Application of improved active disturbance rejection control in superheated steam temperature control of supercritical thermal power generating unit

Abstract

The invention discloses application of improved active disturbance rejection control in superheated steam temperature control of a supercritical thermal power generating unit. Firstly, a superheated steam temperature system of a supercritical unit serves as a research object, and the control difficulty of the superheated steam temperature system is analyzed; and then, designing an improved active-disturbance-rejection control strategy. And finally, verifying the feasibility of the control strategy based on a simulation platform, and carrying out quantitative statistic analysis on the effectiveness of the control strategy by adopting performance indexes. A research object is simplified into a cascade control system, and the dynamic characteristics of the cascade control system are described more accurately. According to the improved active-disturbance-rejection control strategy designed by the invention, the control quality of a superheated steam temperature system can be remarkably improved, and rapid, safe and stable control of the superheated steam temperature is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of the flexible operation control of thermal power generating units, and more specifically, to the application of an improved active disturbance rejection control in the superheated steam temperature control of supercritical thermal power units. Background Art

[0002] In order to reduce the global dependence on the increasingly depleted fossil fuels, the power generated from renewable energy sources such as wind energy and solar energy has been developing rapidly. However, the power generated from new energy sources is greatly affected by environmental factors and has the characteristics of randomness, volatility, and uncertainty. Therefore, thermal power generating units must have strong control capabilities and sufficient flexibility to cope with frequent load changes, provide guarantees for the peak shaving of the power system, and play a good role as the "ballast stone" for power supply during the transition period of China's energy transformation. Therefore, it is urgent to promote the research on the intelligent control theory and methods of thermal power generating units to improve the safety and stability of the power system under the condition of high proportion of renewable energy grid connection and provide a margin for the consumption of large-scale centralized renewable energy power.

[0003] The superheated steam temperature has an important impact on the power generation efficiency and operation safety of supercritical thermal power generating units. However, due to the continuous rapid development of renewable energy power, frequent and wide load fluctuations bring unknown disturbances, making the control of superheated steam temperature more and more challenging. The superheated steam temperature system has characteristics such as a high dynamic order, a strong non-linear degree, and difficult adjustment of control parameters. Traditional control methods cannot achieve an ideal control effect. Therefore, taking the superheated steam temperature system of supercritical units as the controlled object and designing an advanced improved active disturbance rejection control strategy for it is of great significance for improving the flexible operation ability of large-scale thermal power generating units.

[0004] In recent years, active disturbance rejection control (ADRC) has received extensive attention and application due to its simple structure, excellent control performance and anti-disturbance ability, and independence from accurate mathematical models. By using an extended state observer (ESO) to integrate internal and external disturbances, unmodeled dynamics, and parameter uncertainties into a total disturbance and expanding it into a new state for real-time estimation and compensation, ADRC has not only achieved success in simulation experiments but also been successfully applied to the industrial control site of thermal power plants. However, there are strong nonlinear functions in the original active disturbance rejection controller. Although nonlinear gains may be more effective, they also introduce additional complexity in the implementation and tuning of control algorithms. The proposed linear active disturbance rejection controller (LADRC) and its bandwidth parameterization tuning method solve this problem. In this trend, error-based active disturbance rejection control (EADRC) has been proposed and applied to industrial promotion. EADRC inherits and develops the advantages of LADRC. By analyzing the tracking error to determine the state variables, it better conforms to common industrial forms and the requirements of improving tracking accuracy. In addition, a compensation link is added before the control signal is input into the ESO, making the control signal input into the ESO synchronized with the system output signal, which effectively simplifies the control design process for high-order systems. Based on this, the core competitiveness of EADRC relative to traditional PID-type controllers is potentially increased, and it can efficiently handle the control problems of high-order dynamic industrial processes. The parameter tuning of controllers has always been a troublesome and difficult problem, and the selection of key parameters has a crucial impact on the control performance of EADRC. Swarm intelligence algorithms have been widely used in the optimization field due to their simple principles, powerful and accurate search capabilities. Applying swarm intelligence algorithms to the parameter optimization of controllers is undoubtedly a combination of strengths. Therefore, using the improved active disturbance rejection control technology to design a controller for the superheated steam temperature system and combining it with the improved northern goshawk optimization algorithm (MNGO) can significantly improve the control quality of the superheated steam temperature system. Summary of the Invention

[0005] The present invention aims to carry out the application of improved active disturbance rejection control in the superheated steam temperature control of supercritical thermal power units, improve the control quality of the superheated steam temperature system, and achieve the rapid, safe and stable control of superheated steam temperature. This method fully considers the complex dynamic characteristics of the controlled object, the uncertainty of the model, and the disturbances brought about by load changes and changes in the temperature and pressure of desuperheating water during the actual operation of the unit. Combining the advantage of the improved active disturbance rejection technology in real-time estimating and compensating errors, an advanced active disturbance rejection control strategy is designed for it. Based on the designed improved active disturbance rejection controller, under the action of temperature change commands and internal and external disturbances, the models of each operating point of the unit's superheated steam temperature system have achieved high control quality.

