Improvement of predictive control algorithm based on fuzzy fractional order PID

Rongzhen Shi

doi:10.1515/jisys-2022-0288

Article Open Access

Improvement of predictive control algorithm based on fuzzy fractional order PID

Rongzhen Shi

Published/Copyright: October 28, 2023

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From the journal Journal of Intelligent Systems Volume 32 Issue 1

Abstract

The existing predictive control strategy has comprehensive prior knowledge of the controlled process, requires weak continuity of the search space for parameter optimization, and its application is limited to some extent. Therefore, improved research on the fuzzy fractional proportional integral differential (PID) predictive control algorithm is proposed. First, the control principle of PID predictive control equipment is proposed. According to this principle, the structure of the PID predictive control equipment adaptive fuzzy PID energy-saving controller is constructed. Through the PID energy-saving control parameter setting principle and fuzzy control rules, the adaptive fuzzy PID energy-saving control of PID predictive control equipment is realized. Finally, the fractional order PID predictive transfer function model is constructed to improve the predictive control algorithm based on PID optimization technology. The experimental results show that the accuracy and efficiency of the designed algorithm can get the best performance index, and its stability, overshoot, time, and control accuracy are basically unchanged. In the small area temperature control, the disturbance interference is small, the anti-disturbance ability is good, and it has strong robustness.

Keywords: fuzzy fractional order; PID predictive control algorithm; controller structure; parameter setting principle; fuzzy control rules

1 Introduction

1.1 Background

In the classical predictive control theory, PID (proportional integral differential) predictive control algorithm is one of the famous theories. PID predictive control is the control algorithm with the longest history and the most widely used in the development of automatic control of the production process [1]. It has the advantages of a simple principle, practical convenience, strong adaptability, and strong robustness. It can effectively speed up the system response speed, eliminate the steady-state error, and restrain the change of error. It has good applicability for most control systems. Therefore, until today when computer technology is widely used, PID predictive control is still applied to more than 80–90% of the control fields with its excellent characteristics [2].

1.2 Literature review

Relevant scholars have done a lot of research on this. Priyanka et al. [3] proposed a model predictive PID control method for oil pipeline infrastructure based on Internet of Things fusion. Data fusion and model predictive control are combined to formulate the final model for real-time implementation by dealing with different scenario risk rates, so as to improve robustness. According to the scheduled task identification and risk probability characteristics in the oil pipeline, the accurate model is selected. The final control signal will be started using electronic stability control data with the on-site PID control signal rate based on the multi-criteria decision-making method. The proposed prediction model can predict oil pipeline leakage and prevent several steps used in the controller optimization part. Finally, the effectiveness of the proposed controller is verified by a simulation example using the pressure and flow data of a real fluid pipeline under various hard constraints. Wenhua et al. [4] proposed the flow control of reciprocating compressors based on adaptive predictive PID control and established the intake model of the cylinder under the condition of capacity regulation to calculate the load of the first cylinder. Then, an adaptive predictive PID controller is designed to control the pressure ratio in other stages, and the grey prediction model is used to predict the pressure output to overcome the system delay. In order to solve the problem of tuning control parameters, an improved particle swarm optimization algorithm is used to obtain the optimal control parameters. The effectiveness of the adaptive predictive PID control method is verified by a two-stage compressor model simulation. Finally, the flow control scheme is applied to the actual flow control system of a four-stage air reciprocating compressor, and the application results further verify the feasibility and effectiveness of the scheme. Somefun et al. [5] proposed DC motor speed control: optimal closed-loop PID model predictive control. DC motor speed control is one of the lowest control tasks, especially in robotics and other manufacturing industries; other high-level controls depend on it. Generally, when adjusting the parameters of the PID controller to accomplish this task, the established conventional method is used to expose the knowledge of the nominal process model parameters to the control algorithm. This method uses the characteristics of a dynamic process to answer this question, and its performance is based on the popular process model-based method. The simulation results show that the proposed tuning method has good prospects and effectiveness in ensuring the good closed-loop performance of DC motors without using the real process model.

