Coal-fired unit rapid load response control method based on differential feedforward and fuzzy weight

Abstract

The invention relates to a coal-fired unit rapid load response control method based on differential feed-forward and fuzzy weight, which is characterized in that a differential feed-forward link is added before coal feed quantity control, so that the coal feed quantity is instantaneously and greatly adjusted along with the change of the opening degree of a valve, the response delay time of the coal feed quantity is greatly shortened, and a foundation is laid for the unit to rapidly respond to the load change. The opening degree of the main steam valve and the water supply amount are cooperatively controlled, so that the three components are matched with one another, stability of parameters of the unit in the load change process is ensured, and the problem of unit operation instability caused by adjustment of a single parameter is avoided. And a fuzzy rule is utilized to reasonably distribute the weight coefficient of the target function, so that good balance of different control targets is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of load response control of coal-fired units, and in particular relates to a fast load response control method of a coal-fired unit based on differential feedforward and fuzzy weight. Background Art

[0002] The rapid development of renewable energy sources such as wind and solar power has effectively alleviated my country's problems of fossil energy shortages and environmental pollution. However, the associated strong randomness, volatility, and intermittency pose a serious threat to the safe, economical, and stable operation of the power grid. Flexible energy is urgently needed to balance electricity supply and demand. Existing large-scale thermal power plants are seen as an important supplement to intermittent renewable energy. Improving the flexibility of thermal power generating units is crucial to increasing renewable energy. To ensure power balance, the power system needs to have strong ramping capabilities to cope with fluctuations in the system's net load caused by fluctuations in renewable energy output. Coal-fired power, as a conventional power source in my country with relatively mature technology, relatively low cost, and relatively comprehensive functions, urgently needs to improve its regulation capabilities, such as rapid load response, to better adapt to the development of renewable energy, make room for new energy generation, and generate peak output during periods of low wind and solar output and peak load, supporting the high-quality development of renewable energy.

[0003] To improve the rapid load response of coal-fired power plants, various methods have been developed. For example, advanced monitoring and diagnostic technologies are being employed, along with high-precision sensors and monitoring equipment, to provide real-time monitoring of unit operating parameters such as temperature, pressure, flow rate, vibration, as well as information such as coal quality and combustion status. By analyzing and processing this data, operational issues and potential faults can be promptly identified, providing a basis for optimizing operation and maintenance, and ensuring the safety and reliability of the units. During coal-fired power plant operation, when load increases, the main steam valve, coal feed rate, and water supply must be adjusted accordingly. However, due to the inherent characteristics of coal-fired power plants, their load response speed is often slow, making it difficult to quickly meet load fluctuations. This problem can hinder the units' ability to respond promptly to grid load fluctuations, impacting grid stability and economic efficiency, and reducing the units' market competitiveness. Currently, existing technologies for coal-fired power plant load control primarily rely on conventional feedback control methods, which adjust the coal feed rate, main steam valve opening, and water supply by detecting deviations between the unit's current operating parameters and target parameters. However, this approach is difficult to achieve rapid response when the load changes rapidly due to factors such as regulation lag, and cannot well adapt to the requirements of modern power grids for unit flexibility. Therefore, a control method that can effectively improve the load response speed of coal-fired units is urgently needed. Summary of the Invention

[0004] In view of the above situation, in order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide a coal-fired unit rapid load response control method based on differential feedforward and fuzzy weight, which can effectively improve the load response speed of the coal-fired unit and enhance the flexibility and economy of the unit operation.

[0005] The technical solution provided by the present invention is:

[0006] A method for rapid load response control of a coal-fired unit based on differential feedforward and fuzzy weights comprises the following steps:

[0007] Step 1: Differential feedforward signal introduction

[0008] Before controlling the coal feed rate, a differential feedforward link associated with the valve opening rate of change is introduced, and its expression is:

[0009] M ff (s) = K ff s*Δμ(s)

[0010] Among them: K ff is the differential feedforward coefficient, s is the Laplace operator, and Δμ is the rate of change of valve opening. This differential feedforward link captures the dynamic change trend of valve opening and converts its rate of change into a pre-regulation signal for coal feed rate. The total change in coal feed rate is:

[0011] ΔM total (s)=ΔM fb (s)+M ff (s)

