Optimization and Implementation of PLC-Based Multi-Level Fuzzy Control for Furnace Temperature

Abstract: This paper introduces the principle of multi-level fuzzy control and optimizes the algorithm by introducing an offset function based on its characteristics. The implementation of this optimization algorithm in a PLC furnace temperature control system is described in detail, and the optimization effect is compared. The optimization algorithm has achieved good control results in practical applications. Keywords: PLC, fuzzy control, optimization. With the increasing demands for temperature control quality in modern production, some old-style resistance furnaces with poor control accuracy and difficulty in management must be upgraded with new technologies. Research on control algorithms is crucial in this process. This paper mainly introduces the principle and implementation of a new control strategy based on PLC. The system control algorithm adopts multi-level fuzzy control with varying step factors and quantization factors, and introduces an offset function based on experience. Repeated operation of this method in a PLC multi-segment resistance furnace system has proven that the furnace temperature rises quickly, the controlled temperature is high, and excellent control results are achieved. [align] 1. Control System Structure and On/Off Rate Control The hardware of this control system consists of three parts: Siemens S7-200CPU224PLC and expansion module EM235 form the controller, MOC3061 and bidirectional thyristor form the actuator, thermocouple and AD595 form the temperature detection transmitter, and additional alarm, trip, overcurrent and other protection circuits are added. The advantages of the system components are high integration, high reliability and simple structure. This system adopts the zero-crossing trigger power adjustment method, and achieves temperature control by changing the on-time ratio (i.e. on/off rate) of the system in one cycle [1]. In the resistance furnace temperature control system, the relationship between the furnace power and the on/off rate is shown in the following formula: Where, P——resistance furnace power Ue——input resistance effective value R——furnace wire resistance value n (k)——on/off rate, i.e., the number of half-waves on in the control cycle n (T)——the number of half-waves of the power frequency in the control cycle The derivation process of the formula is shown in the reference [2]. As can be seen from equation (1), controlling the switching rate can control the power of the resistance furnace, thereby achieving the purpose of controlling the furnace temperature. The control cycle of this system is 10s, containing 1000 half-waves of power frequency voltage (10ms). The PLC distributes the switching rate n(k) calculated by the algorithm evenly throughout the control cycle and outputs switch signals to control the actuator composed of MOC3061 and bidirectional thyristors. 2. Fuzzy control algorithm and optimization 2.1 Fuzzy control principle and lookup table method Fuzzy control is a language control rule based on fuzzy condition statements. According to fuzzy reasoning and fuzzy decision, the fuzzy control table is queried, the fuzziness is defuzzified, and the accurate control quantity is obtained [3]. Fuzzy control generally uses deviation e and deviation change rate Δe to quantize and form a two-dimensional fuzzy controller. Its structural principle diagram is shown in the dashed box in Figure 1. Its simple process is as follows: e and Δe are obtained from the given r and feedback value y, and quantized into fuzzy quantities e and Δe by quantization factors Ke and Kec respectively. The fuzzy control quantity U is obtained by fuzzy decision, and the accurate output quantity U* is output after inverse quantization by proportional factor Ku. Table 1 Fuzzy Control Rule Table In this algorithm, the universe of discourse for e and Δe is level 13 of [-6, +6], and U is level 15 of [-7, +7]. Their correspondence in the control table is shown in Table 1. The control table is obtained by offline calculation and is a 13×13 matrix. It is stored in the continuous memory units of the PLC from left to right in row order. When executing the algorithm, the offset address of the fuzzy control table is obtained by equation (2) based on the values of e and Δe: Table = 13(e+6) + (Δe+6) (2) Wherein, 13(e+6) is the memory offset address of the row to which it belongs, and (Δe+6Δ) is the offset address of the column to which U belongs in the row. 2.2 Multi-level Fuzzy Control Since the universe of discourse for deviation e and deviation change rate Δe is only level 13, the coverage is limited, the control appears very coarse, the heating rate is slow, it takes a long time to enter steady state, and the steady state error is large. Although increasing the elements in the universe of discourse can improve the control accuracy, it makes the calculation more complicated and the control effect is not significantly enhanced. In order to further improve the control quality, a multi-level fuzzy controller, namely parameter factor self-correcting fuzzy control, was adopted [4]. The multi-level fuzzy controller divides the variation range of e and Δe into multiple nested levels, each with its own domain. When the system trajectory enters a certain level, the controller uses the range of the level as the new domain and modifies the parameters Ke, Kec and Ku. In conventional fuzzy control, if the quantization factors Ke, Kec and the proportional factor Ku