Elsisi and Soliman [6] proposed a flow control scheme based on inlet temperature and pressure ratio. In this scheme, a cylinder intake model was established under capacity adjustment conditions, and the load of the first cylinder was calculated. Then, an adaptive predictive PID (APPID) controller is designed to control the pressure ratios of other stages, and a grey prediction model is used to predict the pressure output to overcome system lag. To solve the problem of control parameter tuning, an improved particle swarm optimization algorithm is adopted to obtain the optimal control parameters. The effectiveness of the adaptive predictive PID control method was verified through simulation of a two-stage compressor model. Finally, the flow control scheme is applied to the actual flow control system of a four stage air reciprocating compressor. In the study of Ismail et al. [7], a proportional-integral controller and an adaptive neuro-fuzzy inference system based on a hybrid genetic algorithm are proposed, and the battery charging balance is realized by using this system. At the same time, the algorithm is compared with the traditional PI controller based on Ziegler Nichols technology. In the dynamic simulation results, the proposed method has better performance for the power system. Mohamed et al. [8] proposed two modern methods of energy management systems based on the improved cost function. Through the implementation of fuzzy logic and Harris Hawks optimization (HHO), the optimal performance of the desalination plant can be achieved at the lowest on-grid price. The attained results demonstrate that the proposed FL and HHO-based EMSs provide high dynamic performance and accurate coordination between various energy resources and BESS. In the study of Elsisi [9], the imperialist competition algorithm is introduced to replace the trial-and-error method to obtain the optimal parameters of the neural network predictive controller to overcome the voltage deviation. The performance of the proposed algorithm is compared with that of the neural network predictive controller designed based on the genetic algorithm and the conventional proportional–integral–differential controller based on Ziegler–Nichols technology. The results show that the proposed algorithm has more advantages in performance. Kumar et al. [10] proposed a centralized model predictive controller (MPC) scheme to minimize voltage and frequency fluctuations. For effective control, normalized performance criteria have been considered, and the recently emerged HHO algorithm has been integrated for the first time for optimal adjustment of MPC weights. The transient response performance of the proposed MPC-HHO controller is compared with various existing controllers in the literature to verify the effectiveness of the controller. Çelik et al. [11] connected the output of the 1 + PD controller to the input of the PID controller, where the frequency and tie-line power deviations are also applied as feedback signals to subsequent controllers. In order to obtain the best results, the controller gain is adjusted simultaneously by the dragonfly search algorithm (DSA). The results show that the DSA optimization (1 + PD) – PID cascade strategy provides better performance than other strategies. Yilmaz et al. [12] discussed the load frequency control of multi-source power systems in two-zone non-inter thermal power systems. In order to improve the performance of the controller, a new objective function was designed, and the value of the objective function was reduced using a symbiotic biological search algorithm (SOAA) to obtain the PID controller parameters. To demonstrate the contribution of this study to the literature, the results of each power system were compared with popular results from high-quality journals. According to the comparison results, although the structure of the SOAA:PID controller is simple, after adjusting using the proposed target function, it is superior to other methods in terms of oscillation, establishment time, maximum positive overshoot, and maximum negative overshoot time field indicators of the frequency and connection line power variation curves. Arya and Kumar [13] analyzed the design and performance of a bacterial foraging optimization algorithm optimized fuzzy PI/PID (FPI/FPID) controller for automatic power generation control in multi-area interconnected traditional/reconfigurable power systems. First, a traditional two-zone non-reheat thermal system is considered, and the gain of the fuzzy controller is tuned using the square error objective function integration. Then, the results are compared with various optimization algorithms to prove the performance of the controller. Sahoo et al. [14] described the load frequency control of multi-micro grid , including renewable energy. Research suggests using fractional order fuzzy PID (FOFPID) controllers for frequency control. In order to adjust FOFPID parameters, a naturally inspired, population-based optimization paradigm was proposed. The stability of the proposed system is verified using a Bode diagram, and the robustness of mHHO against the scalability of existing methods in different dimensions is established. The feasibility and effectiveness of the proposed method are verified by real-time simulation. It can be seen that compared to PID and FPID, the mHHO-based FOFPID controller provides upgraded frequency regulation services [15].

1.3 Research gap and motivation

Overall analysis: With the progress of production and the extensive exploration in the scientific field, certain special challenges have emerged. These include system time delay [16,17] and the control of complex systems with high dimensions, multiple inputs, and multiple outputs. Additionally, traditional predictive control algorithms are inadequate when faced with controlled objects that require high precision predictive control. As a result, there is a growing demand for advancements in predictive control theory.