[0012] Where: ΔM total (s) is the change of total coal feeding amount, ΔM fb (s) is the change of coal feeding rate regulated by PID feedback, M ff (s) is the change of coal feeding rate for feedforward regulation;

[0013] Differential feedforward enables a significant adjustment of the coal feed rate at the instant the valve opening changes, compensating for the pure delay and inertia of the coal feed rate. Comparing the transfer function of the coal feed rate to the load before and after the addition of differential feedforward, the equivalent transfer function of the coal feed rate after the addition of differential feedforward is:

[0014]

[0015] The differential feedforward link is tightly coupled with the main steam valve opening, enabling rapid sensing of load change trends. When the valve opening increases, the differential feedforward link immediately outputs a positive regulation signal, prompting a rapid increase in coal feed. Conversely, when the valve opening decreases, the feedforward signal promptly adjusts the coal feed to reduce it, thereby achieving dynamic matching of coal feed and steam flow, effectively avoiding the problem of slow load response caused by delayed coal feed regulation.

[0016] Step 2: Determination of differential feedforward coefficient and PID parameters

[0017] Construct a multi-objective optimization function that includes load tracking, temperature stability, pressure stability, and control variable changes:

[0018]

[0019] Where: u=[M(t),μ(t),W(t)] is the control vector, e N To meet the tracking error, e T is the main steam temperature error, e p is the main steam pressure error, Δu(t) is the control quantity change, ω1, ω2, ω3, ω4 are weight coefficients, Σω i =1;

[0020] In order to ensure that the above four indicators can be balanced, fuzzy rules are used to dynamically adjust the weight coefficients. The design of fuzzy rules is based on e N , e T , e p The three are inputs, and the weight increments Δω1, Δω2, Δω3, and Δω4 are outputs; the input fuzzy set is divided into 5 levels: {VS (extremely small), S (small), M (medium), L (large), VL (maximum)}, and the input fuzzy set is divided into 5 levels: {NB (negative large), NS (negative small), Z (zero), PS (positive small), PB (positive large)}; ω i (t+1)=ω i (t)+Δω i .

[0021] Step 3: Determine the constraints

[0022] Valve opening constraint conditions: 30% ≤ μ ≤ 90%; at the same time, the opening change rate satisfies

[0023] Coal supply constraints:

[0024] Water supply constraints:

[0025] Main steam temperature control requirements: temperature fluctuation range is controlled within ±10℃;

[0026] Main steam pressure control requirements: pressure fluctuation is limited to ±0.5MPa;

[0027] Step 4: Optimize the objective function

[0028] Use PSO to optimize the objective function to determine the final control parameter K p , T i , T d, K ff ;

[0029] First, 30 particles are randomly generated, each particle consists of a set of PID parameters and differential feedforward coefficients X = [K p , T i , T d , K ff ], each particle adjusts its speed and position according to the local optimum and the global optimum;

[0030] v i =ω*v i +c1*r1*(pbest i -X i )+c2*r2*(gbest-X i )

[0031] Where: v i =[ΔK p , ΔT i , ΔT d , ΔK ff ] is the example update speed, ω is the inertia weight, which controls the search range; c1, c2 are learning factors, which guide the particles to move closer to the optimal position; r1, r2 are random numbers, which increase the search diversity, X i is the particle at the i-th iteration;

[0032] Location Updates:

[0033] X i+1 =X i +v i

[0034] Initialization weight: ω1=ω2=ω3=ω4=0.25, PSO parameter inertia weight ω=0.9, c1=c2=2, number of iterations is 200; repeat iterative optimization, if the multi-objective optimization function J of the new particle is less than pbest i , then update pbest i If it is less than gbest, update gbest; when the iteration reaches 200 times, or the J value change rate of gbest is less than 0.5% in 20 consecutive iterations, stop the iteration and output gbest as the optimal control parameter: [K p , T i , T d , K ff ].

