CN107272422B - Multivariable constraint control method of chip mounter driving system based on reference regulator - Google Patents

Multivariable constraint control method of chip mounter driving system based on reference regulator Download PDF

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CN107272422B
CN107272422B CN201710682236.1A CN201710682236A CN107272422B CN 107272422 B CN107272422 B CN 107272422B CN 201710682236 A CN201710682236 A CN 201710682236A CN 107272422 B CN107272422 B CN 107272422B
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刘延斌
孙维超
高会军
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Harbin Institute of Technology
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Abstract

The invention discloses a multivariable constraint control method of a chip mounter driving system based on a reference regulator, and relates to the multivariable constraint control method of the chip mounter driving system. The invention aims to solve the problems that the starting system of the chip mounter is damaged due to overlarge speed in the moving process or the chip mounter cannot work normally due to the fact that the control input exceeds the maximum input provided by the chip mounter and the like. The invention comprises the following steps: firstly, establishing a dynamic model of a chip mounter driving system moving along an x axis or a y axis, and determining constraint conditions borne by the chip mounter driving system; designing a sampling controller for a chip mounter driving system; predicting the state of the chip mounter driving system and the size of control input when the reference signal does not change under the condition of assuming unmodeled dynamics of the chip mounter driving system and the condition that external disturbance is a constant value; and fourthly, designing a reference regulator to enable the chip mounter driving system to meet the constraint condition in the first step. The method is used for the field of multivariable constraint control of the chip mounter motion system.

Description

Multivariable constraint control method of chip mounter driving system based on reference regulator
Technical Field
The invention relates to the field of multivariable constraint control of a chip mounter motion system, in particular to a multivariable constraint control method of a chip mounter driving system.
Background
In the working process of the chip mounter, according to different requirements, the chip mounter mobile platform is required to meet certain constraint conditions in the movement process, for example, the chip mounter mobile platform must move in a certain range, otherwise, the chip mounter mobile platform is caused to impact the edge of the chip mounter, and damage is caused to chip mounter equipment; the moving speed of the mobile platform of the chip mounter cannot reach infinity, or the moving speed of the mobile platform cannot be too high due to the limitation of the environment where the chip mounter is located; moreover, when the chip mounter works, the maximum voltage and current which can be provided for the chip mounter driving system are limited, namely the maximum control input which can be provided by the chip mounter driving system is limited, and when the required control input quantity exceeds the maximum value which can be provided by the shoe and the driving system, the chip mounter can not work normally. In order to solve the problem that the systems are constrained, a multivariable constraint control method based on a reference regulator needs to be provided.
Disclosure of Invention
The invention aims to solve the problems that the conventional chip mounter driving system is damaged due to overlarge speed in the motion process or the chip mounter cannot work normally due to the fact that control input exceeds the maximum input which can be provided by the chip mounter, and the like, and provides a multivariable constraint control method of the chip mounter driving system based on a reference regulator.
The multivariable constraint control method of the chip mounter driving system based on the reference regulator comprises the following steps of:
establishing a dynamic model of a chip mounter driving system moving along an x axis or a y axis, representing the dynamic model by using a state space model, and determining constraint conditions borne by the chip mounter driving system; the x-axis is transverse and the y-axis is longitudinal;
designing a sampling controller for a chip mounter driving system according to the dynamics model established in the step one;
predicting the state of the chip mounter driving system and the size of control input when the reference signal does not change under the condition of assuming unmodeled dynamics of the chip mounter driving system and the condition that external disturbance is a constant value; the state of the chip mounter driving system comprises the displacement and the speed of a chip mounter mobile platform;
and step four, designing a reference regulator according to the result predicted in the step three, so that the chip mounter driving system meets the constraint condition in the step one.
The invention has the beneficial effects that:
the method of the invention adjusts the reference input signal of the system in real time by designing the reference regulator, thereby limiting the system state or control input within the constraint range.
The reference regulator designed by the invention effectively solves the problem of constraint control of a chip mounter driving system, can realize the constraint on the displacement and speed of a chip mounter mobile platform and the applied control input size, and achieves the purposes of protecting chip mounter equipment and ensuring the control effect. As can be seen from fig. 5-9, during the operation of the pick-and-place machine, the displacement of the pick-and-place machine is constrained within 400mm, the speed is also constrained within a preset range, and the control input amount is almost everywhere less than 70% of the maximum input value.