[0006] The application of the improved active disturbance rejection control (ADRC) in the superheated steam temperature control of a supercritical thermal power unit carried out by the present invention consists of the following four steps:

[0007] S1: Analyze the control difficulties of the superheated steam temperature system of the supercritical unit;

[0008] S2: Establish the structure of the improved active disturbance rejection control strategy for the superheated steam temperature system of the supercritical unit;

[0009] S3: Describe the principle and design steps of the improved active disturbance rejection control technology;

[0010] S4: Rely on the simulation platform to verify and analyze the feasibility of the proposed control strategy.

[0011] S1: Against the backdrop of the continuous and rapid development of new energy power, the power grid requires thermal power units to have a wider load regulation range and a higher load regulation rate, which poses great challenges to the control of superheated steam temperature. Frequent and wide-ranging load changes, as well as strict control requirements for efficiency and safety, will lead to unknown multi-source disturbances. If the fluctuation range of superheated steam temperature exceeds the safety range, irreversible damage will occur to the metal pipes, and even cause the unit to trip unexpectedly. At the same time, when the superheated steam temperature is relatively low, the thermal efficiency of the unit will be greatly reduced. Most studies believe that the superheated steam temperature should be controlled within the range of ±5°C of the set value. Due to the complexity of the superheated steam temperature system, it is difficult to establish an accurate mathematical model, which requires the closed-loop control system to have sufficient robustness to handle model uncertainties and strong nonlinearities caused by load changes. In addition, there is a strong coupling effect between the superheated steam temperature, the reheated steam temperature, and the main steam pressure, and the large inertia-large lag composite characteristics of the system itself lead to a slow response to disturbances. To sum up, under the demand of deep peak shaving, it is very difficult for the superheated steam temperature system to achieve ideal control quality.

[0012] Based on the analysis in S1, it can be seen that due to the complex dynamic characteristics of the superheated steam temperature system of the supercritical unit, it is difficult to achieve ideal control effects. Therefore, an advanced improved active disturbance rejection control strategy structure needs to be designed for it to improve its control quality. Step S2 can be specified as:

[0013] S2.1: For the high-order system in the supercritical thermal power unit, structurally improve the original second-order active disturbance rejection controller based on error (EADRC). The proposed MEADRC can significantly improve the set-point tracking performance and anti-disturbance performance of the high-order system.

[0014] S2.2: Analyze and improve the principle of the Northern Goshawk Optimization (NGO) algorithm in the swarm intelligence optimization algorithm, and introduce various improvement measures to improve the convergence speed and search accuracy of the algorithm to meet the parameter optimization requirements of the designed controller MEADRC.

[0015] S2.3: For the superheated steam temperature system, a cascade control strategy is adopted. MEADRC is used as the controller for the outer-loop inert zone, and proportional control is used in the inner-loop leading zone. The parameters of the outer-loop controller MEADRC are tuned using an improved Northern Goshawk algorithm, which greatly improves the efficiency and accuracy of parameter adjustment. This advanced control technology effectively improves the control quality of the superheated steam temperature system and realizes the fast, safe and stable control of the superheated steam temperature.

[0016] After determining the structure of the improved active disturbance rejection control strategy based on the controlled object, the design steps of the improved active disturbance rejection control technology are specified in S3:

[0017] S3.1: Design of the error-based second-order active disturbance rejection controller EADRC:

[0018] Consider the following second-order system:

[0019]

[0020] where, is a lumped function that includes unmodeled dynamics and unknown external disturbances; b≠0 is the uncertain input gain of the system; the estimated value of b is denoted as b0; the system of Equation (1) can also be expressed as:

[0021]

[0022] At this time, now also includes the uncertainty related to the input gain. In LADRC, f is defined as the total disturbance, but it is not enough in EADRC. EADRC determines the state variables by analyzing the tracking error:

[0023]

[0024] To simplify the control law, an error differential term is introduced on both sides of to obtain a more simplified error-based model:

[0025]

[0026] Assume that F is differentiable and is bounded. Regard as the total disturbance and an extended state, and use the new state variable matrix to design the extended state observer ESO. Let z1, z2, z3 be the estimated values of x1, x2, x3 respectively. Then the ESO can be designed as:

[0027]

[0028] Where L = [l1, l2, l3] is the observer gain of the ESO, and (e-z1) is the observation error. After selecting the appropriate observer gain, the ESO can accurately estimate the system state in real time. The state feedback control law is chosen as:

[0029]

[0030] Among them, u0 is set to k0e, and the derivative of the unknown reference signal has been included in the total disturbance term. The controller gain and observer gain are set to:

[0031]

[0032] Among them, ω c and ω o are the controller bandwidth and observer bandwidth respectively. Compared with the output-based LADRC, EADRC can avoid directly using the differential of the reference input in the control law synthesis, which has important practical significance. The MADRC proposed in this paper inherits the basic principle of EADRC and improves its structure to further improve the control effect.

[0033] S3.2: Design of MEADRC;

[0034] For conventional EADRC, a compensation link is added before the control signal is input to the ESO to delay the time when the control signal enters the ESO, so that the signal input to the ESO remains synchronized. The compensation link is shown in formula (8):

[0035]

[0036] For K / (Ts+1) n This is a clever design for a high-order process. Considering the high-order process with compensation as a whole, we can deduce that:

[0037]

[0038]

[0039] Continue to regard f as part of the total disturbance, and refer to the principle of EADRC and so on. This is equivalent to using a second-order controller to control a second-order system. The order of the compensation link ensures that the order of the controller matches the order of the system. This MEADRC can effectively improve K / (Ts+1) n Control performance of superheated steam temperature system.