[0035] The present invention adds a differential feedforward link before controlling the coal feed rate, so that the coal feed rate can be adjusted instantly and significantly with the change of valve opening, which greatly shortens the response lag time of the coal feed rate and lays the foundation for the unit to quickly respond to load changes. The main steam valve opening and water supply are controlled in a coordinated manner so that the three can cooperate with each other, ensuring the stability of various parameters of the unit during load changes and avoiding the problem of unstable operation of the unit due to the adjustment of a single parameter. The weight coefficients of the objective function are reasonably allocated using fuzzy rules to achieve a good balance for different control objectives. The valve opening change rate is first introduced as a feedforward signal into the coal feed control, breaking through the hysteresis of traditional feedback regulation, realizing instantaneous and significant adjustment of the coal feed rate at the initial stage of load change, integrating multivariable control, and realizing coordinated optimization of load response and key parameter stability, which effectively improves the load response speed of the coal-fired unit, enables the unit to quickly adapt to changes in the grid load, and at the same time ensures that various important parameters of the unit maintain stable operation, thereby improving the peak-shaving capacity and market competitiveness of the unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0037] The specific implementation of the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0038] like Figure 1 As shown, the present invention provides a method for rapid load response control of a coal-fired unit based on differential feedforward and fuzzy weight, comprising the following steps:

[0039] First, analyze the response characteristics of the main steam valve opening, coal supply rate, and water supply rate to load changes:

[0040] 1. Influence of main steam valve opening on load

[0041] The change in the main steam valve opening directly changes the steam flow entering the turbine, which in turn affects the load. Its transfer function model is:

[0042]

[0043] Among them: G μ (s) is the transfer function from main steam valve opening to load, ΔN(s) is the Laplace transform of load change, Δμ(s) is the Laplace transform of valve opening, K μ is the valve opening gain coefficient, T μ is the valve time constant. The model shows that the effect of valve opening change on load is a first-order inertia characteristic, with a fast response and a small time constant;

[0044] 2. Impact of coal feed rate on load

[0045] The change in coal feed rate generates heat through combustion, which is converted into steam energy through heat transfer in the steam-water system and affects the load. The transfer function model is:

[0046]

[0047] Among them: G M (s) is the transfer function from coal feed rate to load, ΔM(s) is the Laplace transform of coal feed rate change, K M is the coal feed gain coefficient, τ M is the pure delay time, T M1 、T M2 The model shows that the effect of coal feed on load has a large pure delay and inertia, and the response is slow, which is the main reason for the load response lag;

[0048] 3. Impact of water supply on load

[0049] Changes in feed water flow affect the boiler steam-water cycle, indirectly affecting steam production and parameters, and thus affecting load. The transfer function model is:

[0050]

[0051] Among them: G W (s) is the transfer function from water flow to load, ΔW(s) is the Laplace transform of water flow change, K W is the water supply gain coefficient, τ W is the pure delay time, T W The effect of water supply on load is a first-order inertia plus pure delay characteristic, and the response speed is between that of valve and coal supply.

[0052] From the above, it can be seen that the valve opening can respond to load changes in a timely manner, but since the fuel cannot be supplied in time, the unit load cannot respond in time; it can be seen that the delay characteristic of the coal feed rate is the main reason for the load lag, and the valve opening can respond to load changes in a timely manner. Therefore, the present invention adds a differential feedforward of the associated valve opening to the coal feed rate control channel, so as to quickly adjust the coal feed rate and then quickly respond to load changes.

[0053] Step 1: Differential feedforward signal introduction

[0054] Before controlling the coal feed rate, a differential feedforward link associated with the valve opening rate of change is introduced, and its expression is:

[0055] M ff (s) = K ff s*Δμ(s)

[0056] Among them: K ffis the differential feedforward coefficient, s is the Laplace operator, and Δμ is the rate of change of valve opening. This differential feedforward link captures the dynamic change trend of valve opening and converts its rate of change into a pre-adjustment signal for coal feed rate. In actual operation, when the grid load command changes, the main steam valve opening is activated first, and the differential feedforward link responds quickly, allowing targeted adjustments to be made to the coal feed rate at an early stage before combustion delay occurs, effectively compensating for the slow response of coal feed rate. After adding the differential feedforward, the total change in coal feed rate is:

[0057] ΔM total (s)=ΔM fb (s)+M ff (s)

[0058] Where: ΔM total (s) is the change of total coal feeding amount, ΔM fb (s) is the change of coal feeding rate regulated by PID feedback, M ff (s) is the change of coal feeding rate for feedforward regulation;

[0059] Differential feedforward enables a significant adjustment of the coal feed rate at the instant the valve opening changes, compensating for the pure delay and inertia of the coal feed rate. Comparing the transfer function of the coal feed rate to the load before and after the addition of differential feedforward, the equivalent transfer function of the coal feed rate after the addition of differential feedforward is:

[0060]

[0061] The differential feedforward link is tightly coupled with the main steam valve opening, enabling rapid sensing of load change trends. When the valve opening increases, the differential feedforward link immediately outputs a positive regulation signal, prompting a rapid increase in coal feed. Conversely, when the valve opening decreases, the feedforward signal promptly adjusts the coal feed to reduce it, thereby achieving dynamic matching of coal feed and steam flow, effectively avoiding the problem of slow load response caused by delayed coal feed regulation.

