CN111386029A - High-precision synchronous control method and system for double-drive motion platform - Google Patents

High-precision synchronous control method and system for double-drive motion platform Download PDF

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CN111386029A
CN111386029A CN202010105956.3A CN202010105956A CN111386029A CN 111386029 A CN111386029 A CN 111386029A CN 202010105956 A CN202010105956 A CN 202010105956A CN 111386029 A CN111386029 A CN 111386029A
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double
linear motor
drive linear
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CN111386029B (en
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高会军
刘志太
潘惠惠
孙维超
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Harbin Institute of Technology
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    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05K—PRINTED CIRCUITS; CASINGS OR CONSTRUCTIONAL DETAILS OF ELECTRIC APPARATUS; MANUFACTURE OF ASSEMBLAGES OF ELECTRICAL COMPONENTS
    • H05K13/00—Apparatus or processes specially adapted for manufacturing or adjusting assemblages of electric components
    • H05K13/08—Monitoring manufacture of assemblages
    • H05K13/0882—Control systems for mounting machines or assembly lines, e.g. centralized control, remote links, programming of apparatus and processes as such
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/06—Linear motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors
    • H02P5/46—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another

Abstract

The invention relates to a high-precision synchronous control method and system for a double-drive motion platform. The method comprises the following steps: determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law; obtaining a double-drive linear motor state equation according to the double-drive linear motor model; according to the double-drive linear motor model and the double-drive linear motor state equation, a cross coupling control idea is adopted, and a low-complexity cross coupling synchronous controller of a double-drive linear motor system is designed; acquiring a preset performance requirement; and adjusting the parameters of the low-complexity cross-coupling synchronous controller according to the preset performance requirement. The invention not only can realize the synchronous control of the double-drive linear motor in the field of the high-speed high-precision chip mounter at present, but also can solve the problems of high control difficulty, low precision and the like caused by the complex system model, the uncertainty of parameter change, external disturbance and the like.

Description

High-precision synchronous control method and system for double-drive motion platform
Technical Field
The invention relates to the field of synchronous control of double-drive motion platforms, in particular to a high-precision synchronous control method and system of a double-drive motion platform.
Background
At present, in the field of high-speed high-precision chip mounters, linear motors are widely applied because the linear motors are directly connected with loads, mechanical transmission devices are eliminated, and various complex problems caused by mechanical transmission are fundamentally eliminated. The mechanical structure of the chip mounter has two types of a single-side driving type and a double-side driving type, the motion of each shaft in the single-side driving type is driven by a single motor, and the maximum load shaft in the double-side driving type is driven by two parallel motors together. The unilateral driving type has the advantages that due to the structural characteristics of the unilateral driving type, the motion of a non-driving side can be delayed, and the load can be vibrated seriously, so that the mounting effect of the chip mounter is greatly influenced. The double-sided driving type can produce a larger thrust, a faster response speed, and excellent motion characteristics. Therefore, the double-side driving type framework is widely applied in the field of high-speed and high-precision chip mounters.
In the dual-drive linear motor system, although the two sides have the same driving mechanism, the motors on the two sides have synchronization errors due to load change, motion, mechanical component change and the like. Not only can the tracking error of a single motor influence the mounting effect of the chip mounter, but also the synchronous error of the motors on two sides can influence the mounting effect, and even the excessive synchronous error can cause the overcurrent protection of the motors to stop working. Therefore, due to the increase of the demand in the field of high-speed and high-precision chip mounters, a simple and efficient control method for designing a dual-drive linear motor system is a practical problem worthy of deep discussion. The simpler the controller, the higher the control bandwidth, the smaller the tracking error and the synchronization error, and the better the high-speed and high-precision effect. Summarizing the control method of the existing bilateral driving linear motor system, the following defects mainly exist:
firstly, the controller is complex in structure and has no good robustness. In the existing control method, the uncertainty such as parameter change, external disturbance and the like in the model is subjected to approximate processing under certain assumed conditions, which easily causes the poor robustness of the controller. In practical application, load changes, motion in the system, and changes in mechanical components all cause some of the controllers to change, and the controllers need to be identified again to obtain accurate controllers, otherwise, the control accuracy is affected.
