A simplified method and system for active disturbance rejection control tuning of nuclear power steam generators with delay function.

Abstract

This invention discloses a simplified method and system for tuning active disturbance rejection control (ADRC) for nuclear power steam generators with time delay. The method includes: establishing a mathematical model of the steam generator; designing a time-delay ADRC controller and equivalently transforming it into a two-degree-of-freedom structure to obtain the equivalent transfer function expression of the steam generator mathematical model and the characteristic equation of the closed-loop system; obtaining the characteristic equation of the closed-loop transfer function through low-frequency approximation, further obtaining the desired tracking speed parameter, and equivalently converting the adjustment of the outer-loop controller gain into the quantitative adjustment of the desired tracking speed parameter; simplifying the analysis of the parameters of the time-delay ADRC controller; and determining the relative time delay margin as a stability index through robustness index analysis to obtain the range of values ​​for the regularized observer bandwidth. This invention improves the mathematical analysis capabilities for modeling and controlling nuclear power equipment, making the TD-ADRC controller more practical in actual nuclear power equipment operation and ensuring the safe operation of nuclear power plants.

Description

Technical Field

[0001] This invention relates to power engineering—nuclear power systems, and more specifically to a simplified method and system for active disturbance rejection control tuning of nuclear steam generators with delay. Background Technology

[0002] Nuclear energy plays a crucial role in building a clean, low-carbon, safe, and efficient energy system. With the increasing proportion of nuclear power plants, the demand for their participation in load-following operation and the development of diversified applications such as combined heat and power (CHP) and seawater desalination is becoming increasingly urgent. The steam generator (SG), as the core equipment of a pressurized water reactor, exhibits strong nonlinearity, non-minimum phase characteristics, time-varying dynamic characteristics, and significant time delay.

[0003] Active Disturbance Rejection Control (ADRC), proposed by Han Jingqing, is a model-free control strategy. It extends the classical PID control framework by incorporating modern control theory. Its core mechanism relies on an Extended State Observer (ESO) to estimate and compensate for internal and external disturbances in real time, thereby significantly improving the anti-interference capability of the control system (such as the water level control system of a steam generator (SG)).

[0004] PID control and three-impulse regulation systems are the most classic and widely used technologies for water level control in nuclear power steam generators. The system employs a parallel structure of a main feedwater regulating valve (high load) and a bypass regulating valve (low load). During low load periods (0-18% or 0-20%), a single-impulse regulator (water level signal only) drives the bypass valve. During high load periods, the system switches to a three-impulse regulator (feedwater flow, steam flow, and steam generator water level) to control the main valve. The programmed water level setpoint varies piecewise with the load, and its dynamic characteristics are verified using a PID control theoretical model and a thermal-hydraulic transient analysis model.

[0005] The main drawbacks of existing technologies can be summarized as follows:

[0006] 1. Difficult parameter tuning: Advanced controllers (such as ADRC and MPC combined with intelligent optimization) usually contain multiple parameters. Their tuning process requires in-depth professional knowledge and a lot of trial and error, which places high demands on field engineers and results in high training costs.

[0007] 2. Complex algorithms and reliance on accurate models: Many high-performance methods (such as robust control and model-based predictive control) rely on accurate mathematical models of the system. In practical engineering, obtaining and maintaining such an accurate model is very difficult, limiting its direct application.

[0008] 3. Insufficient research on adaptability to all operating conditions: The dynamic characteristics of steam generators vary significantly with power levels, but existing ADRC application studies are mostly focused on specific operating conditions, lacking a robust gain scheduling rule that can automatically adapt to changes in all operating conditions. Summary of the Invention

[0009] Purpose of the invention: The purpose of this invention is to provide a simplified method and system for active disturbance rejection control tuning that combines disturbance rejection capability and time-delay robustness for nuclear power steam generators with delayed operation.

[0010] Technical solution: The method described in this invention includes the following steps:

[0011] A mathematical model of a steam generator is established. Based on the first-order time-delay model of the steam generator mathematical model, a time-delay active disturbance rejection controller (ADRC) is designed. The ADRC includes an outer loop controller and an inner loop controller. The outer loop controller is used to compensate for the deviation between the output of the steam generator system and its reference value, and obtains the outer loop controller output. The inner loop controller is used to compensate for the estimated total uncertainty based on the delayed ADRC output and the output of the steam generator system, and calculates the compensated ADRC output based on the outer loop controller output and the total uncertainty.

[0012] The time-delay active disturbance rejection controller is equivalently transformed into a two-degree-of-freedom structure. The equivalent transfer function expression of the steam generator mathematical model and the characteristic equation of the closed-loop system are obtained through the two-degree-of-freedom structure.

[0013] The equivalent transfer function expression of the steam generator mathematical model is approximated at low frequency, and the compensation is integral plus time delay term to obtain the characteristic equation of the closed-loop transfer function after low frequency approximation. The desired tracking speed parameter is then obtained, and the adjustment of the outer loop controller gain is equivalently converted into the quantitative adjustment of the desired tracking speed parameter. The quantitative adjustment of the desired tracking speed parameter further determines the system response speed.

[0014] The lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller are simplified and analyzed using the regularization method to obtain the simplified regularized observer bandwidth.

[0015] Robustness index analysis was performed on the steam generator system to determine the relative time delay margin as a stability index and to obtain the range of values ​​for the regularized observer bandwidth.

[0016] Furthermore, the inner loop controller includes an extended observer and a delay module. The compensated time-delay active disturbance rejection controller output, after passing through the delay module, together with the steam generator system output, serves as the two inputs of the extended observer. The difference between the total uncertainty of the extended observer output and the control quantity of the outer loop controller is amplified by the inner loop controller to obtain the compensated time-delay active disturbance rejection controller output at the next moment. After the compensated time-delay active disturbance rejection controller output is compensated for by the disturbance, it is then passed through the first-order time-delay model of the steam generator mathematical model to obtain the steam generator system output.

[0017] Furthermore, the equivalent transfer function expression and characteristic equations of the closed-loop system of the steam generator mathematical model are obtained through a two-degree-of-freedom structure; specifically including:

[0018] The equivalent transfer function expression is:

[0019] ;

[0020] in, This is the equivalent transfer function expression. It is a time constant. For the Laplace operator, For the time lag, To expand the observer bandwidth;

[0021] Further, the equivalent feedback controller is obtained. and feedforward controller , is represented as:

[0022] ;

[0023] ;

[0024] in, For the outer loop controller gain, For the dimensionless parameters of the inner ring;

[0025] The characteristic equation of the closed-loop system is expressed as:

[0026] ;

[0027] in, For the steam generator system gain;

[0028] Further, it can be transformed into the following separable form:

[0029] .