[0040] S3.3: Improvement of the northern goshawk algorithm;

[0041] Three improvement measures, namely chaotic mapping, optimal value guidance, and Cauchy mutation, are adopted for the Northern Goshawk Optimization (NGO) algorithm. The improved Northern Goshawk Optimization (MNGO) algorithm can effectively avoid the algorithm falling into local optimal solutions and significantly improve the search accuracy and convergence speed of the algorithm. Each Northern Goshawk represents a solution, which is actually the parameter matrix of the controller. The optimal position of the Northern Goshawk population represents the optimal parameters of the controller. First, the Tent chaotic mapping is added during the population initialization process to enhance the randomness and diversity of the population. The calculation formula of the Tent chaotic mapping is shown in Equation (12):

[0042] X i (0) = X min +z i (X max -X min ), i = 1, 2,..., N (11)

[0043]

[0044] Among them, X i (0) represents the initial position of the i-th Northern Goshawk, X max and X min are the upper and lower bounds of the search range respectively, N is the population size, and β is the chaotic coefficient in the Tent mapping.

[0045] The algorithm is divided into two stages: prey recognition and attack, and pursuit and escape:[[]]

[0046] S3.3.1: Prey recognition and attack;

[0047] In this stage, the algorithm conducts a global search with the aim of determining the optimal region. The Northern Goshawk with the best current fitness is selected to guide the population to update its position. After a large number of simulation attempts, it is found that when , the effect of using the optimal value guidance strategy is the best. The improvement formula for the first stage is as follows:

[0048] P i = X k , i = 1, 2,..., N, k = 1, 2,... i - 1, i + 1,..., N (13)

[0049]

[0050]

[0051] Among them, P i is the position of a randomly selected Northern Goshawk in the population, is the new position of the i-th individual after the first stage update, and xbest is the current optimal position of the population. F i and Both represent the fitness function values related to the individual positions. r is a random number between the interval [0, 1], and I is a random number between 1 or 2. Both r and I reflect the randomness of the algorithm in the global search process.

[0052] S3.3.2: Chase and escape;

[0053] The northern goshawk preys on prey within a region with a radius of R, which reflects the local search ability of the algorithm. The position update in this stage includes a certain Cauchy mutation factor, and the Cauchy mutation factor is represented by α. The formula for the improved second stage is as follows:

[0054]

[0055]

[0056]

[0057] Where, is the new position of the i-th individual after the second stage update, T is the maximum number of iterations, and t is the current number of iterations.

[0058] S3.4: Optimization objective;

[0059] To sum up, the parameters that need to be tuned for MEADRC are ω c 、b0 and ω o , and the improved northern goshawk algorithm MNGO is used for optimization. Considering the stability, accuracy, and rapidity required in the industrial control process, the comprehensive objective function is finally selected, as shown in Equation (19):

[0060] F = λ1·∫(w1(t·|e|) + w2·u 2 )dt + λ2·M p (19)

[0061] Where, e is the tracking error, u is the control variable, and M p is the overshoot of the system output. λ1, λ2, w1, and w2 are all weight factors that can be adaptively adjusted according to the actual control requirements.

[0062] Based on the improved active disturbance rejection control structure obtained in Step S3, an improved active disturbance rejection controller for the superheated steam temperature system is established. In Step S4, the feasibility of the proposed control strategy is verified and analyzed relying on the simulation platform, and the specific process is as follows:

[0063] S4.1: Although active disturbance rejection control is a control technique with model independence, adding model information can improve its control performance. Therefore, the transfer function models of the high-temperature superheater of a certain supercritical 600MW once-through boiler at four typical operating points are selected.

[0064] S4.2: Based on the model in step S4.1, an improved active disturbance rejection controller is designed.

[0065] S4.3: The temperature change command T sp set values are respectively input into the superheated steam temperature system models at four typical operating points for tracking performance tests. In the inert zone, MEADRC, EADRC, and LADRC are used for control comparison to verify the effectiveness of the proposed control strategy. The parameters of the outer-loop controller are optimized using the improved northern goshawk algorithm MNGO.

[0066] S4.4: Determine the set values of the inner-loop disturbance d1 and the outer-loop disturbance d2, and input them into the superheated steam temperature system models at four typical operating points for anti-disturbance performance tests. The inner-loop disturbance d1 mainly includes the temperature change and pressure change of the desuperheating water, and the outer-loop disturbance d2 mainly includes load regulation, coal quality change, and combustion instability. In the inert zone, MEADRC, EADRC, and LADRC are used for control comparison to verify the effectiveness of the proposed control strategy, and the parameters of the outer-loop controller are optimized using the improved northern goshawk algorithm MNGO.

[0067] S4.5: Conduct a robustness test on the designed controller. Use the model at the 50% load operating point as the nominal model, and select any two model parameters to have a ±10% perturbation relative to the nominal value. Set the number of samples in the Monte Carlo test to 200 to obtain the response curve cluster of the controlled variable superheated steam temperature T, and observe its dispersion degree. Statistically analyze the change ranges of the control performance indicators overshoot M p 、settling time t s and the ITAE value, and calculate their average value Mean and standard deviation SD. Mean represents the average performance level of the nominal controller for the perturbed model, and SD represents the dispersion degree of the Monte Carlo test. Advantages of the present invention:

[0068] Combined with the development trend of gradually improving the renewable energy power consumption capacity in the field of power production in China, from the perspective of control, an improved active disturbance rejection control strategy is designed for the superheated steam temperature system of supercritical units to improve its control quality and further enhance the flexible operation ability of large-scale thermal power generating units.

