CN108983611B - Temperature-power modeling method of laser soldering power automatic control system - Google Patents
Temperature-power modeling method of laser soldering power automatic control system Download PDFInfo
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The invention discloses a temperature-power modeling method of a laser soldering power automatic control system, which comprises the following steps: acquiring data of temperature and power in the laser soldering process; designing factors including temperature loss; acquiring a difference value between a given target temperature curve and an actual output temperature; selecting an initial moment to form a matrix of difference values after the brazing process is completed by N sampling periods, and obtaining a dynamic characteristic model by using the matrix; based on a thermodynamic formula of a laser soldering process, correcting a dynamic characteristic model by utilizing a linear superposition principle in a discrete time domain to obtain a prediction model of the system; repeatedly adjusting and utilizing iterative recursion simulation processing to obtain an optimal control quantity sequence; the invention eliminates the deviation between the actual system output temperature and the target given temperature in the welding process, reduces the calculated amount in the solving process and shortens the calculating time.
Description
Technical Field
The invention relates to the field of laser soldering control, in particular to a temperature-power modeling method of an automatic laser soldering power control system.
Background
The laser soldering technology is used as a welding method which gives consideration to quality and efficiency, and overcomes the problem of connection reliability of surface-mounted devices caused by the fact that a circuit board cannot bear high temperature for a long time in a traditional welding mode due to the characteristics of low deformation and high precision of a welding product, and the laser soldering technology is just caused by the characteristics. The method is widely applied to circuit assembly welding in special electronic equipment.
In the application of the laser soldering power automatic control system, a proper PID control is designed by a field engineer according to experience mostly, but in the actual production, the design of the corresponding proper PID control for each non-standard part is difficult to achieve by the various types of welding products for the unspecific non-standard parts, and even if the design is achieved, the time is extremely consumed, so that the practical application is not facilitated. If the control effect in the welding device does not meet the set requirement, the welding device needs to be welded again and even is discarded. This all causes direct economic losses.
Based on the above, the present invention provides a temperature-power modeling method for an automatic control system of laser soldering power, which can eliminate the deviation between the actual system output temperature and the target given temperature during the welding process.
Disclosure of Invention
In order to solve the problems that the existing laser soldering power control system has no mathematical model and the corresponding control method is few, the temperature-power modeling method of the laser soldering power automatic control system is provided, which can eliminate the deviation between the actual system output temperature and the target given temperature in the welding process.
The technical scheme adopted by the invention is as follows:
the temperature-power modeling method of the laser soldering power automatic control system comprises the following steps:
acquiring data of temperature and power in the laser soldering process;
designing factors including temperature loss;
acquiring a difference value between a given target temperature curve and an actual output temperature;
selecting an initial moment to form a matrix of difference values after the brazing process is completed by N sampling periods, and obtaining a dynamic characteristic model by using the matrix;
based on a thermodynamic formula of a laser soldering process, correcting a dynamic characteristic model by utilizing a linear superposition principle in a discrete time domain to obtain a prediction model of the system; and
and repeatedly adjusting and utilizing iterative recursion simulation processing to obtain an optimal control quantity sequence.
The invention is further improved in that the temperature power data is acquired and then filtered.
The invention is further improved in that the difference is defined by the balance of heat between the solder bearing device, the pad, the solder paste and the fluid and its dynamics.
The invention is further improved in that the discrete time domain is set to the temperature detection frequency of 0.5 ms/time.
The invention is further improved in that the factors of the temperature loss include heat conduction loss, air convection heat dissipation and corresponding change of specific heat capacity of the solder paste according to different thermodynamic states of the solder paste.
The invention is further improved in that the matrix is:
E＝(e(k0),e(k0+1),...,e(k0+i),...,e(k0+N))T，
wherein k is0At the start of soldering, N is the number of sampling periods, e (k)0+ i) is the error between the target temperature after the i-th sampling period from the start of laser soldering and the actual system output temperature.