1.4 Challenges

Although some progress has been made in the above research, it is difficult to achieve ideal results and achieve optimal control performance by directly applying modern control theory to industrial control. Therefore, on the one hand, people do further research on the industrial system model, using strategies such as parameter identification, adaptive control, robust control, etc.; on the other hand, they start to seek new control algorithms based on numerical calculation and not too dependent on the system model.

1.5 Contribution

The research on the improvement of fuzzy fractional order PID predictive control algorithm is the computer optimal control algorithm generated under this background. The improvement of PID predictive control is sought, and the corresponding application research is carried out. It provides a technical foundation for the industrial application of computers and urges the industry to further devote themselves to the application research of advanced modern predictive control theory in industrial control so as to make up for the shortcomings of traditional PID control.

1.6 Article organization

The research is mainly divided into four parts. The first part is to construct an adaptive fuzzy PID energy-saving controller and complete the adaptive adjustment of PID parameters of fuzzy control. The second part is to improve the fuzzy fractional PID predictive control algorithm, mainly by optimizing the transfer function and parameter variables. The third part analyzes the performance of the optimized controller and judges the performance of the model through indicators such as delay time, transition time, and overshoot effect. The last part is a summary of the research and an analysis of the current shortcomings and future development directions.

2 Improvement of fuzzy fractional order PID predictive control algorithm

2.1 Control principle of PID predictive control equipment

In the energy-saving control of PID predictive control equipment, the conventional predictive control algorithm is usually used. The essence of the whole control process is to use a PID controller [18,19]. Assuming that A a and B b in the control set are membership functions, the relevant principles of PID predictive control equipment control are established, and the mathematical expression of PID controller is established by formula (1) to realize the control of PID predictive control equipment:

(1) C c = A a × α + B b × β .

In formula (1), α and β , respectively, represent the single-input value and output value of predictive control rules. The PID prediction framework diagram is shown in Figure 1.

Figure 1

PID prediction framework diagram.

2.2 PID predictive control equipment adaptive fuzzy PID energy-saving controller structure

The fuzzy fractional order PID control algorithm has simple principles, strong adaptability, and strong robustness. However, the actual PID predictive control equipment is nonlinear, time-varying, and uncertain to some extent, and the PID predictive control algorithm cannot guarantee the control effect. Therefore, a fuzzy fractional order PID predictive control algorithm is proposed [20]. It is applied to energy-saving control of PID predictive control equipment, and fuzzy control is introduced to set PID parameters [21], so as to achieve the best predictive control effect.

The adaptive fuzzy PID controller combines the fuzzy control system and PID controller to form a new controller. The PID controller is described by error and error change rate:

(2) W LK = L 1 × M K + L 2 × N K + L 3 × V K .

In formula (2), M K represents the output of the energy-saving controller, that is, the energy saved by PID predictive control equipment; L 1 stands for the proportional coefficient; L 2 stands for the integral action coefficient; L 3 stands for the differential action coefficient; N K and V K represent the electric quantity error and error change rate of PID predictive control equipment, respectively, which are calculated by formulas (3) and (4), respectively:

(3) N K = Y o ( k ) − Y j ( k ) ,

(4) V K = L 1 + L 2 + L 3 T t .

In formulas (3) and (4), Y o ( k ) and Y j ( k ) represent the reference value and actual output value of the given PID predictive control equipment, and T t represents the sampling period.

In order to improve the performance of the PID energy-saving controller, fuzzy control is introduced for adaptive tuning of PID controller parameters to adapt to parameter changes of PID predictive control equipment and interference caused by working conditions [22]. The fuzzy control system and the PID controller are combined to form a new energy-saving controller structure [23], as shown in Figure 2.

Figure 2

Structure diagram of adaptive fuzzy PID energy-saving controller.

According to the analysis of Figure 2, the adaptive fuzzy PID energy-saving controller is mainly composed of parameter-adjustable PID energy-saving control and fuzzy control. Since the initial values L 1 , L 2 , and L 3 are set in the PID controller, after the above analysis, the parameters L 1 ′ , L 2 ′ , and L 3 ′ input to the PID energy-saving controller are obtained by using formula (4):

(5) L 1 ′ = L 1 × ∑ R FG L 2 ′ = L 2 × ∑ R FG L 3 ′ = L 3 × ∑ R FG .

In formula (5), ∑ R FG represents the specified control parameter deviation of the PID controller, and the control results of PID predictive control equipment can be obtained through the above calculation.