[0069] In the design process of the improved active disturbance rejection control strategy of the present invention, the complex dynamic characteristics and control difficulties of the superheated steam temperature system of supercritical units are fully considered. The improved active disturbance rejection control technology with excellent performance is combined with the improved Northern Goshawk optimization algorithm, so that the designed control strategy can meet the precise control requirements of the power grid for the superheated steam temperature system of thermal power units under the deep peak shaving demand.

[0070] The present invention simplifies the controlled object into a cascade control system, which can more accurately describe the dynamic characteristics of the superheated steam temperature system. The designed improved active disturbance rejection control technology has excellent control performance and anti-interference performance, can significantly improve the control quality of the superheated steam temperature system, and realize the fast, safe and stable control of the superheated steam temperature. Brief Description of the Drawings

[0071] Figure 1 It is the schematic diagram of the superheated steam temperature system involved in the present invention.

[0072] Figure 2 It is the cascade control block diagram of the superheated steam temperature system mentioned in the present invention.

[0073] Figure 3 It is the principle structure diagram of the improved active disturbance rejection controller mentioned in the present invention. Detailed Embodiment

[0074] The following further describes the detailed embodiment of the present invention with reference to the drawings in the specification.

[0075] Please refer to Figure 1 in the drawings of the specification, Figure 1 which is the schematic diagram of the superheated steam temperature system involved in the present invention. This system includes a primary superheater and a secondary superheater. The secondary superheater has a more sluggish response, so special attention is needed. The steam from the water wall passes through the desuperheater and the superheater and obtains heat from the flue gas. Spray desuperheating is the main control method of the superheated steam temperature system, and the desuperheating water is taken from the intermediate stage of the boiler feed pump. The superheated steam temperature is jointly affected by the steam flow rate, the flue gas flow rate and the desuperheating water flow rate. Among these three factors, both the steam flow rate and the desuperheating water flow rate are related to the feed water volume, while the flue gas flow rate is related to the combustion state of the fuel. Therefore, controlling the superheated steam temperature is beneficial to saving water and fuel.

[0076] Please refer to Figure 2 in the drawings of the specification, Figure 2This is the cascade control block diagram of the superheated steam temperature system mentioned in the present invention. The distributed parameter superheat system is approximated as two linear transfer function models, W1(s) and W2(s). The inner-loop transfer function model W2(s) represents the dynamic characteristics from the desuperheater to the inlet temperature of the secondary superheater. The outer-loop transfer function model W1(s) represents the dynamic characteristics from the inlet temperature to the outlet temperature of the secondary superheater. The setpoint r is the expected outlet temperature of the secondary superheater, and the control variable is the opening of the desuperheating water valve. The inner-loop disturbance d1 mainly includes the temperature change and pressure change of the desuperheating water, and the outer-loop disturbance d2 mainly includes load regulation, coal quality change, and combustion instability. The cascade control of the superheater temperature can improve the regulation quality. The MEADRC technology is introduced into the cascade control system. The lead zone uses proportional control, which has a relatively fast response speed and can roughly adjust the superheated steam temperature to quickly eliminate the steam temperature deviation in the lead zone. While MEADRC is used to control the main loop containing high-order links and finely adjust the superheated steam temperature to eliminate external disturbances and overcome the large inertia and large delay characteristics of the controlled object. Therefore, the appropriate combination of MEADRC and the proportional controller realizes the complementary control advantages of the main loop and the secondary loop, which helps to improve the control efficiency.

[0077] Please refer to Figure 3 in the attached drawings of the specification Figure 3 This is the principle structure diagram of the improved active disturbance rejection controller mentioned in the present invention. This controller can achieve real-time accurate tracking and compensation of the estimated quantity and has good control performance and anti-interference performance. This example is based on a certain 600MW ultra-supercritical once-through boiler in China. The method steps include:

[0078] S1: Analyze the control difficulties of the superheated steam temperature system of the ultra-supercritical unit;

[0079] S2: Establish the improved active disturbance rejection control strategy structure for the superheated steam temperature system of the ultra-supercritical unit;

[0080] S3: Describe the principle and design steps of the improved active disturbance rejection control technology;

[0081] S4: Rely on the simulation platform to verify and analyze the feasibility of the proposed control strategy.

[0082] S1: In the context of the continuous and rapid development of new energy power, the power grid requires thermal power units to have a wider load regulation range and a higher load regulation rate, which poses great challenges to the control of superheated steam temperature. Frequent and wide load changes, as well as strict control requirements for efficiency and safety, will lead to unknown multi-source disturbances. If the fluctuation range of superheated steam temperature exceeds the safety range, the metal pipeline will suffer irreparable damage, and even cause the unit to shut down unexpectedly. At the same time, when the superheated steam temperature is relatively low, the thermal efficiency of the unit will be greatly reduced. Most studies believe that the superheated steam temperature should be controlled within the range of ±5°C of the set value. Due to the complexity of the superheated steam temperature system, it is difficult to establish an accurate mathematical model, which requires the closed-loop control system to have sufficient robustness to handle model uncertainties and strong nonlinearities caused by load changes. In addition, there is a strong coupling effect between the superheated steam temperature, the reheated steam temperature, and the main steam pressure, and the large inertia-large lag composite characteristics of the system itself result in a slow response to disturbances. To sum up, under the demand of deep peak shaving, it is very difficult for the superheated steam temperature system to achieve ideal control quality.