The invention is further improved in that the dynamic characteristic model is as follows:
wherein, the error generated in the laser soldering process is recorded as completely known disturbance, k represents the sampling time of soldering, x (k) represents the state vector, and delta u (k) ([ delta w (k))]Δ w (k) represents the power control increment of the laser soldering power control system at the original fixed power, y (k) represents the output measured value of the system, G0And H is a known system parameter.
The invention is further improved in that the modified dynamic characteristic model is:
wherein, x (k) ═ w (k), E (k)]T，y(k)＝[E(k)]W (k) represents a fixed power value in the open-loop control, and e (k) represents an error between an actual system output temperature and a target temperature under the open-loop control.
The invention is further improved in that the prediction model of the system is as follows:
where e (k) ═ e (k +1), e (k +2),. -, e (k + N)]T，D0、B1、C1Is the corrected system parameter.
The invention is further improved in that the process of the iterative recursion simulation processing is as follows:
s1, obtaining a dynamic objective function, specifically, performing algorithm dynamic optimization on the prediction model through an MPC controller, wherein the dynamic objective function is as follows:
Jk＝||Y(k)-Yref(k)||2 Q+||ΔU(k)||2 R，
wherein Y (k) represents a prediction output in the prediction time domain from the time k, and Yref(k) Represents a desired output in a prediction time domain from a time k, Δ u (k) a change in a predicted control amount in the prediction time domain from the time k, Q is an error weighting matrix, R is a control amount weighting matrix, and Q and R are both diagonal matrices;
s2, optimizing the dynamic objective function, specifically, limiting the controlled variable in the prediction time domain, wherein the inequality constraint conditions of the dynamic objective function are as follows:
-ΔUmax≤ΔU(k)≤ΔUmax，
wherein, -Delta UmaxLower limit, Δ U, indicating variation of control amountmaxRepresents an upper limit of the variation of the control amount;
when the prediction input violates the maximum or minimum limit, it is set as a limit value, then the quantity is removed and the calculation process is repeated, obtaining a sub-optimal solution by the least square method, specifically:
defining error trajectory EE (k) Yref(k)-φx(k)-CyΔu(k)-E(k)，
Wherein phi is C1D0，Cy＝C1B1；
The optimized dynamic objective function is as follows:
Jk＝||CYΔU(k)-EE(k)||2 Q+||ΔU(k)||2 R
＝(CyΔU(k)-EE(k))TQ(CyΔU(k)-EE(k))+ΔUT(k)RΔU(k)
＝ΔUT(k)[CyQCy+R]ΔU(k)-2EET(k)QCyΔU(k)+EET(k)QEE(k)
s3, obtaining an optimal control quantity sequence through the optimized dynamic objective function, specifically, deriving the optimized dynamic objective function, making an expression 0, and obtaining the optimal control quantity sequence for eliminating the error between the system output temperature and the target temperature in the laser soldering process according to the necessary conditions of an extreme value as follows:
ΔUopt(k)＝(Cy TQCy+R)-1Cy TQEE(k)，
wherein (C)y TQCy+R)-1Cy TThe value of Q is calculated after system initialization based on the configuration and parameters of the controller.
Compared with the prior art, the invention has the following beneficial effects:
the invention collects the actual system output temperature data under the open-loop control of the fixed power from the industrial field, then carries out filtering processing on the collected open-loop data, takes the error generated in the laser soldering process as the completely known disturbance, and is based on the fact that the established model can be directly corrected by utilizing the linear superposition principle in the discrete time domain (the temperature detection frequency is 0.5 ms/time), thereby obtaining the dynamic model of the laser soldering system, deduces the prediction model of the system by adopting the iterative recursion method according to the obtained dynamic model, then designs the MPC power controller to carry out the automatic control of the laser soldering power, eliminates the deviation between the actual system output temperature and the target given temperature in the welding process, reduces the calculated amount in the solving process, and shortens the calculating time.