[0030] Furthermore, the equivalent transfer function expression of the steam generator mathematical model is approximated using low-frequency methods, and is expressed as:

[0031] ;

[0032] in, This is the equivalent transfer function expression. For the Laplace operator, For the time lag, For intermediate quantities, the expression is: , It is a time constant. To expand the observer bandwidth;

[0033] The closed-loop transfer function after low-frequency approximation is obtained The characteristic equation is expressed as:

[0034] ;

[0035] in, For the outer loop controller gain, The desired tracking speed parameter;

[0036] The expression for the desired tracking speed parameter is further obtained as follows: ;

[0037] The adjustment of the outer loop controller gain is equivalently converted into a quantitative adjustment of the desired tracking speed parameter, expressed as:

[0038] .

[0039] Furthermore, the lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller are simplified and analyzed using regularization methods to obtain the simplified regularized observer bandwidth; specifically:

[0040] Parameter regularization transformation:

[0041] ;

[0042] in, The time delay after regularization For the regularized Laplace operator, To regularize the observer bandwidth, For the Laplace operator, For the time lag, It is a time constant. To expand the observer bandwidth;

[0043] Based on the two-degree-of-freedom structure, the expression for the open-loop transfer function is obtained. :

[0044] ;

[0045] in, For the desired tracking speed parameters, It has no actual physical meaning; the expression is:

[0046] .

[0047] Furthermore, robustness analysis was performed on the steam generator system to determine the relative time delay margin as a stability index, and the range of values ​​for the regularized observer bandwidth was obtained; including:

[0048] When there is an uncertain time delay hour, For the time lag, For time delay error, the relative time delay margin function is adjusted as follows:

[0049] ;

[0050] in, This is the relative time lag margin. and They represent the lag time. The upper and lower bounds of the range of uncertain time delays in the vicinity; when considering uncertain time delays, the nominal open-loop transfer function is corrected as follows:

[0051] ;

[0052] in, The nominal loop transfer function, It is a relative time delay. The time delay after regularization For the regularized Laplace operator, To regularize the observer bandwidth, The desired tracking speed parameter; the relative time delay is defined as... ;

[0053] By considering the condition that the perturbed Nyquist plot passes through the critical point, the following relationship is obtained:

[0054] ;

[0055] in, The complex plane value of the nominal loop transfer function. It is a positive integer;

[0056] Based on relative time lag margin and The changing pattern, in order to satisfy Within the range, the bandwidth of the regularized observer is obtained. The range of values ​​for .

[0057] The system of the present invention includes:

[0058] The steam generator mathematical model building unit is used to establish a mathematical model of the steam generator.

[0059] The time-delay active disturbance rejection controller (ADRC) design unit is used to design an ADRC based on the first-order time-delay model of the steam generator mathematical model. The ADRC includes an outer loop controller and an inner loop controller. The outer loop controller is used to compensate for the deviation between the output of the steam generator system and its reference value, and obtain the outer loop controller output. The inner loop controller is used to compensate for the total uncertainty based on the delayed ADRC output and the output of the steam generator system, and calculate the compensated ADRC output based on the outer loop controller output and the total uncertainty.

[0060] The equivalent transformation unit is used to transform the time-delay active disturbance rejection controller into a two-degree-of-freedom structure, and obtain the equivalent transfer function expression of the steam generator mathematical model and the characteristic equation of the closed-loop system through the two-degree-of-freedom structure.

[0061] The low-frequency approximation unit is used to approximate the equivalent transfer function expression of the steam generator mathematical model at a low frequency. The compensation is an integral plus a time delay term, which yields the characteristic equation of the closed-loop transfer function after the low-frequency approximation. The desired tracking speed parameter is then obtained, and the adjustment of the outer loop controller gain is equivalently converted into the quantitative adjustment of the desired tracking speed parameter. The quantitative adjustment of the desired tracking speed parameter further determines the system response speed.

[0062] The parameter simplification unit is used to simplify the analysis of the lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller using the regularization method, so as to obtain the simplified regularized observer bandwidth.

[0063] The robustness analysis unit is used to perform robustness index analysis on the steam generator system, determine the relative time delay margin as a stability index, and obtain the range of values ​​for the regularized observer bandwidth.

[0064] An electronic device for storing and executing the method includes:

[0065] Memory, used to store computer programs;

[0066] A processor for executing the computer program to implement the method.

[0067] A non-volatile storage medium for storing and executing the method, for storing a computer program, wherein the computer program implements the method when executed by a processor.

[0068] A computer program product for storing and executing the method includes a computer program / instructions that, when executed by a processor, implement the method.

[0069] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) The relative delay margin is used as the core robustness index, which fundamentally ensures the primary safety characteristics of the control system under extreme uncertainty. The present invention breaks through the traditional analysis framework that only focuses on gain margin and phase margin, and innovatively introduces and systematically analyzes the relative delay margin index. Through theoretical derivation and parameter scanning, the quantitative relationship between the observer bandwidth and this margin is clarified, and a clear parameter selection boundary is provided. (2) A set of gain tuning rules for the system is established through equivalent transformation, low-frequency approximation method and parameter regularization method, which successfully solves the usability problem of complex controllers in engineering applications. By using equivalent transformation and low-frequency approximation method, the controller gain and observer bandwidth are decoupled into two independent parameters with clear physical meanings corresponding to the closed-loop response speed and robustness, respectively. and Furthermore, by regularizing the process parameters (such as time constant, delay, etc.), an infinite number of process parameters are normalized to a few nominal parameters, thereby extracting a general stable range; (3) The low-frequency integral-delay characteristics of TD-ADRC (time-delay active disturbance rejection controller) are revealed and utilized through equivalent transformation, giving it strong internal / external disturbance suppression and model mismatch adaptation capabilities; Through equivalent transformation of the block diagram, it is strictly derived that the "equivalent object" of the original FOPTD (first-order plus time-delay model) controlled object of TD-ADRC (time-delay active disturbance rejection controller) is approximately an integral plus pure delay element in the low-frequency range. This characteristic is consistent with the target open-loop characteristics of advanced PID tuning methods such as SIMC in form. Attached Figure Description

[0070] Figure 1 This is a flowchart of the method steps of the present invention;

[0071] Figure 2 This is a schematic diagram of the step response of water level to changes in feedwater flow rate and steam flow rate, where (a) represents feedwater and (b) represents the water level response corresponding to a unit step flow rate of steam.