2.3 Adaptive tuning of PID parameters based on fuzzy control

2.3.1 PID energy saving control parameter setting principle

On the basis of the above control results, the PID parameters of fuzzy control are adaptively adjusted [24]. The setting principles of PID energy-saving control parameters L 1 , L 2 , and L 3 are as follows:

In the case of large ∑ R FG , in order to improve the response speed of PID predictive control equipment and avoid differential overflow caused by the instantaneous increase in the initial stage, it is necessary to take a larger L 1 and a smaller L 3 . In addition, in order to avoid integral saturation and large overshoot of PID predictive control equipment response, it is necessary to delete the integral effect and take L 2 = 0 ;
In the case of medium ∑ R FG value, in order to reduce the response overshoot of PID predictive control equipment and ensure the response speed, L 2 should be taken as small, and L 1 L 3 should be taken as moderate;
When ∑ R FG is small, in order to make the PID predictive control equipment operate stably, the values of L 1 and L 2 need to be increased. In order to prevent the output response from oscillating around the set value and improve the anti-interference performance of the equipment, it is necessary to take a reasonable value of L 3 . The principle is as follows: if ∑ R FG ≤ 0 is small, L 3 is larger; if ∑ R FG > 0 is larger, L 3 is smaller. In general, L 3 is of medium size.

2.3.2 Design of fuzzy control rules based on PID parameter tuning principle

According to the PID parameter setting principle in Section 2.3.1, the fuzzy controller with two inputs and three outputs is selected. The fuzzy controller regards L 1 , L 2 , and L 3 as input language variables and L 1 ′ , L 2 ′ , and L 3 ′ as output language variables.

The value of deviation is (−6, −4, −2, 0, +2, +4, +6). After determining the universe, it is necessary to quantify the variables of the deviation value. If the basic universe of the deviation ∑ R FG is set as the actual change range of the variable value, the quantification factor is

(6) ∑ R FG ′ = ∑ R FG 7 .

Thus, the fuzzy control rules under the PID parameter tuning principle can be obtained.

2.3.3 Realization of adaptive fuzzy PID energy saving control for PID predictive control equipment

After determining the universe of all variables, the membership function was determined [25]. The triangle function is selected as the membership function, as shown in Figure 3.

Figure 3

Membership function curve of input and output.

According to the above analysis, the realization process of PID predictive control equipment energy-saving control based on PID parameter self-adaptive tuning of fuzzy control is as follows.

The values of ∑ R FG at a certain time and ∑ R FG ′ were calculated and then multiplied with their respective quantization factors. According to Figure 2, their membership degree was calculated and multiplied with their respective quantization factors to obtain the fuzzy adjustment values of L 1 , L 2 , and L 3 . At the same time, according to the fuzzy language values of L 1 ′ , L 2 ′ , and L 3 ′ , the corresponding membership degree was calculated, and the fuzzy judgment was carried out through the center of gravity method:

(7) S ls = ∑ i = 1 m u i D g .

In formula (7), u i represents the degree of membership, D g represents the number of degrees of membership, and then the judgment results are multiplied by their respective quantitative factors to obtain the precise adjustment values L 1 ′ , L 2 ′ , and L 3 ′ of L 1 , L 2 , and L 3 , so as to realize the adaptive fuzzy PID energy-saving control of PID predictive control equipment.

3 Improved predictive control algorithm based on fuzzy fractional PID

3.1 Design of fuzzy fractional order PID predictive transfer function model

In order to ensure that the PID predictive control equipment can realize high-speed operation, it is necessary to use corresponding technologies to control it electrically, improve work efficiency, reduce losses, and enhance service life. Using PID optimization technology and electrical control principle, the control system is roughly divided into five modules: active-axis servo drive module, X-axis servo drive module, Y-axis servo drive module, Z-axis servo drive module, and switch total amount control module. In addition, the corresponding high-power circuit, automatic numerical control, and emergency start and stop devices installed in the equipment act. The e60s model system is built-in and equipped with programmable logic controller device and logic control function to achieve effective control. Among them, the electric control is mainly carried out through the formation of the cross tool rest composed of two servo drive shafting X and Z. Since the equipment is generally in the state of 45° angle, in order to avoid the loss of position and data signals caused by the self-weight sliding, it is necessary to establish a corresponding static adjustment mechanism to help solve the problem, so that the working shaft of the equipment can maintain a balanced state.