[0083] Based on the analysis in S1, it can be seen that the superheated steam temperature system of supercritical units is difficult to achieve ideal control effects due to its complex dynamic characteristics. Therefore, an advanced improved active disturbance rejection control strategy structure needs to be designed for it to improve its control quality. Step S2 can be specified as follows:

[0084] S2.1: For the high-order system in supercritical thermal power units, the original second-order active disturbance rejection controller based on error (EADRC) is structurally improved, and the proposed MEADRC can significantly improve the set-point tracking performance and anti-disturbance performance of high-order systems.

[0085] S2.2: Conduct a principle analysis and improvement on the Northern Goshawk Optimization (NGO) algorithm in the swarm intelligence optimization algorithm, and introduce various improvement measures to improve the convergence speed and search accuracy of the algorithm to meet the parameter optimization requirements of the designed controller MEADRC.

[0086] S2.3: For the superheated steam temperature system, a cascade control strategy is adopted. MEADRC is used as the controller for the outer-loop inert zone, and proportional control is used in the inner-loop leading zone. The parameters of the outer-loop controller MEADRC are tuned using the improved Northern Goshawk algorithm, which greatly improves the efficiency and accuracy of parameter adjustment. This advanced control technology effectively improves the control quality of the superheated steam temperature system and realizes the fast, safe, and stable control of superheated steam temperature.

[0087] After determining the improved active disturbance rejection control strategy structure based on the controlled object, the design steps of the improved active disturbance rejection control technology are specified in S3:

[0088] S3.1: Design of the second-order Extended Active Disturbance Rejection Controller (EADRC) based on error:

[0089] Consider the following second-order system:

[0090]

[0091] where, is a lumped function that includes unmodeled dynamics and unknown external disturbances; b≠0 is the uncertain input gain of the system; the estimated value of b is denoted as b0; the system of Equation (1) can also be expressed as:

[0092]

[0093] At this time, now also includes the uncertainty related to the input gain. In LADRC, f is defined as the total disturbance, but it is not enough in EADRC. EADRC determines the state variables by analyzing the tracking error:

[0094]

[0095] To simplify the control law, an error differential term is introduced on both sides of to obtain a more simplified error-based model:

[0096]

[0097] Assume that F is differentiable and is bounded. Regard as the total disturbance and as an extended state, and use the new state variable matrix to design the Extended State Observer (ESO). Let z1, z2, and z3 be the estimated values of x1, x2, and x3 respectively. Then the ESO can be designed as:

[0098]

[0099] where, L = [l1, l2, l3] is the observer gain of the ESO, and (e - z1) is the observation error. After selecting appropriate observer gains, the ESO can accurately estimate the system state in real time. The state feedback control law is selected as:

[0100]

[0101] where, u0 is set to k0e, and the differential of the unknown reference signal has been incorporated into the total disturbance term. The controller gain and the observer gain are set using the pole placement method as:

[0102]

[0103] where, ωc and ω o are the controller bandwidth and the observer bandwidth respectively. Compared with the output-based LADRC, EADRC can avoid directly using the derivative of the reference input in the control law synthesis, which has important practical significance. The MADRC proposed in this paper inherits the basic principle of EADRC and improves its structure, further enhancing the control effect.

[0104] S3.2: Design of MEADRC;

[0105] For the conventional EADRC, a compensation link is added before its control signal is input into the ESO to delay the time for the control signal to enter the ESO, so as to keep the input signal of the ESO synchronized. The compensation link is shown in Equation (8):

[0106]

[0107] For K / (Ts + 1) n type high-order processes, this is a clever design. Regarding the high-order process with the compensation link as a whole, through derivation, it can be obtained that:

[0108]

[0109]

[0110] Continuing to regard f as part of the total disturbance and following the principle of EADRC by analogy. This is equivalent to using a second-order controller to control a second-order system, and the order of the compensation link ensures that the order of the controller matches the order of the system. This kind of MEADRC can effectively improve the control performance of the K / (Ts + 1) n type superheated steam temperature system.

[0111] S3.3: Improvement of the Northern Goshawk Algorithm;

[0112] Three improvement measures, namely chaotic mapping, optimal value guidance, and Cauchy mutation, are taken for the Northern Goshawk Algorithm. The improved Northern Goshawk Algorithm MNGO can effectively avoid the algorithm falling into local optimal solutions and significantly improve the search accuracy and convergence speed of the algorithm. Each Northern Goshawk represents a solution, which is actually the parameter matrix of the controller. The optimal position of the Northern Goshawk population represents the optimal parameters of the controller. First, Tent chaotic mapping is added during the population initialization process to enhance the randomness and diversity of the population. The calculation formula of Tent chaotic mapping is shown in Equation (12):

[0113] X i (0) = X min + z i (X max - X min), i = 1, 2, ..., N(30)

[0114]

[0115] Among them, X i (0) represents the initial position of the i-th northern goshawk, X max and X min are the upper and lower bounds of the search range respectively, N is the population size, and β is the chaos coefficient in the Tent map.