[0072] Figure 3 This is a schematic diagram of the TD-ADRC controller structure;

[0073] Figure 4 This is a schematic diagram of the equivalent two-degree-of-freedom structure of a time-delay active disturbance rejection controller;

[0074] Figure 5 To improve the traditional robustness performance index, regularize the observer bandwidth and The changing pattern;

[0075] Figure 6 The relative time delay margin varies with the regularized observer bandwidth and The changing pattern (relative time lag margin is a potential hidden danger);

[0076] Figure 7 for =1 and Under the condition of 0.3, the parameters of the three regularized observers Nyquist plots for =3, 6 and 10;

[0077] Figure 8 The response curve for a step change in the water level setpoint at a 25% FP power level;

[0078] Figure 9 The response curve for a step change in the water level setpoint at 75% FP power level;

[0079] Figure 10 The response curve for a step change in the water level setpoint at 100% FP power level;

[0080] Figure 11 The response curve of the feedwater pump tripping disturbance at a power level of 25%FP;

[0081] Figure 12 The response curve of the feedwater pump tripping disturbance at a power level of 75% FP;

[0082] Figure 13 The response curves are for a feedwater pump tripping disturbance at 100% FP power level. Detailed Implementation

[0083] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0084] This invention proposes an active disturbance rejection parameter tuning optimization method for steam generators with time-delay characteristics in nuclear power systems, which combines disturbance rejection capability and time-delay robustness. Based on the low-frequency approximation method, the dominant dynamics of the system in the main operating frequency range are extracted (the dominant dynamics refer to the low-frequency dynamic range, which is the main research scope concentrated in the low-frequency dynamic range through the low-frequency approximation method), thus obtaining a more general FOPTD (first-order plus time-delay model) equivalent model. A set of simple and intuitive TD-ADRC (time-delay active disturbance rejection controller) gain tuning rules is designed, which combines strong disturbance rejection capability, engineering friendliness (simple and intuitive tuning rules), and can effectively handle time delays and adapt to varying operating conditions. These rules not only clarify the stability domain of the controller gain, but also provide a simple and easy-to-implement engineering tuning process. They demonstrate outstanding technical adaptability in the nuclear power industry scenario with extremely high safety requirements, improve the mathematical analysis capability for modeling and controlling nuclear power equipment, and make TD-ADRC more practical in the actual operation of nuclear power equipment, ensuring the safe operation of nuclear power plants.

[0085] This invention first establishes a mathematical model of a steam generator and uses a low-frequency approximation method to reduce the target object (i.e., the steam generator mathematical model) to a first-order plus time-delay model (FOPTD model). An equivalent two-degree-of-freedom structure of the TD-ADRC model is established, and the characteristic equation of the closed-loop transfer function is summarized using the low-frequency approximation method. Then, regularization is used to simplify the parameters to be considered, and the impact of parameter variations under different regularizations on system robustness is studied. The relative time-delay margin is innovatively introduced, and its significant impact on the stability of nuclear power steam generator control is analyzed, thereby guiding the parameter tuning range proposed in this invention. Finally, the superiority of the parameter tuning method of this invention is verified, and experimental comparison results are given using simulation software, verifying the control performance and disturbance rejection capability of TD-ADRC under different operating conditions.

[0086] like Figure 1 As shown, the method of the present invention includes the following steps:

[0087] S1. Establish a mathematical model of the steam generator;

[0088] This invention uses the Irving model as the basic object model. The Irving model, proposed by Irving et al., is the most widely used mathematical model for steam generators, and its transfer function is expressed as follows:

[0089] (1)

[0090] The input to the transfer function is the water flow rate. and steam flow The output is the water level. .in, and The damping time constant is For mechanical oscillation period, The magnitude of the mass capacity effect. The amplitude of the contraction-expansion phenomenon. This represents the amplitude of the mechanical oscillation.

[0091] Its physical principle is described as follows:

[0092] The inherent mass capacity effect of the steam generator affects the dynamic response of the system.

[0093] Thermohydraulic effect caused by contraction-expansion phenomenon.

[0094] Mechanical oscillation effect.

[0095] The model parameters identified using experimental data at different power levels are summarized in Table 1. Figure 2 Tables (a) and (b) illustrate the step response of water level to changes in feedwater and steam flow rates. The results show that the system response is strongly dependent on the operating power. At low power levels, a significant inverse (non-minimum phase) response is observed, resulting from lower feedwater flow rates and temperatures. In contrast, at high power levels, the system response exhibits oscillatory characteristics. Notably, as... Figure 2 As shown in (a) and (b), for the same positive step input, the system response directions are opposite, which further highlights the differences in the dynamic characteristics of the system across the full power range.

[0096] Table 1. Mathematical model parameters of the steam generator (varying with operating power)

[0097]

[0098] Substituting the parameters in Table 1 into formula (1) yields the specific mathematical model of the steam generator.

[0099] S2. Design a time-delay active disturbance rejection controller (TD-ADRC) for a steam generator;

[0100] like Figure 3 As shown, the overall structure of the time-delay active disturbance rejection controller includes an outer loop controller and an inner loop controller. The steam generator system output reference quantity... Output of the steam generator system deviation value As the input to TD-ADRC, and also the input to the outer loop controller, the deviation value Gain after outer loop controller Then, the control quantity of the outer loop controller is obtained. The inner-loop controller includes an extended observer (ESO) and a delay module. Inner ring control quantity After delay module The output of the steam generator system Together, they serve as the two inputs to an ESO, and the output of the ESO is... Control quantity of outer loop controller The difference is passed through the inner loop controller gain. The inner loop control quantity was then obtained. Inner ring control quantity After the disturbance amount After compensation, it is then processed through the FOPTD form of the steam generator mathematical model. Then, the output of the steam generator system is obtained. .in, For a dimensionless parameter, the expression is: , Let be the time constant of the steam generator system. For the steam generator system gain; For the introduced delay module, For the time lag, The total uncertainty includes internal dynamic characteristics and external disturbances; the inner-loop control quantity... This represents the output of the time-delay active disturbance rejection controller after compensation.

[0101] The FOPTD form of the mathematical model of the steam generator, which captures its typical monotonic response and time-delay characteristics, is expressed in Laplace form as follows:

[0102] (2)

[0103] in, and They represent the frequency domain input quantities respectively. and output The Laplace transform of . Parameters , and These correspond to the steam generator system gain, time constant, and time delay, respectively. All three parameters change slowly with the actual operating conditions of the steam generator system. Accordingly, the time-domain expression of equation (2) can be written as:

[0104] (3)

[0105] in, For time-domain output, The concentration at the steam generator outlet. For delay interference, This represents the average input on the secondary side.

[0106] In formula (3), various uncertainties and disturbances in the steam generator (SG) system (such as model perturbations, primary coolant disturbances, and pressure fluctuations) are uniformly grouped into a single delayed disturbance term. For time-domain expressions, a time-delay active disturbance rejection controller (TD-ADRC) can be designed, where the extended observer (ESO) is constructed as follows:

[0107] (4)

[0108] Traditional ESOs are typically designed for systems with no or minimal time delay. When the controlled object, such as a steam generator, exhibits significant time delay, directly using a traditional ESO will result in observed values ​​lagging behind the actual state. Introducing a time-delayed ESO allows the observer model to better reflect the actual object, thereby providing a more accurate estimate of the current and future system state and total disturbance.