Based on the aforementioned challenges, it is proposed to achieve a balanced state by considering the parameters and accuracy of the static data in the equipment. The imbalance of the driving machine is primarily caused by the high-frequency vibrations and abnormal noise produced by the driving shaft when operating at high speeds. This paper focuses on conducting a detailed analysis and research on this issue, and presents a well-designed response plan, as depicted in Figure 4.

Figure 4

Specific block diagram of control scheme.

In order to fully ensure the transmission and transformation ability of the predictive control algorithm to the input signal, it will be effectively realized by establishing the fuzzy fractional PID predictive function transfer model of the signal data. The specific block diagram is shown in Figure 5.

$Figure 5 Structure of fuzzy fractional order PID predictive function transfer model.$

Figure 5

Structure of fuzzy fractional order PID predictive function transfer model.

In PID predictive control equipment, the working frequency of the pulse mechanism is generally 20 Hz, accounting for 85% of the total control mechanism. The input voltage is 15 V, and the output voltage is 10 V. The time delay in this transmission process is negligible. Therefore, the time-based control signal transmission function is expressed as the following relationship:

(8) G 12 = V M A M .

In formula (8), V M represents the output voltage value of the system, and A M represents the proportion of the pulse signal with a power of 20 Hz. The current transfer function of the electric push rod is expressed as follows:

(9) G 12 ′ = 1 / K e T m + s .

In formula (9), K e represents the current coefficient, s represents the common electromagnetic speed, and T m represents the common electromechanical time. According to the current transfer function formula, the actual PID predictive control parameters can be substituted to calculate the final results.

3.2 Predictive control algorithm based on PID optimization technology

In most PID predictive control devices, the internal automatic control parameters have changed uncontrollably due to the influence of external factors. In order to effectively ensure the working quality of the system, it is necessary to transfer the data in which the parameters change to the PID optimization controller and reasonably adjust the corresponding data parameter variables through precise calculation and analysis, so that the control parameters are consistent with the actual transmission data settings and finally complete the efficient automatic control system design. As shown in Figure 6, the PID optimization controller can be adjusted in three ways: proportional adjustment, integral adjustment, and differential adjustment according to actual parameters.

Figure 6

PID optimization control structure.

In proportional regulation, parameter integral regulation, and differential regulation, there is a positive proportional relationship between the input known data error and the output signal error. Among them, proportional regulation is the simplest and intuitive regulation mode, while parameter integral regulation is the most efficient but also the most complex mode. Because it will have the problem of steady-state error, in order to make the PID predictive control equipment operate reasonably, it is necessary to introduce the corresponding integral term into the PID optimization controller. This integral term will change with the change of time, so when time continues to grow, this integral term will also increase correspondingly.

Based on this, the controller can be gradually pushed to carry out efficient output, so as to form a closed working chain to ensure the normal operation of the equipment. PID optimal control guidance is completed according to the proportion, differential, and integral of the corresponding mechanism. Based on the special relationship law among the three adjustment mechanisms, they can coordinate and integrate with each other according to the role of the three control mechanisms, which can effectively solve the problem of judgment error and speed error in the control system, adjust the data change rate, and reasonably control the output.

The basic control law of PID optimization technology is

(10) U qe = 1 T 1 ∫ 0 T T d + U ( t ) d t .

In formula (10), U ( t ) represents the signal transformation law under the proportional regulation control program and G ( s ) = represents the control data sample.

After time domain simplification, according to the data transfer model of the Plath transform function, the following can be obtained:

(11) P OI = R ( s ) W ( s ) .

In formula (11), R ( s ) represents the signal transformation law under the parameter integral regulation control program and W ( s ) represents the signal transformation law under the differential regulation program. In this way, specific digital processing can be carried out according to the actual working conditions of the equipment. Assuming that the basic time of the system at the data sampling time point T k is t , the data integration method of the matrix model is used to simulate and replace, so that the data difference can gradually approach the actual value. The expression formula is

(12) D FG = T k , k = 0 , 1 , 2 , … , n .

In formula (12), k represents the data monitoring threshold of the control system. The control algorithm of PID optimization technology based on this data discretization can be obtained according to formula (12):

(13) u ( k ) = D FG × C cv × H JG × X sf .

