A PlD temperature control design without overshoot obtuse inflection point

Abstract: In order to meet the temperature control process requirements of a special metal heat treatment, the system uses industrial computer configuration, PLC control, and special PID adjustment methods. According to different temperature rise stages, the system can adaptively adjust the PID parameters and change the output ratio of the temperature control power in real time, effectively overcoming the overshoot phenomenon caused by the temperature control inertia of the traditional PID controller during the temperature control process. The system can operate completely in accordance with the temperature control process curve set by the user, and control and record the heating process in real time throughout the whole process, strictly implement the planned curve, and especially achieve a control effect with no under-temperature and no overshoot blunt-angle inflection points in the control of the temperature change point. Through the detection of the metallographic structure of the actual product, the scrap phenomenon caused by over-temperature overshoot in the past has been completely eliminated.
Keywords: metal heat treatment; metallographic structure; PLC temperature control; industrial control configuration; PID controller

With the continuous development of today's industrial production, in the process requirements of special metal heat treatment, the PID (Proportional Integral Derivative) temperature control system with overshoot response can no longer meet the needs of special production. It not only needs to strictly implement the predetermined temperature rise curve during the heating process, but also pays special attention to the process control of the temperature inflection point, and must achieve a control effect without under-temperature or over-temperature. Under-temperature cannot meet the predetermined process requirements, and over-temperature may cause permanent damage to the grain structure of the heated workpiece and lead to waste. In the metal heating temperature control system, due to the objective existence of control inertia between the heating source and the heated object, under the influence of time-varying uncertainties such as system noise and load disturbances, if the heating process is required to accurately execute the predetermined temperature curve in real time, it is difficult to achieve using the typical PID control idea. In the past production process, in order to prevent overshoot and overburning, the temperature inflection point was operated at the expense of undertemperature. In pursuit of high product quality, after repeated exploration, research and practice, based on the application of Siemens Smatic S7-200 PLC PID instructions, by practicing the new PID adaptive control theory, timely changes and adjustments to the PID parameters in different temperature sections have been made, breaking through the contradiction between undertemperature and overshoot, and achieving a control result consistent with the system's predetermined temperature rise curve.

1 Introduction to system composition
The basic composition of the system equipment is shown in Figure 1(a). The specific control process is: with the support of the industrial computer configuration software, the predetermined workpiece heating temperature rise curve is interactively input or modified through the human-machine interface. The human-machine interface of the system is shown in Figure 1(b). The operation of the production process is implemented through the corresponding instructions on the human-machine interface. After the equipment is running, the PLC will perform real-time PID adjustment on the power output of the variable frequency power supply according to the configured predetermined temperature rise curve, thereby controlling the induction heating equipment to heat the workpiece. The real-time temperature of the workpiece is sampled by the infrared thermometer and fed back to the PLC to form a temperature closed loop. The real-time data of the system operation process and the operating status information of the field equipment are transmitted to the PLC and the industrial computer by the corresponding sensor devices to implement intelligent control such as data collection and recording, alarm prompts, etc. All operations can be realized through the human-machine interface.

2 Design of PID temperature control without overshoot
2.1 PID instruction algorithm in SIEMENS PLC
In Siemens PLC, since its PID algorithm is a classic PID algorithm, the principle is consistent with the control idea of ​​automation instruments. Its PID control structure is shown in Figure 2, and the input-output relationship is:

In Figure 2, Sv(t) is the input quantity (given value), Pv(t) is the feedback quantity, and C(t) is the output quantity. Deviation value ev(t) = Sv(t)-Pv(t); mv(t) is the output signal of the PID regulator. Kp is the proportional coefficient of the regulator, Mintial is the initial value of the PID loop output, and the PLC programmable controller discretizes the PID formula when adjusting the PID of the controlled quantity. When the sampling period of the system is Ts, the rectangular integral is used to approximate the precise integral; the difference is used to approximate the precise differential, and the PID formula is discretized. Then the output of the controller at the nth sampling is:

Since the temperature rise curve to be executed in the actual production process is the process requirement shown in Figure 3(a), the Sv(t) input (given value) is during the temperature rise stage. The system is given in the form of a step quantity under the action of the sampling period Ts, which is equivalent to giving a step function plus the sum of the deviation value ev n-1 times each time. Therefore, it is inevitable that the temperature overshoot oscillation will occur when implementing PID for temperature regulation. The control result is shown in Figure 3(b). Therefore, the classic PID control result cannot meet the control requirements of Figure 3(a).
2.2 Design improvements made to the PID temperature control algorithm in practice
2.2.1 Introduction of integral separation PID control algorithm
The integral separation PID control algorithm is a PID algorithm that weakens the integral term when encountering limits, which is very effective in eliminating system overshoot. The method is as follows: according to the actual debugging situation, a threshold ε (ε>0) is set manually; when the deviation value |ev(n)|>ε, PD control is used to avoid excessive overshoot and enable the system to respond faster; when the deviation value |ev(n)|≤ε, normal PID control is used to ensure the control accuracy of the system. This requires the introduction of an integral control coefficient β in the identification decision link, and β is taken according to the following conditions.

After the introduction of the integral control coefficient β, the output of the controller at the nth sampling is:

2.2.2 Introduction of PID control algorithm with dead zone
In the actual control system, the sampling period Ts is 100 ms. In order to avoid oscillation caused by too frequent control actions. PID control with dead zone is introduced, and its control block diagram is shown in Figure 4. The corresponding control formula is:

In the formula, dead zone evo is an adjustable parameter, and its specific value is determined according to the actual debugging situation. The smaller the evo value is, the more frequent the control action is, and the purpose of stabilizing the controlled object cannot be achieved; the larger the evo value is, the greater the system lags. According to the actual debugging results, evo=2.0℃ in this temperature control system.
While introducing the dead zone control, this system also sets the value of ev(n) to be recognized according to the ratio when the deviation value ev(n) is greater than a certain upper limit value ev(h), so as to limit the control fluctuation caused by the instantaneous disturbance. This method is simple and effective to ensure the stability of system control.
2.2.3 Introducing the differential-first PID control algorithm
The characteristic of the differential-first PID control algorithm is that it only differentiates the output C(n), but does not differentiate the given value Sv(n). Therefore, when changing the given value, the output is stable (the differential term does not participate), making the change of the controlled quantity relatively gentle. This output differential-first control algorithm is very suitable for occasions where the given value changes frequently, and can effectively suppress the system oscillation caused by the change of the given value. In this project, it is precisely because of the fact that each given value has a step change under the control of the sampling period Ts during the temperature rise stage, so the introduction of the differential-first control algorithm can significantly improve the dynamic characteristics of the system. The differential-first control formula:

2.2.4 PID variable parameter control algorithm with Curie point temperature detection
Since the heating source of this system adopts electromagnetic induction heating, in this way, when the metal is heated to a temperature above the Curie point, the heating efficiency will also change greatly due to the sharp change in magnetic permeability. Therefore, in PID control, the corresponding proportional parameter Kp, integral parameter Ki, and differential parameter Kd will also change accordingly, and the size of the change is a function of the material, size, and production cycle of the heated workpiece. On the other hand, in order to ensure that the control effect has no overshoot and forms an obtuse inflection point, the output mv(n) of the system also needs to be proportionally output. The change of this parameter is also a function related to the workpiece heating process, and its numerical optimization needs to be determined during debugging.