[0109] in, for The differential, for The differential, and These represent the process output estimate and the total uncertainty (including internal dynamics and external disturbances), respectively. Extended observer parameters. and Given by the following expression:

[0110] (5)

[0111] in, To expand the observer bandwidth, this is achieved through the inner loop ( Figure 3 The total uncertainty obtained from the compensation estimate within the dashed box (inner ring) Calculate the controller output after compensation:

[0112] (6)

[0113] in, This represents the compensated time-delay active disturbance rejection controller output, which serves as the input to the steam generator. Output for the outer loop controller;

[0114] Outer loop controller ( Figure 3 The area outside the dashed box is the outer ring, using a simple proportional form:

[0115] (7)

[0116] in, For the outer loop controller gain, This is a reference value for the output of the steam generator system. This refers to the output of the steam generator system.

[0117] S3. Transform the TD-ADRC equivalently into a two-degree-of-freedom structure, and obtain the result from the two-degree-of-freedom structure. The equivalent transfer function expression of the equivalent object to y and the characteristic equation of the closed-loop system;

[0118] The equivalent system can be approximated as follows. For a time-delay-free first-order process, Chen Sen's research has shown that: through an extended state observer (ESO), the process can be approximated from... arrive The equivalent object EP ( Figure 3 The compensation is a pure integrator. If the observer bandwidth is expanded... Large enough, and combined with the outer loop controller (Equation (7)), from arrive Its closed-loop performance can approach the ideal response infinitely. .

[0119] However, these desirable properties no longer hold true when time delays exist in the system. Furthermore, the presence of difficult-to-handle excess terms further increases the difficulty of the analysis. Therefore, to achieve quantitative tuning, this patent innovatively proposes that... Figure 3 Perform an equivalent transformation to obtain Figure 4 The two-degree-of-freedom control structure in the middle, Figure 4 middle, This is a deviation signal. For disturbance, For feedback controller, This is a feedforward controller. To further clarify the controller's operating mechanism. Assume... ,pass Figure 3 Zhong Cong The equivalent object (EP) of y can be derived as equation (8).

[0120] (8)

[0121] in, This is the equivalent transfer function expression. It is a time constant. For the Laplace operator, For the time lag, This represents the observer bandwidth.

[0122] Depend on Figure 4 From this, we can conclude that

[0123] (9)

[0124] but

[0125] (10)

[0126] from Figure 3 It can be seen from the middle

[0127] (11)

[0128] but

[0129] (12)

[0130] By combining equations (10) and (12), we can obtain...

[0131] (13)

[0132] (14)

[0133] in, For feedback controller, It is a feedforward controller.

[0134] The equivalent transformation can be obtained Figure 4 The characteristic equation of the nominal closed-loop system, i.e. You will then get:

[0135] (15)

[0136] It can be further transformed into the following divisible form:

[0137] (16)

[0138] S4, from The equivalent transfer function expression for the equivalent object (EP) to y. A low-frequency approximation is performed, and the compensation is the integral plus the time delay term IPTD. The characteristic equation of the closed-loop transfer function after the low-frequency approximation is obtained, and the desired tracking speed parameter is obtained. The adjustment of the outer loop controller gain is equivalent to the quantitative adjustment of the desired tracking speed parameter. The adjustment of the desired tracking speed parameter further determines the system response speed.

[0139] Unlike integrator-based error compensation for delay-free processes, the innovative discovery of TD-ADRC in this invention makes the error compensation of the FOPTD (first-order plus time delay model) process behave like an IPTD (integral plus time delay) term.

[0140] Therefore, in the low-frequency domain (i.e. (→0), perform low-frequency approximation:

[0141] (17)

[0142] And through the following formula:

[0143] (18)

[0144] The conclusion is , It has no actual physical meaning.

[0145] It is worth noting that, The approximate results are highly similar to those of PI control systems based on traditional SIMC, whose open-loop transfer function is essentially presented in the form of IPTD terms. The key difference lies in the approach taken to achieve this result. In TD-ADRC, the equivalent loop transfer function is approximated as IPTD by simultaneously compensating for disturbances and uncertainties in the ESO loop. It is this difference that gives TD-ADRC a stronger ability to resist uncertainties and disturbances.

[0146] By analogy with the proportional gain in IMC-PI adjustment, the proportional gain in TD-ADRC can be derived from the desired closed-loop transfer function, which can be approximately expressed as:

[0147] (19)

[0148] in, , where is the desired tracking speed parameter.

[0149] therefore,

[0150] (20)

[0151] in, For the outer loop controller gain, The regulation can be equivalently converted to Quantitative regulation, and This determines the system's response speed. This invention patent recommends using it as the default setting, which achieves a reasonable balance between performance and robustness when considering bandwidth limitations imposed by latency. In practical applications, this parameter can... The range can be broadened, depending on the user's preferences in different scenarios. A larger range... This corresponds to taking a more conservative approach when industrial safety receives more attention.

[0152] The subsequent determination only needs to be made in the stability analysis. By determining the tuning range, the value range of all parameters of the TD-ADRC controller can be obtained.

[0153] S5. Apply regularization methods to the TD-ADRC controller parameters. and A simplified analysis was performed to obtain the simplified parameters to be tuned. ;

[0154] To further reduce the number of parameters and facilitate the analysis of a class of generalized processes, the following parameter regularization transformation is introduced:

[0155] (twenty one)

[0156] in, The time delay after regularization For the regularized Laplace operator, This represents the bandwidth for the regularized observer.

[0157] Substitute the parameters to transform the gain, and Figure 3 After reconstructing the control scheme into a two-degree-of-freedom control scheme, the expression for the nominal open-loop transfer function and the corresponding stability conditions are obtained as follows:

[0158] (twenty two)

[0159] Equation (22) can be further transformed into the following stability condition:

[0160] (twenty three)

[0161] in, This is the expression for the open-loop transfer function. For the desired tracking speed parameters, It indicates that it has no actual physical meaning and is the expression after regularization of formula (16).

[0162] In practical engineering applications, regularization of tracking speed parameters The value of is typically between 1 and 3. Within this range, the bandwidth of the regularized observer is adjusted. Applying a sufficient condition will establish a set of process characteristic parameters applicable to any given set. The nominal stability theorem.