Secondly, the steady-state performance and the transient performance of the system cannot be determined a priori. In the existing results, most controllers can ensure that the system error converges to a residual error set, but the size of the residual error set depends on design parameters in the controllers and some unknown bounded terms in the model, so the steady-state performance of the system cannot be determined a priori. Also, these controllers cannot determine the system transient performance a priori. In practical application, the steady-state performance and the transient performance of the system are closely related to the physical characteristics and the safety guarantee of the system.
Thirdly, the controller relies on the mathematical description of the reference trajectory and its derivatives. In most existing controller implementations, not only a mathematical expression of the reference trajectory is required, but also a higher order derivative of the reference trajectory. However, in the mounting process of the mounter, the system can only acquire some discrete target positions in real time, which brings great difficulty to the application of the controller.
Disclosure of Invention
The invention aims to provide a high-precision synchronous control method and system for a double-drive motion platform, which can realize synchronous control of a double-drive linear motor in the field of high-speed high-precision chip mounters at present, and can solve the problems of high control difficulty, low precision and the like caused by the complex system model, parameter change, external disturbance and other uncertainties.
In order to achieve the purpose, the invention provides the following scheme:
a high-precision synchronous control method for a dual-drive motion platform comprises the following steps:
determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law;
obtaining a double-drive linear motor state equation according to the double-drive linear motor model;
according to the double-drive linear motor model and the double-drive linear motor state equation, a cross coupling control idea is adopted, and a low-complexity cross coupling synchronous controller of a double-drive linear motor system is designed;
acquiring a preset performance requirement;
and adjusting the parameters of the low-complexity cross-coupling synchronous controller according to the preset performance requirement.
Optionally, the determining a dual-drive linear motor model according to the dual-drive linear motor system and a newton's second law specifically includes:
determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law:
Figure BDA0002387995710000021
wherein the content of the first and second substances,
Figure BDA0002387995710000031
is a vector of the velocity of the beam,
Figure BDA0002387995710000032
is the acceleration vector, M is the 2 × 2 inertia diagonal matrix, B is the 2 × 2 viscous friction coefficient diagonal matrix;
Figure BDA0002387995710000033
is a 2 × 1 coulomb friction vector, u is a 2 × 1 control input vector, and d is a 2 × 1 double-drive linear motor system uncertainty vector.
Optionally, the obtaining a state equation of the dual-drive linear motor according to the dual-drive linear motor model specifically includes:
obtaining a double-drive linear motor state equation according to the double-drive linear motor model:
Figure BDA0002387995710000034
Figure BDA0002387995710000035
y＝x1；
wherein x is1And x2Respectively state variables.
Optionally, the designing of the low-complexity cross-coupling synchronous controller of the dual-drive linear motor system according to the dual-drive linear motor model and the dual-drive linear motor state equation by using a cross-coupling control concept specifically includes:
determining the comprehensive error of the dual-drive linear motor system by adopting a cross coupling control idea according to the dual-drive linear motor model and the dual-drive linear motor state equation;
constructing a performance function according to the comprehensive error of the dual-drive linear motor system;
and designing a low-complexity cross coupling synchronous controller of the double-drive linear motor system according to the performance function.
A high-precision synchronous control system for a dual-drive motion platform comprises:
the double-drive linear motor model determining module is used for determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law;
the double-drive linear motor state equation determining module is used for obtaining a double-drive linear motor state equation according to the double-drive linear motor model;
the controller design module is used for designing a low-complexity cross coupling synchronous controller of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation;
the performance requirement acquisition module is used for acquiring a preset performance requirement;
and the controller parameter adjusting module is used for adjusting the parameters of the low-complexity cross-coupling synchronous controller according to the preset performance requirement.
Optionally, the module for determining a model of a dual-drive linear motor specifically includes:
the double-drive linear motor model determining unit is used for determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law:
Figure BDA0002387995710000041
wherein the content of the first and second substances,
Figure BDA0002387995710000042
is a vector of the velocity of the beam,
Figure BDA0002387995710000043
is the acceleration vector, M is the 2 × 2 inertia diagonal matrix, B is the 2 × 2 viscous friction coefficient diagonal matrix;
Figure BDA0002387995710000044
is a 2 × 1 coulomb friction vector, u is a 2 × 1 control input vector, and d is a 2 × 1 double-drive linear motor system uncertainty vector.