Drawings
FIG. 1 is a graph of the actual output temperature curve and the target temperature curve of the system under the open loop control of the fixed power of the laser soldering power control system of the present invention;
FIG. 2 is a graph of the actual output temperature of the system after filtering under the open loop control of the fixed power of the laser soldering power control system of the present invention;
FIG. 3 is a graph of the output temperature of the laser soldering power control system of the present invention under the open loop control of the fixed power.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a temperature-power modeling method of an automatic laser soldering power control system, which comprises the following steps:
acquiring data of temperature and power in the laser soldering process;
designing factors including temperature loss;
acquiring a difference value between a given target temperature curve and an actual output temperature;
selecting an initial moment to form a matrix of difference values after the brazing process is completed by N sampling periods, and obtaining a dynamic characteristic model by using the matrix;
based on a thermodynamic formula of a laser soldering process, correcting a dynamic characteristic model by utilizing a linear superposition principle in a discrete time domain to obtain a prediction model of the system; and
and repeatedly adjusting and utilizing iterative recursion simulation processing to obtain an optimal control quantity sequence.
In specific implementation, the filtering processing of the temperature power data is further included after the temperature power data is acquired.
In particular implementation, the difference is defined by the balance of heat among the solder bearing device, the pad, the solder paste and the fluid and its dynamics.
In specific implementation, the discrete time domain is set to be the temperature detection frequency of 0.5 ms/time.
In specific implementation, the factors of the temperature loss include heat conduction loss, air convection heat dissipation and corresponding transformation of specific heat capacity of the solder paste according to different thermodynamic states of the solder paste.
In specific implementation, the matrix is:
E＝(e(k0),e(k0+1),...,e(k0+i),...,e(k0+N))T，
wherein k is0At the start of soldering, N is the number of sampling periods, e (k)0+ i) is the error between the target temperature after the i-th sampling period from the start of laser soldering and the actual system output temperature.
In specific implementation, the dynamic characteristic model is as follows:
wherein, the error generated in the laser soldering process is recorded as completely known disturbance, k represents the sampling time of soldering, x (k) represents the state vector, and delta u (k) ([ delta w (k))]Δ w (k) represents the power control increment of the laser soldering power control system at the original fixed power, y (k) represents the output measured value of the system, G0H is a known system parameter, and the error generated in the whole laser soldering process is marked as a completely known disturbance.
In specific implementation, the modified dynamic characteristic model is as follows:
wherein, x (k) ═ w (k), E (k)]T，y(k)＝[E(k)]W (k) represents a fixed power value in the open-loop control, and e (k) represents an error between an actual system output temperature and a target temperature under the open-loop control.
In specific implementation, the prediction model of the system is as follows:
where e (k) ═ e (k +1), e (k +2),. -, e (k + N)]T，D0、B1、C1Is the corrected system parameter.
In specific implementation, the process of iterative recursion simulation processing is as follows:
s1, obtaining a dynamic objective function, specifically, performing algorithm dynamic optimization on the prediction model through an MPC controller, wherein the dynamic objective function is as follows:
Jk＝||Y(k)-Yref(k)||2 Q+||ΔU(k)||2 R，
wherein Y (k) represents a prediction output in the prediction time domain from the time k, and Yref(k) Represents a desired output in a prediction time domain from a time k, Δ u (k) a change in a predicted control amount in the prediction time domain from the time k, Q is an error weighting matrix, R is a control amount weighting matrix, and Q and R are both diagonal matrices;
s2, optimizing the dynamic objective function, specifically, limiting the controlled variable in the prediction time domain, wherein the inequality constraint conditions of the dynamic objective function are as follows:
-ΔUmax≤ΔU(k)≤ΔUmax，
wherein, -Delta UmaxLower limit, Δ U, indicating variation of control amountmaxRepresents an upper limit of the variation of the control amount;