are too large or too small, a contradiction will arise between speed and steady-state accuracy and settling time, making it difficult to coordinate the relationship between the three. In practice, the system should achieve different control effects according to the requirements of each stage. In the rising stage, speed is the main requirement, while in the steady state, accuracy and adjustment time are required to be higher. This system uses different parameters Ke, Kec and Ku in different ranges of deviation e, as shown in Figure 2. The fuzzy control table is the same. The real-time control quantity (on/off rate n(k)) is calculated by the fuzzy algorithm and output to control the resistance furnace. In this way, fuzzy control with different parameters in different ranges of deviation e reduces steady-state error and improves the control accuracy of the system. 2.3 Optimization of Multi-level Fuzzy Control Since general fuzzy controllers use e and Δe as inputs, they only have proportional-derivative functions and lack integral control. Fuzzy controllers have good dynamic performance, but the steady-state error is large and the elimination time is long. Even with multi-level fuzzy control, steady-state error still exists. Therefore, a function Ug is introduced based on the feedforward control principle. Ug is a function of the given temperature value r. The relationship between Ug and r changes with the system. The value of Ug also has a great influence on the steady-state accuracy of the system. For simplicity, we take Ug = r/k (k is the amplification factor of the object. In practical applications, it can be estimated as the ratio of the steady-state temperature value to the output switching rate). At the same time, to ensure the following performance of Ug, an online modification method is adopted, based on the following formula: Ug(k) = Ug* + Kg × U(k) (3) Where Kg is an empirical value, taken as 0.8, U(k) is the output of the sampling time KT in the multi-level fuzzy controller, and Ug* is the offset function. The block diagram of the optimized multi-level fuzzy control principle is shown in Figure 1. In practical applications, Ug needs to be limited, and Ugmax=r/(K-0.3) and Ugmin=r/(K+0.3) can be taken. The precise output expression of this system is as follows: U=Round(U＊+Ug)=Round(Ku×U+Ug＊+Kg×U) (4) Where, Round() is the rounding operation in PLC instructions. Practice has proven that the optimized multi-level fuzzy control has greatly improved the steady-state performance and steady-state accuracy of the system. 3. Implementation of the optimized multi-level fuzzy control algorithm on PLC The algorithm of this system has been implemented to control two multi-stage resistance furnaces and two single-phase resistance furnaces respectively. The control of two identical single-phase resistance furnaces is used as an example for explanation. The system control cycle is 10s, and the on/off rate is counted by a 10ms timer interrupt. Data is sent at the end of each control cycle to calculate the on/off rate of the next cycle. Since the maximum PLC timer interrupt is 255ms, the 10s interrupt is completed by 50 200ms timer interrupts. The control program includes a main program, an initialization subroutine, a 10ms interrupt subroutine, a 200ms interrupt subroutine, and an alarm trip subroutine. The fuzzy algorithm is completed by the 200ms interrupt subroutine. In the 200ms interrupt program, a counting unit c is set with an initial value of 50. After each interrupt, c is decremented by 1. When c=0, the timer has reached 10s, and data processing is performed. The corresponding parameters, fuzzification deviation e, and deviation change rate Δe are set. The offset address is calculated by equation (2), and the fuzzy control quantity U* is obtained by looking up the table. At the same time, Ug is calculated by equation (3), and the precise control quantity U is obtained according to equation (4). That is, the on/off rate n(k) is stored in the corresponding 10ms interrupt counting unit. The implementation flowchart of the 200ms timer interrupt subroutine is shown in Figure 2. 4. The effect of multi-level fuzzy algorithm optimization on the control effect To verify the control effect of the optimized multi-level fuzzy controller, we conducted the following comparative experiments. The set temperatures for the resistance furnaces are 300℃ for furnace #1 and 200℃ for furnace #2. Fuzzy control is initiated when the deviation e(k) > -200℃. All results below are online real-time results. 4.1 Single-level fuzzy control: The single-level fuzzy control parameters are: when e(k) < -200℃, n(k) = 1000; when e(k) > -200℃, Ke = 30, Kec = 2.0, Ku = 120. The temperature curve is shown in Figure 3, which is drawn in real-time by the Delphi monitoring interface based on data sent by the PLC. As can be seen from Figure 3, the system has a slow heating rate, a long transition process, and good steady-state performance, reaching the set value after 70 minutes of heating. However, there is overshoot and a long elimination time, resulting in a relatively large steady-state error. 4.2 Multi-level fuzzy control system: Three-level fuzzy control is adopted, with specific parameters: when e(k) < -200℃, n(k) = 1000; when e(k) > -200℃, Ke = 30, Kec = 2.0, Ku = 120.

# PLC | Fuzzy Control | Optimization

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Optimization and Implementation of PLC-Based Multi-Level Fuzzy Control for Furnace Temperature

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