[0116] The algorithm is divided into two stages: prey recognition and attack, and pursuit and escape:

[0117] S3.3.1: Prey recognition and attack;

[0118] In this stage, the algorithm conducts a global search with the aim of determining the optimal region. Select the northern goshawk with the best current fitness to guide the population to update its position. After a large number of simulation attempts, it is found that when , the effect of using the optimal value guiding strategy is the best. The improved formula for the first stage is as follows:

[0119] P i = X k , i = 1, 2, ..., N, k = 1, 2, ... i - 1, i + 1, ..., N(32)

[0120]

[0121]

[0122] i is the position of a randomly selected northern goshawk in the population, is the new position of the i-th individual after the first stage update, and xbest is the current optimal position of the population. F i and both represent the fitness function values related to the individual's position. r is a random number between the interval [0, 1], and I is a random number between 1 and 2. Both r and I reflect the randomness of the algorithm in the global search process.

[0123] S3.3.2: Pursuit and escape;

[0124] The northern goshawk preys on its prey within a region with a radius of R, which reflects the local search ability of the algorithm. The position update in this stage includes a certain Cauchy mutation factor, which is represented by α. The improved formula for the second stage is as follows:

[0125]

[0126]

[0127]

[0128] Among them, is the new position of the i-th individual after the second-stage update, T is the maximum number of iterations, and t is the current number of iterations.

[0129] S3.4: Optimization objective;

[0130] To sum up, the parameters that need to be tuned for MEADRC are ω c , b0 and ω o , and the improved Northern Goshawk algorithm MNGO is used for optimization. Considering the stability, accuracy, and rapidity required in the industrial control process, the comprehensive objective function as shown in Equation (19) is finally selected:

[0131] F = λ1·∫(w1(t·|e|)+w2·u 2 )dt + λ2·M p (38)

[0132] Among them, e is the tracking error, u is the control variable, and M p is the overshoot of the system output. λ1, λ2, w1, and w2 are all weight factors that can be adaptively adjusted according to the actual control requirements.

[0133] Based on the improved active disturbance rejection control structure obtained in Step S3, an improved active disturbance rejection controller for the superheated steam temperature system is established. In Step S4, the feasibility of the proposed control strategy is verified and analyzed relying on the simulation platform, and the specific process is as follows:

[0134] In this example, the operating conditions of the high-temperature superheater of the unit at four typical operating condition points are as follows:

[0135] Table 1 Operating conditions of the high-temperature superheater at different load operating condition points

[0136] S4.1: Although active disturbance rejection control is a control technology with model independence, adding model information can improve its control performance; therefore, the transfer function model of the high-temperature superheater of a certain supercritical 600MW once-through boiler at four typical operating condition points is selected;

[0137] S4.2: Based on the model in Step S4.1, design an improved active disturbance rejection controller;

[0138] S4.3: Apply the temperature change command T spThe set values are input into the superheated steam temperature system model at four typical operating points for tracking performance testing. The inert zone is controlled and compared using MEADRC, EADRC, and LADRC to verify the effectiveness of the proposed control strategy. The parameters of the outer loop controller are optimized using the improved Northern Goshawk Optimization (MNGO).

[0139] S4.4: Determine the set values of the inner loop disturbance d1 and the outer loop disturbance d2, and input them into the superheated steam temperature system model at four typical operating points for anti-interference performance testing. The inner loop disturbance d1 mainly includes the temperature change and pressure change of the desuperheating water, and the outer loop disturbance d2 mainly includes load regulation, coal quality change, and combustion instability. The inert zone is controlled and compared using MEADRC, EADRC, and LADRC to verify the effectiveness of the proposed control strategy. The parameters of the outer loop controller are optimized using the improved Northern Goshawk Optimization (MNGO).

[0140] S4.5: Conduct a robustness test on the designed controller. Use the model at the 50% load operating point as the nominal model, and select any two model parameters to have a ±10% perturbation relative to the nominal value. Set the number of samples for the Monte Carlo test to 200 to obtain the response curve cluster of the controlled variable, the superheated steam temperature T, and observe its dispersion. Statistically analyze the overshoot M p of the control performance index, the adjustment time t s and the variation range of the ITAE value, and calculate their average value Mean and standard deviation SD. Mean represents the average performance level of the nominal controller for the perturbed model, and SD represents the dispersion of the Monte Carlo test.

[0141] S4.6: Calculate the fitting degree between the controlled variable, the superheated steam temperature T, and the temperature change command T sp of the superheated steam temperature system. To further quantify the control performance, statistically analyze the overshoot M p of the control performance index, the adjustment time t s , the IAE value, the ITAE value, and the TV value.

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Claims

1. Application of improved active disturbance rejection control in supercritical thermal power unit superheated steam temperature control, characterized in that: It includes the following steps: S1: Analyze the control difficulties of the superheated steam temperature system of a supercritical unit; S2: Establish an improved active disturbance rejection control strategy structure for the superheated steam temperature system of a supercritical unit; S3: Describe the principle and design steps of the improved active disturbance rejection control technology; S4: Rely on a simulation platform to verify and analyze the feasibility of the proposed control strategy.