when the prediction input violates the maximum or minimum limit, it is set as a limit value, then the control quantity is removed and the calculation process is repeated, and a sub-optimal solution is obtained by the least square method, specifically:
defining error trajectory EE (k) Yref(k)-φx(k)-CyΔu(k)-E(k)，
Wherein phi is C1D0，Cy＝C1B1，
The optimized dynamic objective function is as follows:
Jk＝||CYΔU(k)-EE(k)||2 Q+||ΔU(k)||2 R
＝(CyΔU(k)-EE(k))TQ(CyΔU(k)-EE(k))+ΔUT(k)RΔU(k)
＝ΔUT(k)[CyQCy+R]ΔU(k)-2EET(k)QCyΔU(k)+EET(k)QEE(k)
s3, obtaining an optimal control quantity sequence through the optimized dynamic objective function, specifically, deriving the optimized dynamic objective function, making an expression 0, and obtaining the optimal control quantity sequence for eliminating the error between the system output temperature and the target temperature in the laser soldering process according to the necessary conditions of an extreme value as follows:
ΔUopt(k)＝(Cy TQCy+R)-1Cy TQEE(k)，
wherein (C)y TQCy+R)-1Cy TThe value of Q is calculated after system initialization based on the configuration and parameters of the controller. In the above solution, most MPC controllers use a similar:
Jk＝||Y(k)-Yref(k)||2 Q+||ΔU(k)||2 Rand performing dynamic optimization on the quadratic objective function. The dynamic optimization problem in this case takes the form of QP and can be reliably solved using standard software. However, for very large problems, or very fast processes, there may not be enough time to solve the QP. The power control frequency of the laser soldering power control system of 0.5 ms/time belongs to a fast process, so the present invention adopts the processing of the boundary in the DMC + algorithm, i.e. when the predicted input violates the maximum or minimum limit, it is set as a limit value, then the manipulated variable is removed and the calculation process is repeated. Therefore, the suboptimal solution can be obtained by directly adopting the least square method, the suboptimal solution is acceptable under the normal condition, and more importantly, the calculation amount in the solving process is reduced and the calculation time is shortened by the simplified mode. At the same time, calculate Δ Uopt(k) The calculation of the product and the inverse of the matrix is involved, and the calculation amount is large. In practice, however, (C) once the configuration and parameters of the controller are determinedy TQCy+R)-1Cy TQ is a fixed value, and only the error track is updated in real time. Can be calculated after system initialization (C)y TQCy+R)-1Cy TThe value of Q is stored, so that the controller only can be used for multiplication of two matrixes during real-time calculation, and the calculation amount is not large.
The technical principle of the invention is as follows:
and deducing the relation between the surface temperature of the welding bearing device and the output power of the laser generator. In the actual operation of the laser soldering system, a laser source is generated by a laser generator and then irradiates the surface of soldering paste on a welding device, at the moment, the soldering paste absorbs the energy irradiated on the surface of the soldering paste by the laser generator, then the soldering paste is melted and spread, and after the laser generator finishes the set irradiation time, the soldering paste is cooled and solidified into alloy which is spread on the surface of the welding device to finish the welding process requirement. The relation between power and temperature in the whole process can be analyzed from the aspect of energy conservation in the whole working process of laser soldering, part of heat absorbed by the surface of the soldering paste causes the temperature of the soldering paste and the pad to rise, part of heat is consumed through air heat dissipation, and the rest of heat is lost in the heat conduction process. Theoretically, it is impossible to achieve good soldering effect by performing the open-loop control only by the fixed power, because the solder paste is an alloy solder paste in which the components show different characteristics during soldering, that is, the open-loop control at the fixed power may generate an actual system output temperature greatly deviating from the target temperature. It is because of the different characteristics that the components of solder paste exhibit during soldering that cause deviations between the actual system output temperature and the target set temperature during soldering.
In order to quantitatively analyze the relation between the control power and the system output temperature in the laser soldering process, qualitative analysis is firstly carried out on the laser soldering process from the aspect of energy conservation.