[0163] Theorem 1: For any satisfying For a first-order plus pure time delay (FOPTD) process, if the time-delay active disturbance rejection controller (TD-ADRC) regularizes the tracking speed parameters... satisfy And the bandwidth of the regularized observer A closed-loop control system is stable if the following conditions are met:

[0164] (twenty four)

[0165] parameter This represents the desired tracking speed parameter. In actual process control systems, The typical configuration range is 1 to 3. Theorem 1 shows that, in Under the premise of satisfying the explicit bounded condition, the closed-loop system based on TD-ADRC remains stable for any given time delay. Therefore, Equation (24) provides an analytical tuning rule for the bandwidth of the normalized extended state observer (ESO), which can guarantee system stability even in the presence of large and uncertain time delays.

[0166] Proof: This embodiment uses proof by contradiction to prove that all roots of equation (17) have negative real parts. Assume that... and , making If is a root of equation (16), then the following equation holds:

[0167] (25)

[0168] Substitution Verification shows that:

[0169] (26)

[0170] in

[0171] (27)

[0172] Next, we will prove... and First, according to equation (24) and and From the definition of , we can obtain the following equation:

[0173] (28)

[0174] Therefore, we can conclude that:

[0175] (29)

[0176] Next, consider There are two cases. Substituting into equations (28) to (30), we can obtain the following relationship: ;

[0177] Scenario 1: .according to The definitions are as follows:

[0178] (30)

[0179] We can obtain:

[0180] (31)

[0181] Furthermore, due to when hour, about Monotonically increasing, therefore we can conclude:

[0182] (32)

[0183] Therefore, we can obtain .

[0184] Scenario 2: because Therefore:

[0185] (33)

[0186] In addition, by and , Note that equation (20) and Therefore:

[0187] (34)

[0188] By substitution From equations (24) and (34), we can obtain:

[0189] (35)

[0190] It can be verified that when hour, Monotonically increasing. Therefore:

[0191] (36)

[0192] Substitution , and From the definition of , we can draw the following conclusion:

[0193] (37)

[0194] Since it has been proven and Therefore, it can be deduced that Therefore, a conclusion that contradicts equation (26) is obtained, and the proof is complete.

[0195] S6. Perform robustness analysis on the system, determine the relative time delay margin as a stability index, and obtain... The range of values ​​for:

[0196] This invention primarily considers three key robustness and stability metrics: gain margin (GM), stability margin (SM), and relative time delay margin. Gain margin is a traditional metric in automatic control systems. The stability margin is calculated using the formula min... Its physical meaning is the open-loop frequency response in the Nyquist plot. With critical point The minimum distance between them. Maximum sensitivity (denoted as...) This corresponds to the peak value of the sensitivity function and is equal to the reciprocal of the stability margin.

[0197] Relative time delay margin is used to quantify the maximum additional time delay that a closed-loop system can tolerate before reaching critical stability. When there is an uncertain time delay (i.e., ... )hour, For the time lag, For time delay error, the relative time delay margin function can be adjusted accordingly as follows:

[0198] (38)

[0199] in, This is the relative time lag margin. and They represent the lag time. The upper and lower bounds of the range of uncertain time delays in the vicinity. Exceeding these boundaries will cause the closed-loop system to become unstable. When considering uncertain time delays (denoted as...) When the nominal open-loop transfer function (equation (22)) is reached, it should be modified as follows:

[0200] (39)

[0201] in, The nominal loop transfer function, It is a relative time delay;

[0202] Relative time delay is defined as By considering the condition that the perturbed Nyquist plot crosses the critical point, the following relationship is obtained:

[0203] (40)

[0204] in, The complex plane value of the nominal loop transfer function. It is a positive integer.

[0205] Robustness Criterion Defined as obtained from equation (40) The smallest absolute value.

[0206] According to equation (22), the time delay after regularization is traversed. With the desired tracking speed parameters It later became clear that the robustness metric depends entirely on the observer bandwidth. The comprehensive analysis revealed several noteworthy phenomena. =1 and For example, =0.3 Figure 5 The curves showing the stability margin as a function of the normalized observer bandwidth are plotted. It can be observed that traditional robustness metrics (including the gain margin characterizing the system's robustness to gain uncertainty, and the stability margin characterizing robustness to unmodeled low-frequency dynamics) all increase with increasing observer bandwidth. Therefore, from a traditional perspective, a larger observer bandwidth seems preferable, as it can simultaneously improve both the system's performance and robustness metrics.

[0207] However, as Figure 6 As shown, when considering relative time delay margin In some cases, the conclusions drawn from traditional indicators may be misleading. Although in Comprehensive testing was conducted across the range, and a common trend still emerged: contrary to the improving trend of traditional robustness indicators, It decreases significantly with increasing observer bandwidth. Furthermore, it is worth noting that... The curve is A sharp decline occurred at that location. According to... Figure 6 In satisfying Within an acceptable range, the bandwidth of the regularized observer is obtained. The range of values ​​for .

[0208] like Figure 7 As shown in the three typical Nyquist plots, the high The corresponding Nyquist curve lies entirely within the unit circle in the high-frequency region. Therefore, the time delay margin is primarily determined by the gain crossover point—beyond this point, the curve will not encircle the critical point regardless of the magnitude of the uncertain time delay.

[0209] when When the time delay is increased to 6, the situation changes: the Nyquist curve intersects the unit circle twice more. As the time delay increases or decreases, the high-frequency points "A" and "B" move towards the critical point at a faster rate. Therefore, under this condition, the time delay margin is no longer related to the phase margin, but is determined by the high-frequency intersections. This explains why the time delay margin... The surrounding area will drop sharply.

[0210] In summary, the observer bandwidth has a significant impact on both the relative time delay margin and the stability margin. The guiding principles of the tuning method proposed in this invention are as follows:

[0211] along with Due to variations in the relative time delay margin and stability margin, it is impossible for both to simultaneously reach their expected maximum values. Therefore, adjustments should be made based on the characteristics of different first-order plus pure time delay (FOPTD) systems. A compromise adjustment is made. This is done within the range of parameters that are of actual concern in the project (i.e.,...). =1~3、 =1~15), through traversal and It can be observed that: with As the value increases, traditional robustness indicators and relative time delay margins will gradually converge to an increasingly narrow range.

[0212] The scaling parameters of the TD-ADRC of this invention are set to the default value. =1、 =10. For other industrial applications of the TD-ADRC controller, it is possible to... =1~3、 The parameters can be flexibly retuned within the range of 4 to 10. Larger... or smaller This often results in a larger time lag margin, but at the cost of a slower system response speed.

[0213] Simulation verification of the steam generator control system:

[0214] This section uses MATLAB and Simulink to build a steam generator model and an Active Disturbance Rejection Controller (ADRC). To verify the performance of the ADRC controller, test scenarios such as step changes in the water level setpoint and feedwater pump tripping were set up under different power levels. Simultaneously, by applying a step disturbance in steam flow, the controller's disturbance rejection capability under different power levels was further verified. The entire process was simulated in MATLAB / Simulink, and the simulation results were recorded. For ease of comparison, this embodiment also implements... Figures 8 to 10 The simplified internal model control PI (SIMC-PI) tuning method shown improves disturbance rejection performance during the integral process, and its tuning rules are simple and intuitive. Furthermore, this embodiment records time-domain performance indicators such as overshoot and settling time to evaluate and optimize controller performance.