[0062] Furthermore, this differential feedforward link features adaptive adjustment capabilities. By continuously monitoring and analyzing the valve opening rate change under varying operating conditions, the pre-adjustment amplitude of the coal feed can be flexibly adjusted. For example, when the unit is operating at low load, a relatively small valve opening rate change can trigger appropriate coal feed adjustments, avoiding combustion instability caused by over-adjustment. Under high-load conditions, however, a larger valve opening change can drive a rapid response to the coal feed, ensuring that energy supply keeps pace with changes in load demand.

[0063] Step 2: Determination of differential feedforward coefficient and PID parameters

[0064] In order to ensure that the unit responds quickly to load changes while maintaining stability of indicators such as main steam temperature and main steam pressure, a multi-objective optimization function is constructed that includes load tracking, temperature stability, pressure stability, and control variable changes:

[0065]

[0066] Where: u=[M(t),μ(t),W(t)] is the control vector, e N To meet the tracking error, e T is the main steam temperature error, e p is the main steam pressure error, Δu(t) is the control quantity change, ω1, ω2, ω3, ω4 are weight coefficients, ∑ω i =1;

[0067] In order to ensure that the above four indicators can be balanced, fuzzy rules are used to dynamically adjust the weight coefficients. The design of fuzzy rules is based on e N , e T , e p The three are inputs, and the weight increments Δω1, Δω2, Δω3, and Δω4 are outputs; the input fuzzy set is divided into 5 levels: {VS (extremely small), S (small), M (medium), L (large), VL (maximum)}, and the input fuzzy set is divided into 5 levels: {NB (negative large), NS (negative small), Z (zero), PS (positive small), PB (positive large)}; ω i (t+1)=ω i (t)+Δω i .

[0068] The fuzzy rules are shown in Appendix 1. When the deviation of a certain parameter increases, the corresponding weight correction level increases, and the correction levels of other parameters decrease. When the deviations of two or three parameters are large, the "balanced improvement" strategy is adopted to avoid excessive priority of a single target causing other parameters to lose control. The rule table can be iteratively optimized according to the actual operating data of the unit, and the control accuracy can be improved by increasing the number of rules.

[0069] Table 1 Fuzzy rules table

[0070]

[0071]

[0072] Step 3: Determine the constraints

[0073] Valve opening constraint: 30% ≤ μ ≤ 90%. This constraint is intended to prevent the valve from being over-opened or over-closed, thereby avoiding flow capacity limitations due to insufficient opening or system instability caused by excessive opening. At the same time, the opening change rate satisfies This is to prevent the valve from moving too violently, reduce the impact on the pipeline and related equipment, and ensure the safety and stability of the system operation. In actual working conditions, if the valve opening changes too quickly, it may cause water hammer effect and cause irreversible damage to the equipment.

[0074] Coal supply constraints: This range is set to ensure the stability of boiler combustion, avoiding flame extinction and reduced combustion efficiency due to too low a coal feed, or incomplete combustion and coking due to too high a coal feed. The rate of change must be met. This limit allows the system sufficient time to respond to changes in the coal feed and maintain the dynamic balance of the combustion process. For example, if the coal feed increases sharply and is not restricted, it may cause a sudden increase in furnace temperature and disrupt the thermal balance in the furnace.

[0075] Water supply constraints: This constraint ensures the normal operation of the steam-water system. Too low a water flow rate will result in insufficient cooling of the heating surface, leading to serious accidents such as overheating and tube bursting. Too high a water flow rate may affect the steam quality and unit efficiency. The rate of change must be met to ensure that the adjustment of the feedwater flow rate matches the steam load and boiler heat load, avoiding drastic changes in the drum water level due to excessive feedwater fluctuations, which may affect the safe and stable operation of the unit.