Drawings
Fig. 1 is a closed loop system of a chip mounter driving system;
FIG. 2 is a block diagram of a closed loop system with a reference regulator applied;
fig. 3 is a state of the moving platform of the chip mounter system when the reference signal is a step signal and the reference adjuster is not applied;
FIG. 4 is a control input to the system when the reference signal is a step signal and the reference regulator is not applied;
fig. 5 is a motion trajectory of a moving platform of a chip mounter system when a reference signal is a step signal with a reference adjuster;
fig. 6 shows the moving speed of the moving platform of the chip mounter system when the reference signal is a step signal and the reference adjuster is provided;
FIG. 7 is a control input to the system with a reference regulator, where the reference signal is a step signal;
fig. 8 shows the reference signal r (t) ═ x0+100(1-cos(3.14t))(1-e-t) The state of the moving platform of the chip mounter system with the reference regulator;
fig. 9 shows the reference signal r (t) ═ x0+100(1-cos(3.14t))(1-e-t) With control input to the system referenced to the regulator.
Detailed Description
The first embodiment is as follows: the multivariable constraint control method of the chip mounter driving system based on the reference regulator comprises the following steps of:
establishing a dynamic model of a chip mounter driving system moving along an x axis or a y axis, representing the dynamic model by using a state space model, and determining constraint conditions borne by the chip mounter driving system; the x-axis is transverse and the y-axis is longitudinal;
designing a sampling controller for a chip mounter driving system according to the dynamics model established in the step one;
predicting the state of the chip mounter driving system and the size of control input when the reference signal does not change under the condition of assuming unmodeled dynamics of the chip mounter driving system and the condition that external disturbance is a constant value; the state of the chip mounter driving system comprises the displacement and the speed of a chip mounter mobile platform;
and step four, designing a reference regulator according to the result predicted in the step three, so that the chip mounter driving system meets the constraint condition in the step one.
Multivariate constraints refer to constraining the displacement, velocity, and control inputs of the mobile platform of the patch.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the first step, a dynamic model of the chip mounter driving system moving along the x axis or the y axis is established, the dynamic model is represented by a state space model, and the specific process of determining the constraint conditions on the chip mounter driving system is as follows:
neglecting the positioning force and the coulomb friction force when the mobile platform of the chip mounter moves, establishing a dynamic equation when the mobile platform of the chip mounter moves along the direction of the x axis or the y axis according to a Newton's second law, and determining uncertain parameters M and B of a driving system of the chip mounter and a boundary of external disturbance or unmodeled dynamics by a least square identification method:
Figure BDA0001375795200000031
wherein M is approximately equal to 11kg epsilon [ theta ]1min，θ1max]＝[10kg,15kg]For the mass of the mobile platform of the paster, theta1minAnd theta1maxAn upper and a lower bound for M respectively,
Figure BDA0001375795200000032
and
Figure BDA0001375795200000033
respectively, the first derivative and the second derivative of x (t), the displacement of the mobile platform of the patch, u (t) is the control input, B is approximately equal to 7 N.s/m epsilon [ theta ]2min，θ2max]＝[3N·s/m,20N·s/m]Is the viscous drag coefficient of the moving platform, theta2minAnd theta2maxThe upper and lower boundaries of B, d (t) representing the interference of the chip mounter driving system due to factors such as environment in the operation process or some secondary processes ignored in the process of establishing a mathematical model of the chip mounter driving system, which are respectively called external interference and unmodeled dynamics, and the value of the upper boundary of d (t) beingd0The above equation is rewritten as a state space model for 1N:
Figure BDA0001375795200000034
wherein
Figure BDA0001375795200000035
θ1＝M，θ2B, the pick & place machine drive system is constrained in the form:
Figure BDA0001375795200000036
wherein
Figure BDA0001375795200000037
Is a constraint set, x, of a chip mounter driving system1minAnd x1maxAre respectively x1(t) minimum and maximum values of interest, x2minAnd x2maxAre respectively x2(t) minimum and maximum values of preference, uminAnd umaxRespectively, a minimum and a maximum value of u (t) that are desirable.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: the specific process of designing the sampling controller for the chip mounter driving system according to the dynamics model established in the step one in the step two is as follows:
designing an adaptive sampling controller for the system as follows:
Figure BDA0001375795200000038
wherein
Figure BDA0001375795200000039
Representing the kT time theta1Is determined by the estimated value of (c),
Figure BDA00013757952000000310
representing the kT time theta2Is determined by the estimated value of (c),
Figure BDA00013757952000000311
Figure BDA00013757952000000312