[0215] 1. A step change in the water level setpoint;

[0216] To evaluate the performance of the TD-ADRC controller applied to steam generator level control, this embodiment applied a setpoint step disturbance at simulated power levels of 25%FP, 75%FP, and 100%FP (full power): the steam generator level setpoint was increased from 50% to 55% and maintained for 300 seconds. During the simulation, parameters such as steam generator (SG) level, steam pressure, feedwater valve opening, and feedwater flow rate were recorded. The simulation results of the step disturbance at the three different power levels are as follows: Figures 8 to 10 As shown.

[0217] When the steam generator water level setpoint increases, the tracking and guiding signals output by the tracking differentiator (TD) will change accordingly, and the difference between the TD signal and the extended state observer (ESO) estimated signal will increase. The control law (i.e., the output signal) of the active disturbance rejection controller (ADRC) will be adjusted and drive the feedwater valve to operate. The feedwater valve adjusts the feedwater flow rate, ultimately bringing the steam generator water level to the setpoint.

[0218] The steam generator water level curve at 25% FP power is as follows: Figure 8 As shown, detailed control performance indicators are listed in Table 2. When When the value is 3, the rise time of TD-ADRC is 37.8 seconds, almost identical to that of a traditional PID controller, but its overshoot is only 3.4%, far lower than the 21.8% of a PID controller. Similarly, smaller... This will result in a slower response time, but it can improve system stability and provide a greater latency margin. Simulation results show that for the two selected groups... With each value, TD-ADRC exhibits superior control performance.

[0219] Table 2. Comparison of control performance under step changes in water level setpoints at 25%FP

[0220]

[0221] Table 3. Comparison of control performance under step changes in water level setpoints at 75%FP

[0222]

[0223] Table 4. Comparison of control performance under step changes in water level setpoint at 100% FP

[0224]

[0225] As can be seen from Table 2, under the low-power condition of 25%FP, the dynamic characteristics of the steam generator system exhibit significant non-minimum phase characteristics (reverse response) and strong time-varying characteristics, which places high demands on the robustness and disturbance rejection capability of the controller. The data in the table shows that: (1) Compared with the traditional SIMC-PID controller, the two parameter configurations of the TD-ADRC controller show better control performance: the settling time is shortened from 137.3s to 87.6s and 92.3s respectively, and the overshoot is significantly reduced from 21.8% to 3.4% and 1.4%, with a decrease of more than 80%, which effectively suppresses water level fluctuations under low power. (2) The rise time of the TD-ADRC controller (37.8s, 47.3s) is slightly better than that of SIMC-PID (39s), which significantly improves control accuracy and stability while ensuring fast tracking of the set value. (3) The two TD-ADRC configurations show a trade-off between "response speed and overshoot": the configuration with smaller overshoot (1.4%) corresponds to a slightly longer settling time and rise time, which is suitable for scenarios with extremely high requirements for water level stability; the configuration with 3.4% overshoot achieves a more balanced balance between response speed and stability, which can meet the needs of normal low power operation.

[0226] As can be seen from Table 3, under the typical medium power condition of 75%FP, the dynamic characteristics of the steam generator system tend to be stable, but there is still a certain time delay and parameter coupling. At this time, the controller needs to achieve a precise balance between tracking speed and robustness. Analysis of the data in the table shows that: (1) The overshoot of the SIMC-PID controller further increases to 24.3% and the settling time is extended to 143.1s under this condition, indicating that it is less adaptable to the dynamic changes of the system under medium power conditions and it is difficult to meet the requirements of fast response and small overshoot; (2) The TD-ADRC controller still maintains its advantages: the settling time is shortened to 88.2s and 101.3s, and the overshoot is controlled at 3.8% and 1.8%, respectively. Compared with SIMC-PID, the overshoot is reduced by about 84% and the settling time is shortened by about 31%, showing stronger adaptability to the operating conditions; (3) Compared with the low power condition, the overshoot of TD-ADRC under medium power conditions increases slightly (from 3.4%→3.8%, 1.4%→1.8%), but it is still at a very low level, indicating that it can effectively cope with the changes in the dynamic characteristics of the system under medium power conditions and maintain stable control performance.

[0227] As can be seen from Table 4, under the condition of 100%FP full power operation, the load of the steam generator system reaches the rated value, the dynamic response speed is accelerated, and there is a strong thermal-hydraulic coupling effect, which puts forward higher requirements for the controller's fast tracking capability and anti-disturbance robustness. Based on the data in the table, the analysis is as follows: (1) The SIMC-PID controller still has the problems of large overshoot (23.7%) and long settling time (146.8s) under full power. Its fixed parameters are difficult to match the fast dynamic characteristics of the system under full power, which can easily lead to large fluctuations in water level and affect the safety of operation; (2) TD-ADRC The controller exhibits the best overall performance: one set has a set time of only 90.4s, a rise time of 37.8s, and an overshoot of 3.6%, effectively suppressing fluctuations while rapidly tracking the set value; another set has an overshoot as low as 0.6%, achieving almost no overshoot control, with a set time of 99.3s, fully meeting the stringent requirements for water level control accuracy and stability under full power conditions; (3) The overshoot of TD-ADRC under full power conditions (0.6%, 3.6%) is better than that under low and medium power conditions, indicating that it has good adaptability to the fast dynamic characteristics of the system under high power. The core reason is that TD-ADRC estimates and compensates for internal and external disturbances in the system in real time through the extended state observer, effectively offsetting the dynamic coupling effect under full power.

[0228] 2. Water pump tripping;

[0229] Figures 11 to 13 This study demonstrates the performance of three control schemes in steam generator water level regulation under feedwater pump tripping disturbances. Compared with the traditional SIMC-PI method, two different observer bandwidths are used ( and The TD-ADRC controllers of all exhibit superior anti-interference performance.

[0230] by Figure 12 For example, in the test scenario of the water pump tripping, the high observer bandwidth ( The TD-ADRC controller with the fastest response time limits the maximum water level deviation to approximately 3.4% and recovers to the set value within 35 seconds. In contrast, the low observer bandwidth ( The TD-ADRC controller exhibits a smoother but slower dynamic response, with an overshoot of approximately 2.6% and a settling time approaching 53 seconds. This reflects an active trade-off design aimed at achieving greater robustness. Meanwhile, the traditional SIMC-PI control performs significantly worse: the system exhibits continuous oscillations, with a maximum deviation exceeding 8% and a settling time approaching 300 seconds. This confirms that its disturbance rejection performance and recovery speed are inferior to both TD-ADRC control schemes.

