement of various economic factors synchronisation control means provided by the invention, includes the following steps:
S1. it is directed to existing single shaft+The gear deceleration driving method (its structure is as shown in Figure 1), establishes kinematics model;Tool Body is to establish kinematics model using following steps:
A. moment of friction suffered by system is equivalent on motor shaft, and the uncertainty of model is equivalent to distracter, To according to following formula founding mathematical models:
J in formulamFor total rotary inertia of motor and transmission mechanism, θmFor motor angular displacement, f (t) is that system is converted to motor Moment of friction on axis, TaFor transmission mechanism output torque, d (t) is system parameter uncertainty item and external interference item, u (t) For motor output torque, TbFor transmission mechanism input torque, θ is load axis angular displacement, and i is reduction ratio, JbThe idling that is negative is dynamic used Amount;
B. the mathematical model obtained according to step A, using following formula to establish with motor torque is input, load shaft angle position Move the dynamic property equation for output:
J=J in formulab/i+iJm
S2. it is directed to single axial movement, design self-adapting fuzzy frictional compensation device compensates the non-linear friction of system;
Fuzzy rule form are as follows: if (if) condition, (then) conclusion;
For multi-input multi-output system, fuzzy rule is writeable are as follows:
L=1,2 in formula ..., M;
U=U1×U2×...×Un
V=V1×V2×...×Vm
Wherein Ui∈Rn, Vi∈Rm, M is the total quantity of rule, xiAnd yiIt is to output and input vector respectively,WithPoint It is not fuzzy subset UiAnd ViOn fuzzy set, can be by subordinating degree functionWithIt is quantitatively described;
Therefore, in the specific implementation, can be designed using following steps:
A. the input sample point in input space U is transformed into the fuzzy set A in output SPACE V by fuzzy devicelIn;
B. according to the rule in knowledge base, the fuzzy subset of V can be mapped to fuzzy rule R by inference machinemFuzzy subset In;
C. defuzzifier is again by fuzzy rule RmIn fuzzy set be mapped to discrete point set RnIn;
D. weighted mean method is used, using the output F of following formula computing systemi:
J=1 in formula, 2 ..., M, M are the sum of rule,l =1,2 ..., M,For free parameter and composition vectorFor degree of membership letter Number, xiFor input variable;
Simultaneously as frictional force is only related with speed, so the output of adaptive fuzzy system is represented by
Due in general fuzzy system,It is constant, but in the methods of the invention, in order to allow system not Determining parameter and distracter has good adaptability, introduces adaptive algorithm, enablesFor free parameter and composition vectorTo obtain above-mentioned adaptive fuzzy system;
S3. the robustness of system is improved using global synovial membrane control algolithm;
In general, the response of traditional Sliding Mode Variable Structure System is divided into two stages, i.e., reaching mode response with And sliding mode response;Since sliding formwork function is not zero in movement original state, thus tradition SMC system is only in sliding mode mistake Exist in journey to external interference and the probabilistic robustness of object parameters, robust is not present in the reaching mode stage Property;Based on this analysis, a kind of kinematic nonlinearity sliding-mode surface equation can be constructed, so that sliding formwork function also can in movement original state It levels off to zero, there is robustness, i.e. total-sliding-mode control to achieve the purpose that control overall process;
Therefore, the global synovial membrane control algolithm, specifically comprises the following steps:
(1) using following formula as global sliding mode function s:
E is tracking error and e=θ-θ in formulad, θ is actual motion track, θdFor ideal motion profile, c is greater than 0 Constant, g (t) are that the function and g (t) designed to reach global sliding mode must satisfy following 3 conditions: condition 1:G (t) → 0 when condition 2:t → ∞;Condition 3:g (t) has first derivative;
Specifically, the function expression of g (t) can be designed as g (t)=g (0) e-kt
(2) using following formula as control law:
In formulaFor the estimated value of J, Δ J isMaximum deviation, D be disturb d (t) maximum value, g be g (t) contracting It writes, KDFor positive control gain, sgn (s) is sign function,For the output valve of self-adapting fuzzy frictional compensation device;
S4. the double drive traffic signal coordination based on the control of two shaft position error couplers is established;
For dual drive system, can set the synchronous error of axis 1,2 as
I.e.
I.e.