Optionally, the dual-drive linear motor state equation determining module specifically includes:
the double-drive linear motor state equation determining unit is used for obtaining a double-drive linear motor state equation according to the double-drive linear motor model:
Figure BDA0002387995710000045
Figure BDA0002387995710000046
y＝x1；
wherein x is1And x2Respectively state variables.
Optionally, the controller design module specifically includes:
the comprehensive error determining unit is used for determining the comprehensive error of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation;
the performance function constructing unit is used for constructing a performance function according to the comprehensive error of the dual-drive linear motor system;
and the controller design unit is used for designing the low-complexity cross coupling synchronous controller of the double-drive linear motor system according to the performance function.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a high-precision synchronous control method and system for a double-drive motion platform, and solves the problems that in the design of a control scheme of a double-drive linear motor system in the existing high-speed high-precision chip mounter, a controller is complex, the control precision is not high, and the control effect cannot be preset. According to a Newton second law, considering uncertainties such as viscous friction, coulomb friction, external disturbance and model errors existing in the system, and establishing a model of the dual-drive linear motor system; meanwhile, the comprehensive error of the system is determined according to the idea of cross-coupling control, and a cross-coupling synchronous controller with low complexity is designed, so that the system can realize high-speed and high-precision synchronous control under the condition that uncertainty such as model error, parameter change, external disturbance and the like exists, and the comprehensive error of the system can meet the preset performance. And experiments are carried out on the double-drive linear motor platform, the effectiveness of the proposed controller method is verified, and the purpose of realizing high-speed high-precision synchronous control is achieved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a high-precision synchronous control method for a dual-drive motion platform according to the present invention;
FIG. 2 is a schematic diagram of a dual drive linear motor system according to the present invention;
FIG. 3 is a pictorial view of the experimental platform of the dual-drive linear motor in accordance with example 1;
FIG. 4 is a response curve of linear motor displacement over time as referred to in example 1;
FIG. 5 is a response curve of the composite error of the linear motor related to example 1 over time;
FIG. 6 is a response curve of the linear motor synchronization error over time as referred to in example 1;
fig. 7 is a response curve of a linear motor control signal relating to example 1;
fig. 8 is a structural diagram of the high-precision synchronous control system of the dual-drive motion platform of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a high-precision synchronous control method and system for a double-drive motion platform, which can realize synchronous control of a double-drive linear motor in the field of high-speed high-precision chip mounters at present, and can solve the problems of high control difficulty, low precision and the like caused by the complex system model, parameter change, external disturbance and other uncertainties.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1:
FIG. 1 is a flow chart of a high-precision synchronous control method for a dual-drive motion platform according to the present invention. As shown in fig. 1, a high-precision synchronous control method for a dual-drive motion platform includes:
step 101: according to a double-drive linear motor system and a Newton second law, determining a double-drive linear motor model, which specifically comprises the following steps:
determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law:
Figure BDA0002387995710000061
wherein the content of the first and second substances,
Figure BDA0002387995710000062
is a vector of the velocity of the beam,
Figure BDA0002387995710000063
is the acceleration vector, M is the 2 × 2 inertia diagonal matrix, B is the 2 × 2 viscous friction coefficient diagonal matrix;
Figure BDA0002387995710000064
is a 2 × 1 coulomb friction vector, u is a 2 × 1 control input vector, d is a 2 × 1 double-drive linear motor system uncertainty vector, q ═ y1(t),y2(t)]T，
Figure BDA0002387995710000065
Figure BDA0002387995710000066
M＝diag[M1,M2]，B＝diag[B1,B2]，
Figure BDA0002387995710000067
u＝[u1,u2]T，d＝[d1,d2]T. The uncertainty vector of the double-drive linear motor system comprises model errors, parameter changes, external disturbance and the like.
Figure BDA0002387995710000068
Smooth friction models are commonly used to approximate the coulomb friction, i.e.
Figure BDA0002387995710000069
A＝diag[A1,A2]TIs a 2 × 2 coulomb coefficient of friction diagonal matrix,
Figure BDA00023879957100000610
Sc1(. and S)c2(. is a smooth function for approximating a symbolic function, qd＝[y1d,y2d]TWhich is used to indicate the reference position of the linear motor.
Step 102: and obtaining a state equation of the double-drive linear motor according to the double-drive linear motor model.