[0231] The above results further verify that adjusting the observer bandwidth... TD-ADRC can effectively balance response speed and overshoot; even under strong disturbances such as feedwater pump tripping, its dynamic performance and stability are still better than traditional PI control.

[0232] Table 5. Comparison of control performance of feedwater pump tripping disturbance under 25% FP

[0233]

[0234] Table 6. Comparison of control performance of feedwater pump tripping disturbance at 75% FP

[0235]

[0236] Table 7 Comparison of control performance of feedwater pump tripping disturbance under 100% FP

[0237]

[0238] As can be seen from Table 5, under the 25%FP low power condition, the feedwater pump tripping is typical, which will cause a sudden change in feedwater flow, and then cause a large fluctuation in the steam generator water level, which puts strict requirements on the controller's anti-interference ability and rapid recovery ability. Based on the data in the table, the analysis is as follows: (1) Compared with the SIMC-PID controller, the TD-ADRC controller with the two parameter configurations has a significant advantage in anti-interference performance: the settling time is greatly shortened from 261.3s to 80.5s ( ) and 54.1s ( The recovery speed increased by about 69%~79%; the rise time decreased from 209.7s to 57.8s and 36.3s, and the water level recovery speed after disturbance increased by about 72%~83%; (2) In terms of maximum deviation control, TD-ADRC ( The maximum water level deviation was reduced from 7.8% to 4.8%, a decrease of 38%, effectively suppressing the water level fluctuation amplitude in the initial stage of disturbance; TD-ADRC ( Although the maximum deviation increased slightly to 5.9%, it was still significantly lower than SIMC-PID and the recovery speed was faster; (3) As can be seen from the comparison, TD-ADRC estimates and compensates for the water pump tripping in real time through the extended state observer, which quickly offsets the impact of sudden changes in water flow on the water level and shows stronger anti-disturbance robustness under low power conditions.

[0239] As can be seen from Table 6, under the medium power condition of 75%FP, the thermal-hydraulic coupling of the system is enhanced, and the impact of the feedwater pump tripping disturbance is more complex. The controller needs to achieve a balance between quickly suppressing the disturbance and maintaining water level stability. Analyzing the data in the table, we can see that: (1) The SIMC-PID controller still exhibits the following defects under this condition: the settling time is 267.1s, the rise time is 213.4s, and the maximum deviation is 8%, making it difficult to quickly suppress the water level fluctuation caused by the feedwater pump tripping; (2) Both TD-ADRC configurations have achieved performance breakthroughs: the settling time has been shortened to 77.6s respectively. ) and 52.3s ( ), shortened by about 71%~80% compared to SIMC-PID; rise time reduced to 53s and 35s, and water level recovery speed increased by about 75%~84% after disturbance; (3) in maximum deviation control, TD-ADRC ( The best performance was achieved by reducing the maximum deviation from 8% to 2.6%, a reduction of 67.5%, almost controlling the water level fluctuation range to 1 / 3 of that of SIMC-PID; TD-ADRC ( The maximum deviation was 3.4%, which was slightly higher than expected. It has a more flexible configuration but a faster recovery speed, and parameters can be flexibly selected according to actual needs.

[0240] As can be seen from Table 7, under the condition of 100%FP full power, the system load reaches the rated value, and the pump tripping disturbance will aggravate the transient fluctuation of the water level. Moreover, the thermal-hydraulic coupling effect is the strongest, and the requirements for the controller are the highest. Based on the data in the table, the analysis is as follows: (1) The SIMC-PID controller still has the problems of long settling time (253.7s), long rise time (202.1s), and large maximum deviation (8%) under full power. The fixed parameters cannot effectively cope with the strong disturbance and fast dynamic characteristics under full power, which can easily lead to the water level deviating from the set value for a long time, threatening the safe operation of the unit; (2) The TD-ADRC controller shows the best anti-disturbance performance: the settling time is reduced to 71.3s ( ) and 49.9s ( Compared to SIMC-PID, the rise time is shortened by about 72%~80%; the rise time is reduced to 48.7s and 32.9s, and the water level recovery speed after disturbance is increased by about 76%~84%; (3) In terms of maximum deviation control, both TD-ADRC configurations control the water level fluctuation within 3.4%, of which TD-ADRC ( The figure is 3.3%, TD-ADRC ( The efficiency was 3.4%, which is more than 57% lower than the 8% of SIMC-PID. This effectively suppressed the drastic water level fluctuations caused by the pump tripping at full power, and verified its excellent anti-interference ability under strong coupling and fast dynamic conditions.

[0241] The system of the present invention includes:

[0242] The steam generator mathematical model building unit is used to establish a mathematical model of the steam generator.

[0243] The time-delay active disturbance rejection controller (ADRC) design unit is used to design an ADRC based on the first-order time-delay model of the steam generator mathematical model. The ADRC includes an outer loop controller and an inner loop controller. The outer loop controller is used to compensate for the deviation between the output of the steam generator system and its reference value, and obtain the outer loop controller output. The inner loop controller is used to compensate for the total uncertainty based on the delayed ADRC output and the output of the steam generator system, and calculate the compensated ADRC output based on the outer loop controller output and the total uncertainty.

[0244] The equivalent transformation unit is used to transform the time-delay active disturbance rejection controller into a two-degree-of-freedom structure, and obtain the equivalent transfer function expression of the steam generator mathematical model and the characteristic equation of the closed-loop system through the two-degree-of-freedom structure.

[0245] The low-frequency approximation unit is used to approximate the equivalent transfer function expression of the steam generator mathematical model at a low frequency. The compensation is an integral plus a time delay term, which yields the characteristic equation of the closed-loop transfer function after the low-frequency approximation. The desired tracking speed parameter is then obtained, and the adjustment of the outer loop controller gain is equivalently converted into the quantitative adjustment of the desired tracking speed parameter. The quantitative adjustment of the desired tracking speed parameter further determines the system response speed.

[0246] The parameter simplification unit is used to simplify the analysis of the lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller using the regularization method, so as to obtain the simplified regularized observer bandwidth.

[0247] The robustness analysis unit is used to perform robustness index analysis on the steam generator system, determine the relative time delay margin as a stability index, and obtain the range of values ​​for the regularized observer bandwidth.

[0248] An electronic device for storing and executing the method includes:

[0249] Memory, used to store computer programs;

[0250] A processor for executing the computer program to implement the method.

[0251] A non-volatile storage medium for storing and executing the method, for storing a computer program, wherein the computer program implements the method when executed by a processor.

[0252] A computer program product for storing and executing the method includes a computer program / instructions that, when executed by a processor, implement the method.

