A control algorithm for waveguide path induction soldering with product positioning

In the article, the problem of developing a control algorithm is described for the induction soldering process of aluminium alloy waveguide paths. The authors suggest a solution using logic controllers in two loops: controlling the speed at which product elements heat up and controlling the waveguide assembly movement relative to the plane of the inductor. The proposed solutions are based on the analysis of the thermal processes occurring in the waveguide pipe and the flange/coupler. Based on the results of numerical experiments, forms of control actions in the system and their parameters were selected. The proposed approach to generating such a control was tested in a series of waveguide path soldering field experiments and the obtained graphs showing the heating of product elements allow the efficiency of the developed logic controllers to be confirmed. The application of the proposed approach provides the high quality regulation of the induction heating process and also the possibility to obtain reliable permanent connections between elements of waveguide paths. Through the flexible adjustment of the proposed logic controller parameters, the high versatility of their use can be demonstrated.


Introduction
The technological processes of induction soldering are of key importance in a number of industries. Perfection of these processes is vital in ensuring a high quality product and in improving productivity [1,2].
The AST 250 pyrometers were selected as non-contact temperature sensors as they best satisfy the above requirements.
In the study of thermal fields during the waveguide element induction heating, it was determined that for the automation of the process of waveguide path element induction soldering 2 pyrometers are sufficicent: one for temperature control on the waveguide flange and the other on the waveguide tube.
The results of experimental studies of the induction soldering process of various sizes waveguide paths revealed the following pattern: software power control of the heating allows the reproduction of the temporal temperature characteristic only for one element of the connection waveguide tube. The temperature of the second element, the flange (coupling area), may significantly differ from the temperature of the pipe by 30÷70 degrees Celsius. With the right choice of starting distance from the flange to the inductor, it is possible to reduce the temperature difference in the vicinity of the melting solder temperature. However, it is not possible to completely eliminate the range of temperatures because of the scatter of the waveguide tube thickness, which can be over 20% of the nominal thickness. This problem can be solved by the automatic adjustment of the distance from the flange to the inductor during the technological process of soldering. The structure of the control system is doublecircuit linked.
In connection with this, a new dual-circuit functional diagram for the automated process control system of induction soldering was developed (Fig. 1), by changing the power supplied to the inductor and the distance from the inductor to the heated product. Such a control scheme allows the heating of waveguide path elements to be performed according to a given law, ensuring the desired temperature distribution on the heated object. Control of the process technological parameters is performed by the computer using error signals obtained as a result of the comparison of the program temperature with pyrometers controlling the temperature of the waveguide tube and flange [11,12]

Approaches to regulation in the control system of the soldering technological process
The double-loop process control system for the induction soldering of aluminium alloy waveguide paths in terms of automatic control systems can be represented by a diagram as follows (Fig. 2): In the figure the following notation is used: -V proc is setpoint speed of heating; -T st is temperature stabilization; -q gen is generator power transferred to the brazed product; -K%, (h) is the distribution of energy between the generator elements of the product as a percentage.
For the most trivial tasks, maintaining a given heating mode is suitable for the parametric integral differential (PID) controller. However, in this task, one of the control circuits (the distance between the inductor and the device) is indirect and the use of PID control on all stages of the process is ineffective. For example, the introduction of the control loop integral component of the drive leads to a deterioration in the quality of control. It is connected to the relatively high inertia of the control object, which has already resulted in an integral link in the in the control loop, and it is not possible to improve this procedure.
Modern research considers the types and combinations of parametric (P) and differential (D) controllers, which would allow the heating rate and the temperature difference among product elements to be controlled independently of the control loop: the P-controller allows the temperature difference to be controlled, and the D-controller allows the heating rate of each of the elements to be managed.
Due to the introduction of the control loop of the workpiece position relative to the window of the inductor, the control system acquires the properties of being multi-connected and nonlinear. The mutual influence of loops can be weakened through the pulse control where is the control interval; is the waiting interval; ( ⁄ ) is the calculation of the remainder from dividing x1 by x2; t is time.
Such an approach means that it is not necessary to calculate precise measures of mutual influence of loops and improves the quality of control for the following reasons: -it eliminates the problem of high inertia of the control object relative to the control device; -it decreases the mutual influence of the loops. In this case, the choice of sufficiently small intervals of control and waiting (200 -400 ms) allows renders the mutual influence of control loops negligible relative to the control.