In formula (13), C cv represents the parameter integral control regulation relationship, H JG represents the differential regulation relationship, and X sf represents the sampling setting sequence, then the time deviation at the k control position is u ( k ) , and the time deviation at the k − 1 control position is u ( k − 1 ) .

In this way, the deviation between the actual time and the predictive control time in the control equipment can be accurately calculated according to the above process, so as to ensure the unity of the state of the control mechanism, so as to reduce the corresponding loss, and improve the working efficiency of the equipment, so as to improve the research on the predictive control algorithm based on fuzzy fractional PID.

In the power system, the excitation system is an important part of the synchronous generator, which directly affects the operation characteristics of the generator. Since the excitation regulator has the regulation function, the excitation system will automatically increase or decrease the supplied excitation current, so that the terminal voltage of the generator can return to the given level, ensuring a certain regulation accuracy. In practice, conventional PID control or predictive function control cannot meet the nonlinear and time-varying characteristics of the system. However, the predictive control algorithm based on fuzzy fractional PID overcomes the constraints of nonlinearity and time-varying by adding adjustable parameters and greatly optimizes the control effect.

4 Experimental analysis

In order to verify the effectiveness of the improved research on the fuzzy fractional order PID predictive control algorithm, an experiment needs to be carried out. In the process of the experiment, the PID predictive control of reference [3] algorithm, reference [4] algorithm, and this algorithm are compared and designed, respectively, by using the control structure. Among them, the algorithms in the studies of Priyanka et al. [3] and Wenhua et al. [4] use the PID regulator as the main regulator and the P regulator as the auxiliary regulator. The improved algorithm uses the improved genetic optimization fuzzy PID controller as the main regulator and the P regulator as the auxiliary regulator. In order to ensure the fairness of the experiment, other experimental environments and experimental parameters are consistent. Parameter settings are shown in Table 1.

Table 1

Parameter setting table

Serial number	Parameter	Content
1	Learning efficiency setting	0.20
2	Inertia coefficient setting	0.01
3	Value range of initial value of weight coefficient	[−0.6, 0.6]
4	Load	20, 40, 60, 80 and 100%
5	Static error	There is a corresponding proportional relationship between input and output

The detailed operation process is shown in Figure 7.

$Figure 7 Experimental flow chart of fuzzy fractional order PID predictive control.$

Figure 7

Experimental flow chart of fuzzy fractional order PID predictive control.

It can be seen from Figure 7 that since the control system in the fuzzy fractional order PID predictive control process is mainly composed of the controlled system, detector, detection feedback mechanism, and other links, the big data fuzzy PID control method is used to complete the experimental process control. After the system is disturbed by different factors, the state parameters generated in the process will change immediately, and the change information of all state parameters can be accurately predicted through the sensor. Accurately control the speed change to ensure the stability of surface processing. When the sensor detects that the parameter conversion is completed, the big data fuzzy PID control unit is used to set the constraint conditions, compare the deviation of different performance indicators, and correct the system input parameters through the host output correction signal to ensure that the set conditions and indicators are converted during the experiment, the stability reaches the best state, and the fuzzy fractional PID predictive control is realized.

On the basis of the above experimental parameters and experimental process, the predictive control process is divided into three stages with the same predictive control duration, and the duration of each stage is fixed at 60 min. The stability changes under different predictive control stages are analyzed. The experimental results are shown in Figure 8.

Figure 8

Stability analysis results of different predictive control stages.

By analyzing the experimental data in Figure 8, it can be seen that in different predictive control stages, the stability of fuzzy fractional PID predictive control is always in a relatively stable state, and the influence of spindle speed on the stability is relatively small. It can be seen that this algorithm can better control the stability.

In order to further verify the effectiveness of the algorithm in this article, the output responses of different predictive control algorithms are analyzed under the condition of step input. Figure 9 shows the experimental results.

Figure 9

Simulation waveform curve results of predictive control with different algorithms.

According to Figure 9, the algorithm in the study of Priyanka et al. [3] has about 30% overshoot, long adjustment time, many oscillation times, and poor energy-saving control effect. In the algorithm in the study of Wenhua et al. [4], although the energy-saving control method has good stability and no overshoot and oscillation, its control accuracy is low. The output of the fuzzy fractional order PID predictive control of this algorithm has no overshoot, and the rising speed is the fastest, and the stability and control accuracy are better. This algorithm can get the best performance index for the accuracy and efficiency of fuzzy fractional PID predictive control, which verifies the effectiveness of this algorithm.