The above steps can also be used for rewriting the state equation of the double-drive linear motor system. Defining a state variable x1＝q＝[x1,1,x1,2]T，x2＝q＝[x2,1,x2,2]T，x1And x2Respectively, state variables, and rewriting a double-drive linear motor model expressed by the formula (1) into a double-drive linear motor state equation:
Figure BDA0002387995710000071
Figure BDA0002387995710000072
y＝x1(2)。
step 103: according to the double-drive linear motor model and the double-drive linear motor state equation, a cross coupling control idea is adopted, and a low-complexity cross coupling synchronous controller of a double-drive linear motor system is designed, and the method specifically comprises the following steps:
and determining the comprehensive error of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation.
And constructing a performance function according to the comprehensive error of the double-drive linear motor system.
And designing a low-complexity cross coupling synchronous controller of the double-drive linear motor system according to the performance function.
Step 104: and acquiring a preset performance requirement.
Step 105: and adjusting the parameters of the low-complexity cross-coupling synchronous controller according to the preset performance requirement.
Adjusting a parameter k in a controlleri,j，
Figure BDA0002387995710000073
μi,jβ, i, j is 1,2, makes the double-drive linear motor system realize better synchronous control effect, and the tracking error and the synchronous error of system are all as little as possible promptly, satisfy preset performance requirement to double linear motor can stably and accurately track the reference track.
Fig. 2 is a schematic diagram of a mechanism of a dual-drive linear motor system according to the present invention. As shown in FIG. 2, the working platform has two axes of X and Y, arrow Y indicates the positive direction of Y axis, and the Y axis in the research platform has two linear motors of Y1 and Y2, respectively, and the research content is the synchronous control problem of the two linear motors of Y1 and Y2. The X-axis is another linear motor in the stage connected to Y1 and Y2, and is not within the scope of this patent study, and the labels in the figures are for illustration of the stage structure only. See the physical diagram in fig. 3.
Example 2:
unlike embodiment 1, in the high-precision synchronous control method for a dual-drive motion platform of this embodiment, in step 103, the process of determining the system comprehensive error is to define the tracking error as e ═ e1,e2]TDefining the synchronization error as ∈ ═ epsilon1,ε2]TDefining the composite error as z1＝[z1,1,z1,2]TThe specific expression is as follows:
e＝x1-x1d(3)
ε1＝e1-e2,ε2＝e2-e1(4)
z1＝e+βε (5)
wherein x is1d＝qdβ is a positive cross-coupling parameter.
Example 3:
different from embodiment 1 or 2, in the high-precision synchronous control method for the dual-drive motion platform of this embodiment, in step 103, the process of constructing the preset performance function is to construct the following preset performance function, which represents the prior condition that the steady-state performance and the transient performance of the state error of the dual-drive linear motor system are to meet:
Figure BDA0002387995710000081
wherein
Figure BDA0002387995710000082
μi,j＞0。
Figure BDA0002387995710000083
And mui,jAnd > 0 represents the maximum initial value constraint, the maximum steady state error and the minimum convergence rate of the system state error respectively.
Figure BDA0002387995710000084
Is selected to satisfy the following conditions:
Figure BDA0002387995710000085
wherein z isi,j(0) Is the initial value of the composite error.
Example 4:
different from embodiment 3, in the high-precision synchronous control method for the dual-drive motion platform of this embodiment, the design process of the low-complexity cross-coupled synchronous controller in step 103 is as follows:
(1) the intermediate controller a is designed. For the dual-drive linear motor models described in equations (1) and (2), an intermediate controller a ═ a is designed1,a2]THas the following forms:
a＝-k1P1(8)
wherein k is1＝diag[k1,1,k1,2]Is a control gain matrix, k1,1＞0，k1,2Control gain factor positive > 0; p1＝[P1,1,P1,2]TIs a variable in formula (8) satisfying:
Figure BDA0002387995710000086
(2) the final model output controller u is designed. First an intermediate control error z is defined2＝[z2,1,z2,2]THas the following forms:
z2＝x2-a (10)
for the dual-drive linear motor models described in equations (1) and (2), the final model output controller u ═ u is designed1,u2]THas the following forms:
u＝-k2P2(11)
wherein k is2＝diag[k2,1,k2,2]Control gain matrix, k2,1＞0，k2,2Control gain factor positive > 0; p2＝[P2,1,P2,2]TIs a variable in formula (11) satisfying:
Figure BDA0002387995710000091
example 5:
different from embodiment 4, in the high-precision synchronous control method for the dual-drive motion platform of the present embodiment, the process that the system comprehensive error satisfies the preset performance in step 103 is as follows:
defining normalized error state vector ξ ═ ξ1,1,ξ1,2,ξ2,1,ξ2,2]TWherein
Figure BDA0002387995710000092
Derived from the normalized error ξ
Figure BDA0002387995710000093
Wherein
Figure BDA0002387995710000094
Figure BDA0002387995710000095
Figure BDA0002387995710000096
Figure BDA0002387995710000097
Wherein
Figure BDA0002387995710000098
Define open set omegaξ
Figure BDA0002387995710000099
From the formulae (7) and (13) it is possible to obtain a molar ratio of-1 < ξi,j(0) < 1, so ξ (0) ∈. omegaξAt the same time, because
(1) The nonlinear part in the double-drive linear motor models (1) and (2) meets the local Ripises condition;
(2) reference track qdContinuous smoothness of and its derivatives are bounded;
(3) the proposed intermediate controller a and the continuous smoothness of the control signal u.