for the virtual sampling control law, the position of the mobile platform of the chip mounter at the kT moment is x1[k]The position error is z1[k]＝x1[k]-r[k]At a velocity of x2[k]The velocity difference is z2[k]＝x2[k]-α1[k]，r[k]For sampling the input signal, T is the sampling time, k1、k2>0 is a parameter of the controller, and 0 is,
Figure BDA0001375795200000041
for the robust term in the controller, ε is used to regulate
Figure BDA0001375795200000042
And sgn (h [ k ]]·z2k) The parameter of the error magnitude between, tanh represents the hyperbolic tangent function, sgn represents the sign function,
Figure BDA0001375795200000043
to represent
Figure BDA0001375795200000044
Operator pi through smooth projection1(theta) the value after the action of the compound,
Figure BDA0001375795200000045
representing the passing of the projection operator pi2(theta) value after the action, smooth projection operator pii(θ), i ═ 1,2, should have the following properties
Figure BDA0001375795200000046
Figure BDA0001375795200000047
Specifically, the following forms can be selected
Figure BDA0001375795200000048
εiFor adjusting smooth projection operator pii(theta) and projection operator
Figure BDA0001375795200000049
The size of the error between the two parameters,
Figure BDA00013757952000000410
Figure BDA00013757952000000411
are respectively the parameter theta1And theta2Should have the following properties:
Figure BDA00013757952000000412
if it is
Figure BDA00013757952000000413
Figure BDA00013757952000000414
Others
The following forms can be selected specifically:
Figure BDA00013757952000000415
wherein i is 1, 2;
the resulting closed loop system is shown in block diagram form in fig. 1.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: in the third step, under the condition that unmodeled dynamics of the chip mounter driving system and external disturbance are assumed to be constant values, the specific process of predicting the state of the chip mounter driving system and the magnitude of the control input when the reference signal does not change is as follows:
defining a judgment function:
Figure BDA0001375795200000051
wherein
Figure BDA0001375795200000052
The definition of the representation is shown,
Figure BDA0001375795200000053
when the input signal is r [ tau ]]Initial position x1Initial velocity of x2The position of the mobile platform of the time-paster at the moment T,
Figure BDA0001375795200000054
when the input signal is r [ tau ]]Initial position x1Initial velocity of x2The speed of the mobile platform of the time-varying paster at the moment T,
Figure BDA0001375795200000055
when the input signal is r [ tau ]]The position of the mobile platform of the paster is
Figure BDA0001375795200000056
At a speed of
Figure BDA0001375795200000057
Control input of a chip mounter driving system;
supposing that the external interference and unmodeled dynamics of the chip mounter driving system are constant values after t moment, predicting a reference input signal v of the modelpt[k]At Δ t0The time becomes constant in the following manner:
Figure BDA0001375795200000058
using an approximate model of a chip mounter driving system:
Figure BDA0001375795200000059
predicting a state of a system and controlling a maximum and a minimum x of an input during a future Δ t time period1pmax,x1pmin,x2pmax,x2pmin,upmax,upmin(ii) a Then at this point:
Figure BDA00013757952000000510
Figure BDA00013757952000000511
εvis a constant greater than 0, rc(t + kT) is the value of the reference signal after the initial adjustment at time t + kT.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: in the fourth step, according to the result predicted in the third step, the specific process of designing the reference regulator is as follows:
the reference regulator is designed as follows:
v[k]＝v[k-1]+κ[k](rc[k]-v[k-1]),kT≤t<(k+1)T
wherein v [ k ]]Is the output of the reference regulator; k [ k ]]＝K(x1[k],x2[k],v[k-1],rc[k]) For reference regulator parameters, K (x)1[k],x2[k],v[k-1],rc[k]) The definition is as follows:
if there is a constant lambda epsilon [0,1 ∈ ]]So that
Figure BDA0001375795200000061
Then K (x)1,x2,v,rc) Is defined as follows
Figure BDA0001375795200000062
Wherein
Figure BDA0001375795200000063
Show to make
Figure BDA0001375795200000064
Figure BDA0001375795200000065
The maximum λ that holds;
if there is no lambda epsilon [0,1 ]]Make it
Figure BDA0001375795200000066
Is established, then
Figure BDA0001375795200000067
Other steps and parameters are the same as in one of the first to fourth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the resulting block diagram of the closed loop control system with the applied reference regulator is shown in fig. 2. The reference regulator and controller are applied to a particular placement machine. The a/D sampling time is taken to be 0.125ms, and the desired output is a step signal r (t) of 100. The design controller parameters were: k is a radical of1＝5000，k28000. The parameter adaptive coefficients are: gamma ray1＝γ 2100. Suppose that a real system is constrained as follows
Figure BDA0001375795200000068
Fig. 3 and 4 respectively show the motion state of the moving platform of the mounter system and the magnitude of the control input when the reference regulator is not applied, and it can be seen that the system of the mounter system is stopped because the control input is too large, exceeding the maximum value that can be provided by the mounter. Fig. 5, 6 and 7 show the motion trajectory, motion speed and control input magnitude for the placement machine system motion stage with reference to the actuators.