The following assumptions were made: (1) the power output of the semiconductor laser is not attenuated; (2) the temperature data detected by the welding device has no deviation with the temperature data of the actual welding device; (3) the integral temperature of the welding-bearing devices is consistent; then according to the law of thermodynamics, the law of conservation of energy, one can obtain:
∫W(t)*Klaserdt＝∫Knn*Kshape*S*T(t)dt+Hf*S*(T(t)-TB)
+mSn*CSn*(T(t)-TB)+MCu*Ccu*(T(t)-TB)
wherein W (t) is the laser output power of the semiconductor laser generator, Klaser is the laser absorption rate of the solder bearing device, Knn is the material thermal conductivity coefficient of the solder bearing device, Khape is the material thermal conductivity geometric coefficient, HfIs the air convection coefficient, S is the pad area, MCuIs the quality of the bonding pad (the bonding pad is mostly made of copper), mSnThe quality of the soldering paste (the main component of the soldering paste is tin), TB represents room normal temperature, T (t) represents the measured temperature of a welding device at the time t, CcuIs the specific heat capacity of copper, CSnFor the specific heat capacity of the solder paste (solder paste), it should be noted that the solder paste is a lead-free solder paste alloy and hence is CSnThe following relationship is given:
the above formula can be understood as the energy absorbed by the solder bearing device, i.e. the energy lost by heat conduction + the energy of air convection heat transfer + the energy of solder paste rising. It can be seen that the absorbed energy is not fully absorbed by the solder paste and the pads due to the thermal conduction losses and the presence of convective air dissipation. Meanwhile, the specific heat capacity of the solder paste is correspondingly changed along with the difference of the thermodynamic state of the solder paste, so that the complex relation between the output temperature of the system and the control power in the brazing process is caused, and the control of the output temperature of the system to track a target temperature curve becomes difficult.
The invention collects the actual system output temperature data under the open-loop control of the fixed power from the industrial field, then carries out filtering processing on the collected open-loop data, takes the error generated in the laser soldering process as the completely known disturbance, and is based on the fact that the established model can be directly corrected by utilizing the linear superposition principle in the discrete time domain (the temperature detection frequency is 0.5 ms/time), thereby obtaining the dynamic model of the laser soldering system, deduces the prediction model of the system by adopting the iterative recursion method according to the obtained dynamic model, then designs the MPC power controller to carry out the automatic control of the laser soldering power, as shown in figures 1 to 3, the invention can see that the deviation between the actual system output temperature and the target given temperature in the welding process is eliminated, and the calculated amount in the solving process is reduced, the calculation time is shortened.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. The temperature-power modeling method of the laser soldering power automatic control system is characterized by comprising the following steps of:
acquiring data of temperature and power in the laser soldering process;
designing factors including temperature loss;
acquiring a difference value between a given target temperature curve and an actual output temperature;
selecting an initial moment to form a matrix of difference values after the brazing process is completed by N sampling periods, and obtaining a dynamic characteristic model by using the matrix;
based on a thermodynamic formula of a laser soldering process, correcting a dynamic characteristic model by utilizing a linear superposition principle in a discrete time domain to obtain a prediction model of the system; and
and repeatedly adjusting and utilizing iterative recursion simulation processing to obtain an optimal control quantity sequence.
2. The temperature-power modeling method of an automatic laser soldering power control system according to claim 1, characterized in that: and filtering the temperature power data after acquiring the temperature power data.
3. The temperature-power modeling method of an automatic laser soldering power control system according to claim 1, characterized in that: the difference is defined by the balance of heat between the solder bearing device, the pad, the solder paste and the fluid and its dynamics.
4. The temperature-power modeling method of an automatic laser soldering power control system according to claim 1, characterized in that: the discrete time domain is set to be the temperature detection frequency of 0.5 ms/time.
5. The temperature-power modeling method of an automatic laser soldering power control system according to claim 1, characterized in that: factors of the temperature loss include heat conduction loss, air convection heat dissipation and corresponding change of specific heat capacity of the solder paste according to different thermodynamic states of the solder paste.
6. The temperature-power modeling method of an automatic laser soldering power control system according to claim 1, characterized in that the matrix is:
E＝(e(k0),e(k0+1),...,e(k0+i),...,e(k0+N))T，
wherein k is0At the start of soldering, N is the number of sampling periods, e (k)0+ i) is the error between the target temperature after the i-th sampling period from the start of laser soldering and the actual system output temperature.