ξ (t) can be obtained at time [0, τmax) Has existence and uniqueness, and satisfies
Figure BDA0002387995710000101
Example 6:
different from embodiment 1, in the high-precision synchronous control method for the dual-drive motion platform of this embodiment, step 105 illustrates that both the tracking error and the synchronization error of the dual-drive linear motor are as small as possible, and the process that the reference trajectory can be accurately tracked is as follows:
(1) defining a Lyapunov function:
Figure BDA0002387995710000102
definition of x1＝[χ1,1,χ1,2]TWherein
Figure BDA0002387995710000103
Definition of κ ═ κ1,κ2]TWherein κ isj＝ξ2,jρ2,j，j＝1,2。
To V1And obtaining by derivation:
Figure BDA0002387995710000104
wherein
Figure BDA0002387995710000105
By the formula (19),
Figure BDA0002387995710000106
the degree of boundedness of the key board,
Figure BDA0002387995710000107
is bounded and theta1,j＞0，k1,jIs greater than 0, j is 1,2
Figure BDA0002387995710000108
Wherein
Figure BDA0002387995710000109
Γ1＝[Γ1，1,Γ1，2]TIs a vector of 2 × 1, and
Figure BDA00023879957100001010
Figure BDA00023879957100001011
k 1＝min{k1，1，k1，2}。
from the formula (21), when
Figure BDA00023879957100001012
When the temperature of the water is higher than the set temperature,
Figure BDA00023879957100001013
so that there are
Figure BDA0002387995710000111
From equation (22), the intermediate control signal a and its derivatives
Figure BDA0002387995710000112
At a time interval [0, τ ]max) The inside is bounded.
(2) Defining a Lyapunov function:
Figure BDA0002387995710000113
definition of x2＝[χ2,1,χ2,2]TWherein
Figure BDA0002387995710000114
To V2And obtaining by derivation:
Figure BDA0002387995710000115
wherein
Figure BDA0002387995710000116
By the formula (19),
Figure BDA0002387995710000117
the degree of boundedness of the key board,
Figure BDA0002387995710000118
is bounded by k1,jAvailable > 0
Figure BDA0002387995710000119
Wherein gamma is2＝-M-1Bx2-M-1Fc(x2)+M-1d-χ2I.e. by
Figure BDA00023879957100001110
Figure BDA00023879957100001111
k 2＝min{k2，1，k2，2}。
Obtainable from formula (24) when
Figure BDA00023879957100001112
When the temperature of the water is higher than the set temperature,
Figure BDA00023879957100001113
and is provided with
Figure BDA00023879957100001114
As can be seen from equation (25), the control output u is controlled over a time period [0, τ ]max) The inside is bounded.
Example 7:
different from embodiment 6, in the high-precision synchronous control method for the dual-drive motion platform of this embodiment, the step four is to make the tracking error and the synchronous error of the dual-drive linear motor as small as possible, and the process of stably tracking the reference trajectory is as follows:
from the formulae (9), (12), (13) and (19),
Figure BDA0002387995710000121
that is to say
Figure BDA0002387995710000122
Wherein
Figure BDA0002387995710000123
Is a non-empty compact set, and
Figure BDA0002387995710000124
let τ bemaxInfinity, so there is a point in time t' ∈ [0, τmax]So that
Figure BDA0002387995710000125
Clearly contradict the above results. Thus τmaxInfinity. All closed loop signals in the system are bounded and
Figure BDA0002387995710000126
the above description shows that the dual-drive motion platform can stably track the reference track.