2. Application of the improved active disturbance rejection control in the superheated steam temperature control of a supercritical thermal power unit according to claim 1, characterized in that: The specific analysis of the control difficulties of the superheated steam temperature system of a supercritical unit described in step S1 is as follows: S1: Against the backdrop of the continuous and rapid development of new energy power, the power grid requires thermal power units to have a wider load regulation range and a higher load regulation rate, which poses great challenges to the control of superheated steam temperature. Frequent and wide load changes, as well as strict control requirements for efficiency and safety, will lead to unknown multi-source disturbances. If the fluctuation range of superheated steam temperature exceeds the safety range, the metal pipeline will suffer irreparable damage, and even cause the unit to trip unplanned. At the same time, when the superheated steam temperature is low, the thermal efficiency of the unit will be greatly reduced. Most studies believe that the superheated steam temperature should be controlled within the range of ±5°C of the set value. Due to the complexity of the superheated steam temperature system, it is difficult to establish an accurate mathematical model, which requires the closed-loop control system to have sufficient robustness to handle model uncertainties and strong nonlinearities caused by load changes. In addition, there is a strong coupling effect between the superheated steam temperature, the reheated steam temperature, and the main steam pressure, and the large inertia-large lag composite characteristics of the system itself result in a slow response to disturbances. To sum up, under the demand of deep peak shaving, it is very difficult for the superheated steam temperature system to achieve ideal control quality.

3. Application of the improved active disturbance rejection control in the superheated steam temperature control of a supercritical thermal power unit according to claim 1, characterized in that: Establish an improved active disturbance rejection control strategy structure for the superheated steam temperature system of a supercritical unit. The specific implementation steps of the improved active disturbance rejection control strategy for the superheated steam temperature system in step S2 include: S2.1: For the high-order system in a supercritical thermal power unit, structurally improve the original second-order active disturbance rejection controller based on error EADRC. The proposed MEADRC can significantly improve the set-point tracking performance and anti-disturbance performance of the high-order system; S2.2: Conduct a principle analysis and improvement on the Northern Goshawk Optimization algorithm NGO in the swarm intelligence optimization algorithm, and introduce various improvement measures to improve the convergence speed and search accuracy of the algorithm to meet the parameter optimization requirements of the designed controller MEADRC; S2.3: Adopt a cascade control strategy for the superheated steam temperature system. Use MEADRC as the controller in the outer-loop inert zone and use proportional control in the inner-loop lead zone. The parameters of the outer-loop controller MEADRC are tuned using the improved Northern Goshawk algorithm, which greatly improves the efficiency and accuracy of parameter adjustment. This advanced control technology effectively improves the control quality of the superheated steam temperature system and realizes the fast, safe, and stable control of superheated steam temperature.