[0076] Main steam temperature control requirements: Main steam temperature is a key parameter for measuring the economic and safety of unit operation. Excessive temperature will cause excessive thermal stress on pipelines and equipment materials, shortening their service life and even causing safety accidents. Excessive temperature will lead to a decrease in the thermal efficiency of the unit. Controlling the temperature fluctuation range within ±10°C can effectively guarantee the reliability and economy of unit operation and ensure that the steam has good working capacity when entering the turbine.

[0077] Main steam pressure control requirements: Main steam pressure stability is crucial to the unit's power output and equipment safety. Excessive pressure may cause pressure-bearing components to exceed their design capacity, while too low pressure cannot meet the turbine's work requirements, reducing the unit's power generation efficiency. Limiting pressure fluctuations to ±0.5 MPa helps maintain stable unit operation and ensures efficient and safe operation under different load conditions.

[0078] Step 4: Optimize the objective function

[0079] Use PSO to optimize the objective function to determine the final control parameter K p , T i , T d , K ff ;

[0080] First, 30 particles are randomly generated, each particle consists of a set of PID parameters and differential feedforward coefficients X = [Kp , T i , T d , K ff ], each particle adjusts its speed and position according to the local optimum and the global optimum;

[0081] v i =ω*v i +c1*r1*(pbest i -X i )+c2*r2*(gbest-X i )

[0082] Where: v i =[ΔK p , ΔT i , ΔT d , ΔK ff ] is the example update speed, ω is the inertia weight, which controls the search range; c1, c2 are learning factors, which guide the particles to move closer to the optimal position; r1, r2 are random numbers, which increase the search diversity, X i is the particle at the i-th iteration;

[0083] Location Updates:

[0084] X i+1 =X i +v i

[0085] Initialization weight: ω1=ω2=ω3=ω4=0.25, PSO parameter inertia weight ω=0.9, c1=c2=2, number of iterations is 200; repeat iterative optimization, if the multi-objective optimization function J of the new particle is less than pbest i , then update pbest i If it is less than gbest, update gbest; when the iteration reaches 200 times, or the J value change rate of gbest is less than 0.5% in 20 consecutive iterations, stop the iteration and output gbest as the optimal control parameter: [K p , T i , T d , K ff ].

[0086] In practical application, 4000 sets of real-time operating data of a 300MW coal-fired unit under typical operating conditions were selected and the above method was used to search for the optimal control parameters [K p , T i , T d , K ff ], and built a feedforward link in the DCS, writing the control parameters into the DCS control system. Then, a variable load disturbance test was conducted, with the target load increasing from 200MW to 240MW. The following conclusions were drawn:

[0087] Target load change: ΔN d =40MW, valve opening increases Δμ=ΔN d / K μ =40 / 2=20% (take K μ =2MW / %). This calculation clarifies the corresponding adjustment of valve opening when the target load changes, providing a basic basis for subsequent control system parameter adjustment.

[0088] Differential feedforward module output: ΔM ff =K ff *dμ / dt, the valve completes the opening change within 10s, then dμ / dt=2% / s, take K ff =1.2 / (h·%·s), we can get ΔM ff =1.2*2=2.4t / (h·s). During the 10s change in valve opening, the coal feed rate needs to be instantly increased by 24t / h. This rapid adjustment of the coal feed rate can effectively reduce the lag in load response.

[0089] Feedwater adjustment calculation: To maintain stable operation of the coal-fired unit's steam-water system, the feedwater rate must be adjusted synchronously with the water-coal ratio. Given a water-coal ratio of K = 6.5, ΔW = 6.5 * 24 = 156 t / h. By strictly adjusting the feedwater rate according to the water-coal ratio, the boiler's evaporation rate can be matched to the coal feed rate, avoiding steam-water imbalance and ensuring safe and stable unit operation.

[0090] With other conditions remaining unchanged, the advantages of this method compared to traditional PID control are as follows: the target load response time is significantly shortened from 6.2 minutes using traditional PID to 3.8 minutes, greatly improving the unit's ability to quickly respond to load changes. At the same time, main steam temperature fluctuations are controlled within ±5°C, and main steam pressure fluctuations are controlled within ±0.3MPa, a significant improvement compared to the traditional PID's ±10°C and ±0.5MPa, respectively. Through pre-adjustment of the coal feed rate in the feedforward link and parameter adjustment of the multi-objective optimization module, the load response performance of the coal-fired unit is significantly improved. This effectively ensures the stability of key parameters during unit operation, providing a strong guarantee for the unit's efficient, safe, and stable operation.