Example 8:
in the experimental platform of the dual-drive linear motor system shown in fig. 3, the inertia coefficients are M respectively1＝0.3125(V/m/s2)，M2＝0.3125(V/m/s2) (ii) a Viscous friction coefficient of B1＝0.6(V/m/s)，B20.6 (V/m/s); the coefficient of coulomb friction is A1＝0.145(V)，A20.145 (V); the approximate model of the coulomb friction is
Figure BDA0002387995710000127
Selecting parameters of a controller: the initial value of the motor is x in the initial state of the system1,1＝0，x1,20; the preset performance parameter is selected as
Figure BDA0002387995710000128
μ1,1＝2，
Figure BDA0002387995710000129
μ1,2＝2，
Figure BDA00023879957100001210
μ2,1＝2，
Figure BDA00023879957100001211
μ 2,22; the gain parameter of the controller is selected as k1,1＝8000，k1,2＝15，k2,1＝8000，k2,2＝15。
The low-complexity cross-coupling synchronous controller has the following effects:
selecting the reference track of the system as x1d,1＝10sin(π/2×t)，x1d,210sin (pi/2 × t), where 10mm is the amplitude.
Fig. 4 is a response curve of linear motor displacement over time according to example 1.
Fig. 5 is a response curve of the composite error of the linear motor related to example 1 with time. Compared with the traditional PID method, the method can obtain better effect and meet the preset performance of design.
Fig. 6 is a response curve of the synchronous error of the linear motor related to example 1 with time. Compared with the traditional PID method, the synchronization control method can realize better synchronization effect.
Fig. 7 is a response curve of a linear motor control signal according to example 1. Compared with the traditional PID method, the control signal oscillation of the synchronous control method is smaller.
Example 9:
corresponding to the method of the embodiment 1, the invention also provides a high-precision synchronous control system of the double-drive motion platform. Fig. 8 is a structural diagram of the high-precision synchronous control system of the dual-drive motion platform of the invention. As shown in fig. 8, a high-precision synchronous control system for a dual-drive motion platform includes:
and the double-drive linear motor model determining module 201 is used for determining a double-drive linear motor model according to a double-drive linear motor system and a Newton's second law.
And the double-drive linear motor state equation determining module 202 is configured to obtain a double-drive linear motor state equation according to the double-drive linear motor model.
And the controller design module 203 is used for designing a low-complexity cross coupling synchronous controller of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation.
A performance requirement obtaining module 204, configured to obtain a preset performance requirement.
A controller parameter adjusting module 205, configured to adjust a parameter of the low-complexity cross-coupled synchronous controller according to the preset performance requirement.
The module 201 for determining a dual-drive linear motor model specifically includes:
the double-drive linear motor model determining unit is used for determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law:
Figure BDA0002387995710000131
wherein the content of the first and second substances,
Figure BDA0002387995710000132
is a vector of the velocity of the beam,
Figure BDA0002387995710000133
is the acceleration vector, M is the 2 × 2 inertia diagonal matrix, B is the 2 × 2 viscous friction coefficient diagonal matrix;
Figure BDA0002387995710000134
is a 2 × 1 coulomb friction vector, u is a 2 × 1 control input vector, and d is a 2 × 1 double-drive linear motor system uncertainty vector.
The double-drive linear motor state equation determining module 202 specifically includes:
the double-drive linear motor state equation determining unit is used for obtaining a double-drive linear motor state equation according to the double-drive linear motor model:
Figure BDA0002387995710000141
Figure BDA0002387995710000142
y＝x1；
wherein x is1And x2Respectively state variables.
The controller design module 203 specifically includes:
and the comprehensive error determining unit is used for determining the comprehensive error of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation.
And the performance function constructing unit is used for constructing a performance function according to the comprehensive error of the dual-drive linear motor system.