ε=Te
The control target of the twin shaft coordinated movement of various economic factors is i.e. so that εi→ 0, i.e., the tracking error situation of change of each axis reaches unanimity;
On this basis, the feed back input amount that coupling error is coordinated as the twin shaft designed below is introduced, is defined as:
E=e+ α ε=(I+ α T) e
The wherein synchronous error proportionality coefficient that α is positive;There are e → 0, ε → 0 in obvious E → 0 item;
To tracking double-shaft moving system, mathematical model is writeable are as follows:
Q=[q in formula1,q2]TFor vector composed by the respective freedom degree direction of double drive, J=diag { J1,J2Be etc. The inertial matrix of effect, Ff=[f1,f2]TFor with speedRelevant non-linear friction item, d=[d1,d2]TIt is disturbed for extraneous outside It is dynamic, u=[u1,u2]TFor the input torque of each axis;
By attached drawing 2 it is found that the expression formula of the control amount u of double drive coordinated movement of various economic factors synchronously control proposed by the present invention are as follows:
In formulaFor the estimation of inertial matrix J, c=diag { c1,c2It is sliding-mode surface parameter matrix,For the PD feedback control amount of position synchronous error, KD、KEPAnd KEDIt is the parameter square of positive value for element Battle array, c are the constant greater than 0, and sgn (s) is sign function, and G is the gravity compensation on vertical direction, q=[q1,q2]TFor double drive Vector composed by respective freedom degree direction, qdFor the d power of coordinate q, the d power that the second order in formula for q is led, the i.e. seat Put on the d power of acceleration, s be sliding formwork functional vector andE is feed back input amount and E=(I+ α T) e, I is Unit matrix, the synchronous error proportionality coefficient that α is positive,E=[e1 e2]T, e1And e2For the position of twin shaft, KNIncludeThe compensation term and interference upper bound D and satisfaction of evaluated error WithFor the adaptive friction compensation item and satisfaction of each axisΘiFor Fuzzy system parameter vector and its rate of approaching is designed as Θi=-s Γiξi, Γ is Strict Positive Real constant;
S5. the double drive traffic signal coordination established using step S4 controls existing single shaft+The gear deceleration driving System, to complete double drive coordinated movement of various economic factors synchronously control.

Claims (6)

1. a kind of double drive coordinated movement of various economic factors synchronisation control means, includes the following steps:
S1. it is directed to existing single shaft+The gear deceleration driving method, establishes kinematics model;
S2. it is directed to single axial movement, design self-adapting fuzzy frictional compensation device compensates the non-linear friction of system;
S3. the robustness of system is improved using global synovial membrane control algolithm;
S4. the double drive traffic signal coordination based on the control of two shaft position error couplers is established;
S5. the double drive traffic signal coordination established using step S4 controls existing single shaft+The gear deceleration driving, from And complete double drive coordinated movement of various economic factors synchronously control.
2. double drive coordinated movement of various economic factors synchronisation control means according to claim 1, it is characterised in that needle described in step S1 To existing single shaft+The gear deceleration driving method, kinematics model is established, specially establishes kinematics mould using following steps Type:
A. moment of friction suffered by system is equivalent on motor shaft, and the uncertainty of model is equivalent to distracter, thus According to following formula founding mathematical models:
J in formulamFor total rotary inertia of motor and transmission mechanism, θmFor motor angular displacement, f (t) is that system is converted onto motor shaft Moment of friction, TaFor transmission mechanism output torque, d (t) is system parameter uncertainty item and external interference item, and u (t) is electricity Machine output torque, TbFor transmission mechanism input torque, θ is load axis angular displacement, and i is reduction ratio, JbFor load rotating inertia;
B. the mathematical model obtained according to step A, using following formula to establish with motor torque is input, load axis angular displacement is The dynamic property equation of output:
J=J in formulab/i+iJm
3. double drive coordinated movement of various economic factors synchronisation control means according to claim 2, it is characterised in that set described in step S2 Self-adapting fuzzy frictional compensation device is counted, is specially designed using following steps:
A. the input sample point in input space U is transformed into the fuzzy set A in output SPACE V by fuzzy devicelIn;
B. according to the rule in knowledge base, the fuzzy subset of V can be mapped to fuzzy rule R by inference machinemFuzzy subset in;
C. defuzzifier is again by fuzzy rule RmIn fuzzy set be mapped to discrete point set RnIn;
D. weighted mean method is used, using the output F of following formula computing systemi:
J=1 in formula, 2 ..., M, M are the sum of rule,L=1, 2 ..., M,For free parameter and composition vector For subordinating degree function, xi For input variable.