2．2．5 改进后的PID控制算法综述
根据本项目温控工艺要求的特点，在基于传统PID算法的理念下，经上述改进使该系统成为一具有一定自适应能力的系统，它能够识别环境条件的变化，并自动校正PID控制参量，这与传统的PID控制算法的显著区别在于它具有“辨识→决策→修改”的功能，即不间断地采样系统(被控对象)的阶段状态参数并加以辨识后与系统事先给定的准则相比较后实时决策、修改PID的算法，以使系统不断地趋向最理想的控制效果。改进后的PID算法的系统框图如图5所示。

3 Performance indicators of non-overshoot PID temperature control design
The main performance indicators of non-overshoot PID temperature control design: From the perspective of self-control theory, the temperature control of this system is essentially a nonlinear system, and the uncertain factors in the time domain are complex and changeable. The performance indicators are comprehensively reflected in the following general aspects.
3.1 Stability
Stability is the basic requirement for the control system. According to the stability requirement of the adaptive PID control algorithm system, it means that the variables such as the state, input, output and parameters of the system are always bounded under the changes of various conditions, that is, under the correction of the control algorithm, the error converges after closed-loop adjustment. In this system, the programmable controller uses Siemens Smatic S7-200 PLC. The relevant variables in the system have been normalized, that is, the references of digital quantities are standardized between 0.0 and 1.0. Therefore, in the process of system temperature control, it is convergent and bounded. At the same time, in the process of detecting, identifying and making decisions on real-time data, all parameters are identified with upper and lower limits in the program, which effectively ensures the stability of the execution results.
3.2 Maintainability
The maintainability of this system mainly refers to the convenience of software maintenance and operator application. In the actual production process, the specifications and models of products are diverse, so the corresponding PID parameters in the temperature control process also need to be changed accordingly. In the human-machine interface of this system, through the control configuration, after the operator enters the specification number of the product, the recipe data is automatically called in the control configuration to initialize the basic parameters of the PID; on the other hand, the software of this system, whether it is configuration programming or PLC programming, adopts a modular structure, so the modification and maintenance of the system program is extremely convenient. According to the general rules of the automatic control system, the process data of the system operation are collected and recorded in the database in real time, which can provide source data for the traceability of product production and processing quality in real time.
3.3 Robustness
As mentioned above, the controlled object of this temperature control system is the power output of the electromagnetic induction heating source. In the actual field environment, the interference of the strong electromagnetic field and the operation of various electromechanical equipment have various known or unknown disturbances on the PID control. In order to solve this problem, in addition to taking corresponding measures in hardware, in the design of PID temperature control, by applying the above-mentioned various parameter limits and identification, the system is guaranteed to work stably in actual production operation and is insensitive to the start and stop disturbances of adjacent electromechanical equipment or variable frequency power supply.

4 Conclusion
4.1 Experimental effect of PID control without overshoot
The improved PID control algorithm effectively solves the difficulty of the original temperature control in the actual production process, and its control effect is shown in Figure 6. The curve in Figure 6 (a) is the temperature control curve before the improved PID temperature control algorithm is adopted, and the temperature control curve in Figure 6 (b) is the temperature control effect recorded in real time by the PID algorithm discussed in this paper. The rare thing is that the control at the temperature change inflection point is an ideal obtuse angle, and the overall temperature control effect is basically consistent with the predetermined temperature trend. Compared with the past, in the actual production process, it not only avoids the rework caused by under-temperature, but also eliminates the waste caused by over-temperature, effectively improving the quality of product heat treatment.

4.2 Design conclusion of PID temperature control without overshoot
In modern control theory, there are endless control concepts derived from the classical PID control theory, such as neurons, neural networks, fuzzy PID control algorithms, etc. However, if you want to select an ideal control algorithm in production practice, you must repeatedly adjust and modify it through engineering practice, not sticking to theoretical parameters or method restrictions, and directly screen and combine suitable control algorithms in the control system test based on engineering experience, so that the system can achieve the most optimized operating state. Although the PID algorithm in this project has achieved the expected effect, the actual PID parameters running in each temperature range are obtained during debugging, and are given in the form of recipes in the upper configuration for the product specifications of each model, which makes the early debugging quite cumbersome. Therefore, there is still room for further exploration and practice in the intelligent design of parameter adaptation.