And the controller design unit is used for designing the low-complexity cross coupling synchronous controller of the double-drive linear motor system according to the performance function.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (8)

1. A high-precision synchronous control method for a dual-drive motion platform is characterized by comprising the following steps:
determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law;
obtaining a double-drive linear motor state equation according to the double-drive linear motor model;
according to the double-drive linear motor model and the double-drive linear motor state equation, a cross coupling control idea is adopted, and a low-complexity cross coupling synchronous controller of a double-drive linear motor system is designed;
acquiring a preset performance requirement;
and adjusting the parameters of the low-complexity cross-coupling synchronous controller according to the preset performance requirement.
2. The high-precision synchronous control method for the double-drive motion platform according to claim 1, wherein the determining a double-drive linear motor model according to a double-drive linear motor system and Newton's second law specifically comprises:
determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law:
Figure FDA0002387995700000011
wherein the content of the first and second substances,
Figure FDA0002387995700000012
is a vector of the velocity of the beam,
Figure FDA0002387995700000013
is the acceleration vector, M is the 2 × 2 inertia diagonal matrix, B is the 2 × 2 viscous friction coefficient diagonal matrix;
Figure FDA0002387995700000014
is a 2 × 1 coulomb friction vector, u is a 2 × 1 control input vector, and d is a 2 × 1 double-drive linear motor system uncertainty vector.
3. The high-precision synchronous control method for the double-drive motion platform according to claim 2, wherein the obtaining of the state equation of the double-drive linear motor according to the double-drive linear motor model specifically comprises:
obtaining a double-drive linear motor state equation according to the double-drive linear motor model:
Figure FDA0002387995700000015
Figure FDA0002387995700000016
y＝x1；
wherein x is1And x2Respectively state variables.
4. The high-precision synchronous control method for the double-drive motion platform according to claim 1, wherein the designing of the low-complexity cross-coupling synchronous controller for the double-drive linear motor system by adopting a cross-coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation specifically comprises:
determining the comprehensive error of the dual-drive linear motor system by adopting a cross coupling control idea according to the dual-drive linear motor model and the dual-drive linear motor state equation;
constructing a performance function according to the comprehensive error of the dual-drive linear motor system;
and designing a low-complexity cross coupling synchronous controller of the double-drive linear motor system according to the performance function.
5. The utility model provides a two motion platform high accuracy synchronous control systems that drive which characterized in that includes:
the double-drive linear motor model determining module is used for determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law;
the double-drive linear motor state equation determining module is used for obtaining a double-drive linear motor state equation according to the double-drive linear motor model;
the controller design module is used for designing a low-complexity cross coupling synchronous controller of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation;
the performance requirement acquisition module is used for acquiring a preset performance requirement;
and the controller parameter adjusting module is used for adjusting the parameters of the low-complexity cross-coupling synchronous controller according to the preset performance requirement.
6. The high-precision synchronous control system for the dual-drive motion platform according to claim 5, wherein the dual-drive linear motor model determining module specifically comprises:
the double-drive linear motor model determining unit is used for determining a double-drive linear motor model according to a double-drive linear motor system and a Newton second law:
Figure FDA0002387995700000021
wherein the content of the first and second substances,
Figure FDA0002387995700000022
is a vector of the velocity of the beam,
Figure FDA0002387995700000023
is the acceleration vector, M is the 2 × 2 inertia diagonal matrix, B is the 2 × 2 viscous friction coefficient diagonal matrix;
Figure FDA0002387995700000024
is a 2 × 1 coulomb friction vector, u is a 2 × 1 control input vector, and d is a 2 × 1 double-drive linear motor system uncertainty vector.
7. The high-precision synchronous control system for the double-drive motion platform according to claim 6, wherein the double-drive linear motor state equation determining module specifically comprises:
the double-drive linear motor state equation determining unit is used for obtaining a double-drive linear motor state equation according to the double-drive linear motor model:
Figure FDA0002387995700000031
Figure FDA0002387995700000032
y＝x1；
wherein x is1And x2Respectively state variables.
8. The high-precision synchronous control system for the dual-drive motion platform as claimed in claim 5, wherein the controller design module specifically comprises:
the comprehensive error determining unit is used for determining the comprehensive error of the double-drive linear motor system by adopting a cross coupling control idea according to the double-drive linear motor model and the double-drive linear motor state equation;
the performance function constructing unit is used for constructing a performance function according to the comprehensive error of the dual-drive linear motor system;
and the controller design unit is used for designing the low-complexity cross coupling synchronous controller of the double-drive linear motor system according to the performance function.
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