7. The temperature-power modeling method of an automatic laser soldering power control system according to claim 6, characterized in that the dynamic characteristic model is:
wherein, the error generated in the laser soldering process is recorded as completely known disturbance, k represents the sampling time of soldering, x (k) represents the state vector, and delta u (k) ([ delta w (k))]Δ w (k) represents the power control increase of the laser soldering power control system under the original fixed powerQuantity, y (k) represents the output measurement of the system, G0And H is a known system parameter.
8. The temperature-power modeling method of an automatic laser soldering power control system according to claim 7, wherein the modified dynamic characteristics model is:
wherein, x (k) ═ w (k), E (k)]T，y(k)＝[E(k)]W (k) represents a fixed power value in the open-loop control, and e (k) represents an error between an actual system output temperature and a target temperature under the open-loop control.
9. The temperature-power modeling method of an automatic laser soldering power control system according to claim 8, characterized in that the predictive model of the system is:
where e (k) ═ e (k +1), e (k +2),. -, e (k + N)]T，D0、B1、C1Is the corrected system parameter.
10. The temperature-power modeling method of an automatic control system of laser soldering power according to claim 9, characterized in that the process of iterative recursion simulation processing is:
s1, obtaining a dynamic objective function, specifically, performing algorithm dynamic optimization on the prediction model through an MPC controller, wherein the dynamic objective function is as follows:
Jk＝||Y(k)-Yref(k)||2 Q+||ΔU(k)||2 R，
wherein Y (k) represents a prediction output in the prediction time domain from the time k, and Yref(k) Indicating that the time from k is in advance(k) the change of the predicted control quantity in the prediction time domain from the time k, Q is an error weighting matrix, R is a control quantity weighting matrix, and Q and R are diagonal matrices;
s2, optimizing the dynamic objective function, specifically, limiting the controlled variable in the prediction time domain, wherein the inequality constraint conditions of the dynamic objective function are as follows:
-ΔUmax≤ΔU(k)≤ΔUmax，
wherein, -Delta UmaxLower limit, Δ U, indicating variation of control amountmaxRepresents an upper limit of the variation of the control amount;
when the prediction input violates the maximum or minimum limit, it is set as a limit value, then the control quantity is removed and the calculation process is repeated, and a sub-optimal solution is obtained by the least square method, specifically:
defining error trajectory EE (k) Yref(k)-φx(k)-CyΔu(k)-E(k)，
Wherein phi is C1D0，Cy＝C1B1，
The optimized dynamic objective function is as follows:
Jk＝||CYΔU(k)-EE(k)||2 Q+||ΔU(k)||2 R
＝(CyΔU(k)-EE(k))TQ(CyΔU(k)-EE(k))+ΔUT(k)RΔU(k)
＝ΔUT(k)[CyQCy+R]ΔU(k)-2EET(k)QCyΔU(k)+EET(k)QEE(k)
s3, obtaining an optimal control quantity sequence through the optimized dynamic objective function, specifically, deriving the optimized dynamic objective function, making an expression 0, and obtaining the optimal control quantity sequence for eliminating the error between the system output temperature and the target temperature in the laser soldering process according to the necessary conditions of an extreme value as follows:
ΔUopt(k)＝(Cy TQCy+R)-1Cy TQEE(k)，
wherein (C)y TQCy+R)-1Cy TThe value of Q is calculated after system initialization based on the configuration and parameters of the controller.
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Inventor after: Hong Xihe Inventor after: Zhang Tao Inventor after: Chen Zhihua Inventor after: Shu Longfei Inventor after: Bao Yunan Inventor before: Hong Xihe Inventor before: Chen Zhihua Inventor before: Shu Longfei Inventor before: Bao Yunan |
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Denomination of invention: Temperature power modeling method of laser soldering power automatic control system Effective date of registration: 20220124 Granted publication date: 20210831 Pledgee: Wuhan area branch of Hubei pilot free trade zone of Bank of China Ltd. Pledgor: Wuhan Brilliant Tech Co.,Ltd. Registration number: Y2022420000026 |