Reference trajectory r (t) x0+100(1-cos(3.14t))(1-e-t) The sampling time, controller parameters and parameter adaptation coefficients are unchanged. Suppose that a real system is constrained as follows:
Figure BDA0001375795200000069
fig. 8 and 9 show the motion state of the pick & place machine system motion stage and the control input magnitude, respectively, with reference to the actuators.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (2)

1. The multivariable constraint control method of the chip mounter driving system based on the reference regulator is characterized by comprising the following steps of: the multivariable constraint control method of the chip mounter driving system based on the reference regulator comprises the following steps of:
establishing a dynamic model of a chip mounter driving system moving along an x axis or a y axis, representing the dynamic model by using a state space model, and determining constraint conditions borne by the chip mounter driving system; the method comprises the following specific steps of:
establishing a dynamic model of the chip mounter driving system moving along an x axis or a y axis, representing the dynamic model by using a state space model, and determining the constraint conditions on the chip mounter driving system, wherein the specific process comprises the following steps:
neglecting the positioning force and the coulomb friction force when the mobile platform of the chip mounter moves, establishing a dynamic equation when the mobile platform of the chip mounter moves along the direction of the x axis or the y axis according to the Newton's second law, and determining the uncertainty parameter theta of the driving system of the chip mounter by a least square identification method1And theta2And the bounds of the outside perturbation or unmodeled dynamics:
Figure FDA0002327868570000011
wherein theta is1∈[θ1min，θ1max]For the mass of the mobile platform of the paster, theta1minAnd theta1maxAre each theta1The upper and lower bounds of (a) and (b),
Figure FDA0002327868570000012
is x1First derivative of (t), x1(t) is the displacement of the motorized platform of the patch,
Figure FDA0002327868570000013
is x2First derivative of (t), x2(t) the speed of movement of the mobile platform of the chip mounter, u (t) the control input of the driving system of the chip mounter, theta2∈[θ2min，θ2max]Is the viscous drag coefficient of the moving platform, theta2minAnd theta2maxAre each theta2D (t) represents the external interference received by the chip mounter driving system or the unmodeled dynamics of the chip mounter driving system, and the upper bound is d0；
The chip mounter driving system is constrained in the following form:
Figure FDA0002327868570000014
wherein
Figure FDA0002327868570000015
Is a constraint set, x, of a chip mounter driving system1minAnd x1maxAre respectively x1Minimum and maximum values of (t), x2minAnd x2maxAre respectively x2Minimum and maximum values of (t), uminAnd umaxMinimum and maximum values of u (t), respectively;
designing a sampling controller for a chip mounter driving system according to the dynamics model established in the step one;
predicting the state of the chip mounter driving system and the size of control input when the reference signal does not change under the condition of assuming unmodeled dynamics of the chip mounter driving system and the condition that external disturbance is a constant value; the state of the chip mounter driving system comprises the displacement and the speed of a chip mounter mobile platform, and the specific steps are as follows:
under the condition that unmodeled dynamics of a chip mounter driving system and external disturbance are assumed to be constant values, the specific process of predicting the state of the chip mounter driving system and controlling the input size when a reference signal does not change is as follows:
defining a judgment function:
Figure FDA0002327868570000021
Figure FDA0002327868570000022
when the input signal is r [ tau ]]Initial position x1Initial velocity of x2The position of the mobile platform of the time-paster at the moment T,
Figure FDA0002327868570000023