In PID predictive control equipment, due to the complexity of the environment, the change of equipment parameters will also affect the predictive control results. Assume that the ventilation rate of PID predictive control equipment changes from the current 20 to 16 h/time, and other parameters remain unchanged. Under step input, the anti-parameter mismatch ability of three different control algorithms after parameter change to verify the robustness of the algorithm is observed. The results before parameter mismatch are consistent with those in Figure 10. The parameter mismatch results are shown in Figure 10.

Figure 10

After parameter mismatch.

By analyzing Figure 10, it can be seen that after the parameter mismatch, the output response transition time of the algorithm in the study of Priyanka et al. [3] is delayed, and the steady-state error is larger than before. The algorithm of the study of Wenhua et al. [4] not only has about 10% overshoot but also has a large steady-state error after parameter mismatch. After the parameter mismatch, the stability, overshoot, time, and control accuracy of the proposed algorithm are basically unchanged.

By analyzing the above experimental process, it can be seen that when the parameters of PID predictive control equipment change, the performance of other energy-saving control algorithms will deteriorate due to the change of parameters. This algorithm is not sensitive to the change of parameters, which shows that this algorithm has good robustness. The comparison results of performance indicators of different algorithms for predictive control processes are shown in Table 2.

Table 2

Comparison results of performance indexes of predictive control process with different algorithms

Different algorithms	Delay time [ t d ] (s)	Transition time [ t s ] (s)	Overshoot (%)
The algorithm of Priyanka et al. [3]	100	2,000	31
The algorithm of Wenhua et al. [4]	120	1,800	30
Algorithm in this article	80	600	0

It can be seen from the experimental results in Table 2 that the algorithm of Priyanka et al. [3] and the algorithm of Wenhua et al. [4] have large system overshoot in the process of small area temperature predictive control, and the algorithm in this article effectively suppresses the system overshoot. In terms of adjustment time, the adjustment time of the algorithm in this article is far less than that of the algorithm in the studies of Priyanka et al. [3] and Wenhua et al. [4], which shows that the algorithm in this article is less disturbed when carrying out small area temperature control, has better anti-disturbance ability than the traditional algorithm, and has strong robustness.

To sum up, this algorithm can get the best performance index for the accuracy and efficiency of fuzzy fractional PID predictive control, which verifies the effectiveness of this algorithm. After the parameter mismatch, the stability, overshoot, time, and control accuracy of this algorithm are basically unchanged. The algorithm in this article is less disturbed in the small area temperature control, and its anti-disturbance ability is better than the traditional algorithm, so it has strong robustness.

5 Conclusion and prospect

Through the construction and experiment of a predictive control algorithm based on fuzzy sequential PID, the following conclusions are proved.

Based on the improved fuzzy hierarchical PID predictive control algorithm, the optimal performance indicators of PID predictive control accuracy and efficiency can be obtained, which verifies the effectiveness of the algorithm.
After the parameter mismatch, the fuzzy hierarchical PID predictive control algorithm still exhibits good performance, with a system delay time of 80 s. The transition time is 600, and the overshoot is 0%.
The algorithm in this article has less interference in small-area temperature control, and its anti-interference ability is superior to traditional algorithms, with strong robustness.

The method proposed in this article has been successfully applied to small-area temperature prediction and control, but there are still shortcomings and broader development prospects. When the algorithm is used to control the water level and temperature of a water tank, the characteristics of the actual object are inconsistent with those of the transfer function, resulting in a certain optimization space for control delay. Therefore, when selecting actual objects, subsequent research should try to conform to the characteristics of the transfer function, thereby further improving the real-time performance of the model. The algorithm also has broader application prospects, such as in industrial control and industrial practice. Subsequent research can link this algorithm with industry for research.

Funding information: The research was supported by the "Blue Project" of Nanjing Vocational College of Information Technology; the Natural Science Fund Project of Nanjing Vocational College of Information Technology (No. YK20201402).
Author contributions: The manuscript was written by Rongzhen Shi.
Conflict of interest: Author states no conflict of interest.
Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Received: 2022-12-08

Revised: 2023-03-27

Accepted: 2023-05-06

Published Online: 2023-10-28

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/jisys-2022-0288

Keywords for this article

fuzzy fractional order; PID predictive control algorithm; controller structure; parameter setting principle; fuzzy control rules

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