Claims

1. A simplified method for tuning active disturbance rejection control (ADRC) for a delayed nuclear steam generator, characterized in that, Includes the following steps: A mathematical model of a steam generator is established. Based on the first-order time-delay model of the steam generator mathematical model, a time-delay active disturbance rejection controller (ADRC) is designed. The ADRC includes an outer loop controller and an inner loop controller. The outer loop controller is used to compensate for the deviation between the output of the steam generator system and its reference value, and obtains the outer loop controller output. The inner loop controller is used to compensate for the estimated total uncertainty based on the delayed ADRC output and the output of the steam generator system, and calculates the compensated ADRC output based on the outer loop controller output and the total uncertainty. The time-delay active disturbance rejection controller is equivalently transformed into a two-degree-of-freedom structure. The equivalent transfer function expression of the steam generator mathematical model and the characteristic equation of the closed-loop system are obtained through the two-degree-of-freedom structure. The equivalent transfer function expression of the steam generator mathematical model is approximated at low frequency, and the compensation is integral plus time delay term to obtain the characteristic equation of the closed-loop transfer function after low frequency approximation. The desired tracking speed parameter is then obtained, and the adjustment of the outer loop controller gain is equivalently converted into the quantitative adjustment of the desired tracking speed parameter. The quantitative adjustment of the desired tracking speed parameter further determines the system response speed. The lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller are simplified and analyzed using the regularization method to obtain the simplified regularized observer bandwidth. Robustness index analysis was performed on the steam generator system to determine the relative time delay margin as a stability index and to obtain the range of values ​​for the regularized observer bandwidth.

2. The method according to claim 1, characterized in that, The inner loop controller includes an extended observer and a delay module. The compensated time-delay active disturbance rejection controller output, after passing through the delay module, together with the steam generator system output, serves as the two inputs of the extended observer. The difference between the total uncertainty of the extended observer output and the control quantity of the outer loop controller is amplified by the inner loop controller to obtain the compensated time-delay active disturbance rejection controller output at the next moment. After disturbance compensation, the compensated time-delay active disturbance rejection controller output is then processed through the first-order time-delay model of the steam generator mathematical model to obtain the steam generator system output.

3. The method according to claim 1, characterized in that, The equivalent transfer function expression and characteristic equations of the closed-loop system of the steam generator mathematical model are obtained through a two-degree-of-freedom structure; specifically including: The equivalent transfer function expression is: ； in, This is the equivalent transfer function expression. It is a time constant. For the Laplace operator, For the time lag, To expand the observer bandwidth; Further, the equivalent feedback controller is obtained. and feedforward controller , is represented as: ； ； in, For the outer loop controller gain, For the dimensionless parameters of the inner ring; The characteristic equation of the closed-loop system is expressed as: ； in, For the steam generator system gain; Further, it can be transformed into the following separable form: 。 4. The method according to claim 1, characterized in that, The equivalent transfer function expression of the steam generator mathematical model is approximated using a low-frequency method and is expressed as follows: ； in, This is the equivalent transfer function expression. For the Laplace operator, For the time lag, For intermediate quantities, the expression is: , It is a time constant. To expand the observer bandwidth; The closed-loop transfer function after low-frequency approximation is obtained The characteristic equation is expressed as: ； in, For the outer loop controller gain, The desired tracking speed parameter; The expression for the desired tracking speed parameter is further obtained as follows: ; The adjustment of the outer loop controller gain is equivalently converted into a quantitative adjustment of the desired tracking speed parameter, expressed as: 。 5. The method according to claim 1, characterized in that, The lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller are simplified and analyzed using a regularization method to obtain the simplified regularized observer bandwidth; specifically: Parameter regularization transformation: ； in, The time delay after regularization For the regularized Laplace operator, To regularize the observer bandwidth, For the Laplace operator, For the time lag, It is a time constant. To expand the observer bandwidth; Based on the two-degree-of-freedom structure, the expression for the open-loop transfer function is obtained. : ； in, For the desired tracking speed parameters, It has no actual physical meaning; the expression is: 。 6. The method according to claim 1, characterized in that, Robustness analysis was performed on the steam generator system to determine the relative time delay margin as a stability index, and the range of values ​​for the regularized observer bandwidth was obtained; including: When there is an uncertain time delay hour, For the time lag, For time delay error, the relative time delay margin function is adjusted as follows: ； in, This is the relative time lag margin. and They represent the lag time. The upper and lower bounds of the range of uncertain time delays in the vicinity; when considering uncertain time delays, the nominal open-loop transfer function is corrected as follows: ； in, The nominal loop transfer function, It is a relative time delay. The time delay after regularization For the regularized Laplace operator, To regularize the observer bandwidth, The desired tracking speed parameter; the relative time delay is defined as... ; By considering the condition that the perturbed Nyquist plot passes through the critical point, the following relationship is obtained: ； in, The complex plane value of the nominal loop transfer function. It is a positive integer; Based on relative time lag margin and The changing pattern, in order to satisfy Within the range, the bandwidth of the regularized observer is obtained. The range of values ​​for .

7. A simplified active disturbance rejection control tuning system for a delayed nuclear steam generator, characterized in that, include: The steam generator mathematical model building unit is used to establish a mathematical model of the steam generator. The time-delay active disturbance rejection controller (ADRC) design unit is used to design an ADRC based on the first-order time-delay model of the steam generator mathematical model. The ADRC includes an outer loop controller and an inner loop controller. The outer loop controller is used to compensate for the deviation between the output of the steam generator system and its reference value, and obtain the outer loop controller output. The inner loop controller is used to compensate for the total uncertainty based on the delayed ADRC output and the output of the steam generator system, and calculate the compensated ADRC output based on the outer loop controller output and the total uncertainty. The equivalent transformation unit is used to transform the time-delay active disturbance rejection controller into a two-degree-of-freedom structure, and obtain the equivalent transfer function expression of the steam generator mathematical model and the characteristic equation of the closed-loop system through the two-degree-of-freedom structure. The low-frequency approximation unit is used to approximate the equivalent transfer function expression of the steam generator mathematical model at a low frequency. The compensation is an integral plus a time delay term, which yields the characteristic equation of the closed-loop transfer function after the low-frequency approximation. The desired tracking speed parameter is then obtained, and the adjustment of the outer loop controller gain is equivalently converted into the quantitative adjustment of the desired tracking speed parameter. The quantitative adjustment of the desired tracking speed parameter further determines the system response speed. The parameter simplification unit is used to simplify the analysis of the lag time parameter and extended observer bandwidth parameter of the time-delay active disturbance rejection controller using the regularization method, so as to obtain the simplified regularized observer bandwidth. The robustness analysis unit is used to perform robustness index analysis on the steam generator system, determine the relative time delay margin as a stability index, and obtain the range of values ​​for the regularized observer bandwidth.

8. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1-6.

9. A non-volatile storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the method as described in any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-6.

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