Claims

1. A method for rapid load response control of coal-fired units based on differential feedforward and fuzzy weight, characterized in that: The following steps are involved: Step 1: Differential feedforward signal introduction Before controlling the coal feed rate, a differential feedforward link associated with the valve opening rate of change is introduced, and its expression is: M ff (s)=K ff s*Dm(s) Among them: K ff is the differential feedforward coefficient, s is the Laplace operator, and Δμ is the rate of change of valve opening. This differential feedforward link captures the dynamic change trend of valve opening and converts its rate of change into a pre-regulation signal for coal feed rate. The total change in coal feed rate is: ΔM total (s)=ΔM fb (s)+M ff (S) Where: ΔM total (s) is the total coal feeding change, ΔMfb(s) is the coal feeding change adjusted by PID feedback, M ff (s) is the change of coal feeding rate for feedforward regulation; Differential feedforward enables a significant adjustment of the coal feed rate at the instant the valve opening changes, compensating for the pure delay and inertia of the coal feed rate. Comparing the transfer function of the coal feed rate to the load before and after the addition of differential feedforward, the equivalent transfer function of the coal feed rate after the addition of differential feedforward is: The differential feedforward link is tightly coupled with the main steam valve opening, enabling rapid sensing of load change trends. When the valve opening increases, the differential feedforward link immediately outputs a positive regulation signal, prompting a rapid increase in coal feed. Conversely, when the valve opening decreases, the feedforward signal promptly adjusts the coal feed to reduce it, thereby achieving dynamic matching of coal feed and steam flow, effectively avoiding the problem of slow load response caused by delayed coal feed regulation. Step 2: Determination of differential feedforward coefficient and PID parameters Construct a multi-objective optimization function that includes load tracking, temperature stability, pressure stability, and control variable changes: Where: u=[M(t),μ(t),W(t)] is the control vector, e N To meet the tracking error, e T is the main steam temperature error, e p is the main steam pressure error, Δu(t) is the control quantity change, ω1, ω2, ω3, ω4 are weight coefficients, Σω i =1; In order to ensure that the above four indicators can be balanced, fuzzy rules are used to dynamically adjust the weight coefficients. The design of fuzzy rules is based on e N , e T , e p The three are inputs, and the weight increments Δω1, Δω2, Δω3, and Δω4 are outputs; the input fuzzy set is divided into 5 levels: {VS (extremely small), S (small), M (medium), L (large), VL (maximum)}, and the input fuzzy set is divided into 5 levels: {NB (negative large), NS (negative small), Z (zero), PS (positive small), PB (positive large)}; ω i (t+1)=ω i (t)+Δω i . Step 3: Determine the constraints Valve opening constraint condition: 30%≤μ≤90%; The opening change rate satisfies Coal supply constraints: Water supply constraints: Main steam temperature control requirements: temperature fluctuation range is controlled within ±10℃; Main steam pressure control requirements: pressure fluctuation is limited to ±0.5MPa; Step 4: Optimize the objective function Use PSO to optimize the objective function to determine the final control parameter K p , T i , T d , K ff ; First, 30 particles are randomly generated, each particle consists of a set of PID parameters and differential feedforward coefficients X = [K p , T i , T d , K ff ], each particle adjusts its speed and position according to the local optimum and the global optimum; in i =ω*v i +c1*r1*(pbest i -X i )+c2*r2*(gbest-X i ) Where: v i =[ΔK p , ΔT i , ΔT d , ΔK ff ] is the example update speed, ω is the inertia weight, which controls the search range; c1, c2 are learning factors, which guide the particles to move closer to the optimal position; r1, r2 are random numbers, which increase the search diversity, X i is the particle at the i-th iteration; Location Updates: X i+1 =X i +v i Initialization weight: ω1=ω2=ω3=ω4=0.25, PSO parameter inertia weight ω=0.9, c1=c2=2, number of iterations is 200; repeat iterative optimization, if the multi-objective optimization function J of the new particle is less than pbest i , then update pbest i If it is less than gbest, update gbest; when the iteration reaches 200 times, or the J value change rate of gbest is less than 0.5% in 20 consecutive iterations, stop the iteration and output gbest as the optimal control parameter: [K p , T i , T d , K ff ].

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