when the input signal is r [ tau ]]Initial position x1Initial velocity of x2The speed of the mobile platform of the time-varying paster at the moment T,
Figure FDA0002327868570000024
when the input signal is r [ tau ]]The position of the mobile platform of the paster is
Figure FDA0002327868570000025
At a speed of
Figure FDA0002327868570000026
Control input of a chip mounter driving system;
supposing that the external interference and unmodeled dynamics of the chip mounter driving system are constant values after t moment, predicting a reference input signal v of the modelpt[k]At Δ t0The time becomes constant in the following manner:
Figure FDA0002327868570000027
using an approximate model of a chip mounter driving system:
Figure FDA0002327868570000028
predicting the state of the drive system of the film sticking machine in the future delta t time period and controlling the maximum value and the minimum value x of the input1pmax，x1pmin，x2pmax，x2pmin，upmax，upmin(ii) a Then at this point:
Figure FDA0002327868570000029
Figure FDA00023278685700000210
εvis a constant greater than 0, rc(t + kT) is the value of the reference signal after the initial adjustment at the time of t + kT;
step four, designing a reference regulator according to the result predicted in the step three, so that the chip mounter driving system meets the constraint condition in the step one, wherein the specific process of designing the reference regulator is as follows:
the reference regulator is designed as follows:
v[k]＝v[k-1]+κ[k](rc[k]-v[k-1])，kT≤t<(k+1)T
wherein v [ k ]]Is the output of the reference regulator к [ k ]]＝K(x1[k]，x2[k]，v[k-1]，rc[k]) For reference regulator parameters, K (x)1[k]，x2[k]，v[k-1]，rc[k]) The definition is as follows:
if there is a constant lambda epsilon [0,1 ∈ ]]So that
Figure FDA00023278685700000211
Then K (x)1，x2，v，rc) Is defined as follows
Figure FDA0002327868570000031
Wherein
Figure FDA0002327868570000032
The definition of the representation is shown,
Figure FDA0002327868570000033
show to make
Figure FDA0002327868570000034
The maximum λ that holds;
if there is no lambda epsilon [0,1 ]]Make it
Figure FDA0002327868570000035
Is established, then
Figure FDA0002327868570000036
2. The multivariable constraint control method for a reference conditioner-based mounter drive system according to claim 1, wherein: the specific process of designing the sampling controller for the chip mounter driving system according to the dynamics model established in the step one in the step two is as follows:
the self-adaptive sampling controller is designed for a chip mounter driving system and comprises the following steps:
Figure FDA0002327868570000037
wherein T is the sampling time, and T is the sampling time,
Figure FDA0002327868570000038
representing the kT time theta1Is determined by the estimated value of (c),
Figure FDA0002327868570000039
representing the kT time theta2Estimate of (a), α1[k]For the virtual sampling control law, the position of the mobile platform of the chip mounter at the kT moment is x1[k]The position error is z1[k]At a velocity of x2[k]The velocity difference is z2[k]，，u[k]Representing the magnitude of the control input at time kT, k2> 0 is the sampling controller parameter, h k]For robust terms in the sampling controller, ε is the regulation
Figure FDA00023278685700000310
And sgn (h [ k ]]·z2[k]) The parameter of the error magnitude between, tanh represents the hyperbolic tangent function, sgn represents the sign function,
Figure FDA00023278685700000311
to represent
Figure FDA00023278685700000312
Operator pi through smooth projection1(theta) the value after the action of the compound,
Figure FDA00023278685700000313
representing the passing of the projection operator pi2(θ) post-effect value;
smooth projection operator pii(θ), i is 1,2 is defined as follows
Figure FDA00023278685700000314
εiFor adjusting smooth projection operator pii(theta) and projection operator
Figure FDA00023278685700000315
The size of the error between the two parameters,
Figure FDA0002327868570000041
Figure FDA0002327868570000042
are respectively the parameter theta1And theta2The specific form of the adaptive law adjusting function is as follows:
Figure FDA0002327868570000043
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