4. Application of the improved active disturbance rejection control in the superheated steam temperature control of a supercritical thermal power unit according to claim 1, characterized in that: Describe the principle and design steps of the improved active disturbance rejection control technology, including: S3.1: Design of the second-order active disturbance rejection controller EADRC based on error; Consider the following second-order system: wherein, is a lumped function that includes unmodeled dynamics and unknown external disturbances; b≠0 is the uncertain input gain of the system; the estimated value of b is denoted as b0; the system of Equation (1) can also be expressed as: At this time, Now it also includes the uncertainty related to the input gain. In LADRC, f is defined as the total disturbance, but it is not enough in EADRC. EADRC determines the state variables by analyzing the tracking error: To simplify the control law, an error differential term is introduced on both sides of to obtain a more simplified error-based model: Assume that F is differentiable and bounded. Regard as the total disturbance and take it as an extended state. Use the new state variable matrix to design an Extended State Observer (ESO). Let z1, z2, and z3 be the estimates of x1, x2, and x3 respectively. Then the ESO can be designed as follows: Among them, \(L = [l_1, l_2, l_3]\) is the observer gain of the ESO, and \((e - z_1)\) is the observation error. After selecting appropriate observer gains, the ESO can accurately estimate the system state in real time. The state feedback control law is selected as: Among them, \(u_0\) is set to \(k_0e\), and the derivative of the unknown reference signal has been incorporated into the total disturbance term. The controller gains and observer gains are set using the pole placement method as: where, ω c and ω o are the controller bandwidth and the observer bandwidth respectively. Compared with the output-based LADRC, the EADRC can avoid directly using the derivative of the reference input in the control law synthesis, which has important practical significance. The MADRC proposed in this paper inherits the basic principle of the EADRC and improves its structure, further enhancing the control effect. S3.2: Design of MEADRC; For the conventional EADRC, a compensation link is added before its control signal is input into the ESO to delay the time for the control signal to enter the ESO, so as to keep the signal input into the ESO synchronized. The compensation link is shown in Equation (8): For K / (Ts + 1) n This is a clever design for high-order processes of the type. Regarding the high-order process with a compensation link as a whole, it can be derived through deduction that: Continuing to consider f as part of the total disturbance, by analogy with the principle of EADRC. This is equivalent to using a second-order controller to control a second-order system, and the order of the compensation link ensures that the order of the controller matches the order of the system. This kind of MEADRC can effectively improve the control performance of the n superheated steam temperature system of type K / (Ts + 1). S3.3: Improvement of the Northern Goshawk algorithm; Three improvement measures, namely chaotic mapping, optimal value guidance, and Cauchy mutation, are taken for the Northern Goshawk algorithm. The improved Northern Goshawk algorithm MNGO can effectively avoid the algorithm falling into local optimal solutions and significantly improve the search accuracy and convergence speed of the algorithm. Each Northern Goshawk represents a solution, which is actually the parameter matrix of the controller. The optimal position of the Northern Goshawk population represents the optimal parameters of the controller. First, Tent chaotic mapping is added during the population initialization process to enhance the randomness and diversity of the population. The calculation formula of Tent chaotic mapping is shown in Equation (12): X i (0) = X min +z i (X max -X min ), i = 1, 2, ..., N (11) Among them, X i (0) represents the initial position of the i-th northern goshawk, X max and X min are the upper and lower bounds of the search range respectively, N is the population size, and β is the chaos coefficient in the Tent map. The algorithm is divided into two stages: prey recognition and attack, and pursuit and escape; S3.3.1: Prey recognition and attack; The algorithm conducts a global search at this stage with the aim of determining the optimal region. The northern goshawk with the best current fitness is selected to guide the population for position update. After a large number of simulation attempts, it is found that when the effect of using the optimal value guiding strategy is the best. The improved formula in the first stage is as follows: P i = X k , i = 1, 2,..., N, k = 1, 2,... i - 1, i + 1,..., N (13) Among them, P i is the position of a randomly selected northern goshawk in the population, is the new position of the i-th individual after the first-stage update, and xbest is the current optimal position of the population. F Pi 、F i and both represent the fitness function values related to the individual positions. r is a random number between the interval [0, 1], and I is a random number between 1 or 2. Both r and I reflect the randomness of the algorithm in the global search process. S3.3.2: Pursuit and escape; The Northern Goshawk preys on prey within a region with a radius of \(R\), which reflects the local search ability of the algorithm. The position update in this stage includes a certain Cauchy mutation factor, which is represented by \(\alpha\). The improved formula for the second stage is as follows: Among them, is the new position of the i-th individual after the second-stage update, T is the maximum number of iterations, and t is the current number of iterations. S3.4: Optimization objective; In summary, the parameters to be tuned for MEADRC are ω c , b0, and ω o , and an improved northern goshawk algorithm MNGO is used for optimization. Considering the stability, accuracy, and rapidity required in the industrial control process, the comprehensive objective function is finally selected as shown in Equation (19): F = λ1·∫(w1(t·|e|)+w2·u 2 )dt + λ2·M p (19) where e is the tracking error, u is the control variable, and M p is the overshoot of the system output. λ1, λ2, w1, and w2 are all weight factors that can be adaptively adjusted according to actual control requirements.

5. The application of the improved active disturbance rejection control in the superheated steam temperature control of a supercritical thermal power unit according to claim 1, characterized in that: Based on the improved active disturbance rejection control technology designed in Step S3, in Step S4, the feasibility of the proposed control strategy is verified and analyzed relying on the simulation platform, specifically including: S4.1: Although active disturbance rejection control is a control technology with model independence, adding model information can improve its control performance; therefore, the transfer function model of a certain supercritical 600MW once-through boiler high-temperature superheater at four typical operating condition points is selected; S4.2: Based on the model in Step S4.1, an improved active disturbance rejection controller is designed; S4.3: Input the temperature change command T sp set values into the superheated steam temperature system models of four typical operating conditions respectively for tracking performance tests; in the inert zone, MEADRC, EADRC, and LADRC are used for control comparison to verify the effectiveness of the proposed control strategy; the parameters of the outer-loop controller are optimized using the improved northern goshawk algorithm MNGO; S4.4: Determine the set values of the inner-loop disturbance d1 and the outer-loop disturbance d2, and input them into the superheated steam temperature system models at four typical operating points for anti-interference performance testing. The inner-loop disturbance d1 mainly includes the temperature change and pressure change of the desuperheating water, and the outer-loop disturbance d2 mainly includes load regulation, coal quality change, and combustion instability. The inert zone is controlled and compared using MEADRC, EADRC, and LADRC to verify the effectiveness of the proposed control strategy. The parameters of the outer-loop controller are optimized using the improved northern goshawk algorithm MNGO. S4.5: Conduct a robustness test on the designed controller. Take the model at the 50% load operating point as the nominal model, and select any two model parameters to have a ±10% perturbation relative to the nominal value. Set the number of samples in the Monte Carlo test to 200 to obtain the response curve cluster of the controlled variable, the superheated steam temperature T, and observe its dispersion degree. Statistically analyze the variation ranges of the control performance indicators overshoot M p , adjustment time t s , and the ITAE value, and calculate their average value Mean and standard deviation SD. Mean represents the average performance level of the nominal controller for the perturbed model, and SD represents the dispersion degree of the Monte Carlo test. S4.6: Calculate the controlled variable superheated steam temperature T and the temperature change command T of the superheated steam temperature system sp The fitting degree of the set value. To further quantify the control performance, statistically analyze the overshoot M of the control performance index p , the adjustment time t s , the IAE value, the ITAE value, and the TV value;

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