The heating speed control loop
When regulating the heating speed, control is based on the logical integral controller for the deviation of the heating temperature for the soldered elements of the product above a certain threshold. In addition, separate modes of operation can be selected depending on the stage of the process: -warm-up; -main heating; -stabilization phase. As a result of exploratory research, for the first control loop (temperature control), the control dependence could be represented as a logical function (2): (2) where is the sensitivity temperature of the measuring device (pyrometer); is the difference in the rates of increase between the controlled temperature (on one of the elements of the soldered assembly) and the heating rate program. It is calculated by the formula: is the heating rate program; is the heating rate of the soldered assemble element; is the tolerance threshold of the controlled heating rate; is the temperature of the soldered assemble element (on which is the control loop); is the stabilization mode temperature; is the permissible limit of exceeding the stabilization temperature; is the change constant of the control signal at the stage of preheating to the stabilization temperature; is the change constant of the control signal at the temperature stabilization phase; is the change constant of the control signal when exceeding the permissible heating The control of the process of waveguide induction soldering can be divided into separate stages, each of which can be in various conditions. On the basis of system state analysis, it is possible to allocate the desired control law at a certain stage to the system state. Since the system is non-stationary, multivariable and nonlinear, the control problem cannot be solved in a trivial way using a standard control law, and requires a structural solution that covers all of the many possible states. Table 1 presents the correlation of the technological process stages, the control object state and the ideas of control. Initial temperature spread of the soldered elements.
As soon as possible, eliminate the amount of misalignment.
Heating the workpiece to the soldering temperature The transient or steadystate value in a system in which the temperatures of the elements are equal and have the same rate of increase Ensure the convergence of the temperature of the elements and the equalization of the rates of their growth.
Keeping the heating rate and the temperature difference within acceptable limits. Melting of solder with formation of soldered joint.
A nonlinear process accompanied by a change in the temperature fields due to heat exchange between the elements Maintaining the temperature at a given level -the melting point of the solder.
Avoid overheating of the main material.
For every control idea presented in Table 1 is suitable a particular control law, which is implemented in a separate logic controller with defined coefficients. This statement is supported by the results of the mathematical modelling of the system, by searching for the main regulators using different gain values (Figures 3 and 4).  Y axistemperature, X axistime.
As can be seen in Figure 3, the P-controller allows graphs of the heating element temperatures to be plotted closer to each other. However, the system is in an oscillatory state, and the magnitude of the error signal is constantly changing. This P-controller with a small gain allows small deviations of the system from a given regime to be corrected.
From Figure 4 it can be seen that the D-regulator allows the rate of heating to be equalized, but the magnitude of the temperature difference between the soldered elements remains constant. As can be deduced from the above, the development of the control law on the basis of different combinations of P-and D-controllers can fully satisfy the needs for quality control. Table 2 presents the relationship between the ideas identified for control and their implementation in the form of certain types of regulators. Table 2. Relationship of control ideas and regulators The idea of control Regulator As soon as possible, eliminate the temperature mismatch P-regulator (with high gain).
Ensuring the convergence of temperatures and their equalization of velocities.
The retention of the heating rate and the temperature difference. P-controller (low gain). PD -regulator. Maintaining the temperature at the melting point of the solder Preventing overheating of the main material According to the results of experimental studies, the dependence for control for the second control circuit has been found and can be represented by a logical function (3): where is the sensitivity temperature of the measuring device (pyrometer); is the difference in the rate of increase in temperature of elements. It is calculated as: is the temperature difference between the assembled elements. It is calculated as: is the current flange temperature; is the current waveguide temperature; is the current flange heating rate; is the current tube heating rate; is the upper threshold of regulator activation; is the lower threshold of regulator activation; is the threshold for regulating the temperature of the process; gain factors of individual regulators; is the common coefficient of reduction to one order. The above mathematical models for the regulation have already been implemented within an automated control system.

Experimental studies
Authors used 3 sizes of waveguide tubes and flanges/couplings when conducting experimental studies for testing the proposed approach to the control of the induction soldering of aluminium alloy waveguide paths: 1) 58×25 mm; 2) 35×15 mm; 3) 19×9.5 mm. Figures 5, 6, 7 show the graphs of the soldering process. In each case, high-quality solder joints were obtained.  Y axistemperature, X axistime.

Discussion of results
The graphs in Figures 5, 6 and 7 show that the differences in the sizes of soldered products do not have a significant impact on the quality of control. The proposed logic controllers (2, 3) for the induction soldering technological process can be used without reconfiguration of their settings for each individual size.
At each stage of soldering the idea of control (Tab. 1) was successfully realized, which confirms the correctness of the choice of control laws and the conditions of their application.
In Figure 5, the temperature of the product elements was recorded with a small-time difference and have a small initial misalignment, so there is almost no overshoot before melting the solder. Furthermore, upon reaching the melting temperature, the process of stabilizing the product element temperatures occurs with the subsequent formation of high quality solder joints.
In Figure 6, initial overheating of the waveguide pipe is visible, wherein the system reaches a steady state before melting the solder, after which the temperature graphs reconverge and the solder joints are formed. In addition, it is clear that the resulting non-linear process of redistribution of the product element temperature fields can be regulated by the end of the melting of the solder and the joint being completed.
In Figure, 7, as a result of the initial distribution of temperatures occurs a quickly fading oscillatory process, after which the system in a steady state brings the technological process to the stage of the solder melting and its successful completion.
In all these cases, high-quality solder joints were achieved. In addition, all of the graphs showing the processes of induction soldering (Fig. 5, 6 and 7) show that the choice of pulse character for controlling the automated system reduces the impact of the cross-coupling of loops to an insignificant level and improves the quality of control.

Conclusion
The following results were obtained in the current study: 1) the form and the types of regulators that allow the induction soldering process for aluminium alloy waveguide paths to be controlled without any need to reconfigure their internal state, which indicates the versatility of their use for a wide range of waveguide sizes; 2) the application of impulse control in the system allowed the cross-influence in the system to be reduced to a negligible level, thereby providing an appropriate regulatory process; 3) using the developed control system allows a high-quality soldering connection to be obtained for aluminium alloy waveguide paths.
Thus, the study addresses the problem of generating effective control for the double-circuit system for the induction soldering of aluminium alloy waveguide paths, which assures the high quality of soldered joints and reduces the human impact on the technological process.