4. double drive coordinated movement of various economic factors synchronisation control means according to claim 3, it is characterised in that complete described in step S3 Office's synovial membrane control algolithm, specifically comprises the following steps:
(1) using following formula as global sliding mode function s:
E is tracking error and e=θ-θ in formulad, θ is actual motion track, θdFor ideal motion profile, c is normal greater than 0 Number, g (t) is that the function and g (t) designed to reach global sliding mode must satisfy following 3 conditions: condition 1:G (t) → 0 when condition 2:t → ∞;Condition 3:g (t) has first derivative;
(2) using following formula as control law:
In formulaFor the estimated value of J, Δ J isMaximum deviation, D be disturb d (t) maximum value, g be g (t) abbreviation, KDFor Positive control gain, sgn (s) are sign function,For the output valve of self-adapting fuzzy frictional compensation device.
5. double drive coordinated movement of various economic factors synchronisation control means according to claim 4, it is characterised in that described in order to reach Global sliding mode and the function expression of function g (t) designed is g (t)=g (0) e-kt
6. double drive coordinated movement of various economic factors synchronisation control means according to claim 5, it is characterised in that built described in step S4 The double drive traffic signal coordination of the two shaft position error couplers that are based on control specially is coordinated to transport using formula as double drive The control amount u of dynamic synchronously control:
In formulaFor the estimation of inertial matrix J, c=diag { c1,c2It is sliding-mode surface parameter matrix,For the PD feedback control amount of position synchronous error, KD、KEPAnd KEDIt is the parameter square of positive value for element Battle array, c are the constant greater than 0, and sgn (s) is sign function, and G is the gravity compensation on vertical direction, q=[q1,q2]TFor double drive Vector composed by respective freedom degree direction, qdFor the d power of coordinate q, s be sliding formwork functional vector andE is Feed back input amount and E=(I+ α T) e, I are unit matrix, the synchronous error proportionality coefficient that α is positive,E= [e1 e2]T, e1And e2For the position of twin shaft, KNIncludeThe compensation term of evaluated error and interference upper bound D and meet KN=[KN1, KN2,KN3,KN4]TWith | di(t)|≤DiFor the adaptive friction compensation item and satisfaction of each axisΘiFor fuzzy system parameter to It measures and its rate of approaching is designed as Θi=-s Γiξi, Γ is Strict Positive Real constant.
CN201910161291.5A 2019-03-04 2019-03-04 Double drive coordinated movement of various economic factors synchronisation control means Pending CN109839826A (en)

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CN110879567A (en) * 2019-11-29 2020-03-13 中国科学院微电子研究所 Synchronous control method and system
CN112904707A (en) * 2019-12-04 2021-06-04 中南大学 Synchronous control method of dual-drive vertical lifting servo system under variable load condition
CN112904707B (en) * 2019-12-04 2022-05-20 中南大学 Synchronous control method of dual-drive vertical lifting servo system under variable load condition
CN111281743A (en) * 2020-02-29 2020-06-16 西北工业大学 Self-adaptive flexible control method for exoskeleton robot for upper limb rehabilitation
CN112147942A (en) * 2020-10-26 2020-12-29 西安工业大学 FPGA + DSP-based dual-motion platform synchronous control system and control method
CN112799304A (en) * 2021-01-06 2021-05-14 武汉理工大学 Dual-motor synchronous control method and device based on time-varying friction compensation
CN112799304B (en) * 2021-01-06 2022-06-14 武汉理工大学 Dual-motor synchronous control method and device based on time-varying friction compensation
CN112904741A (en) * 2021-01-14 2021-06-04 上海交通大学 High-precision synchronous control method and system for double-drive gantry truss system
CN115580189A (en) * 2022-11-08 2023-01-06 哈尔滨工业大学 High-speed gantry double-drive synchronous control method and system with disturbance suppression function
CN115580189B (en) * 2022-11-08 2023-07-25 哈尔滨工业大学 High-speed gantry double-drive synchronous control method and system with disturbance suppression

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