Thermal time lag process ADRC design method with time lag robustness

Abstract

The invention discloses a thermal working time lag process ADRC design method with time lag robustness. The thermal working time lag process ADRC design method comprises the steps that 1, a transfer function model of a first-order inertia time lag process of a thermal process is established; step 2, establishing a time-delay ADRC structure based on model information driving; 3, obtaining a proportional gain with expected closed-loop dynamic representation and a corresponding observer bandwidth setting rule through low-frequency approximation; step 4, scaling control parameters of the ADRC system according to the transfer function model established in the step 1, and setting default adjustment parameters of proportional gain and observation bandwidth; 5, carrying out equivalent two-degree-of-freedom conversion on the closed-loop system, analyzing the nominal stability of the ADRC system based on a double-track method, and obtaining a nominal stability domain of the control parameters; and step 6, in the nominal stability domain obtained in the step 4, according to the regularization rule of the ADRC scaling parameter and the demand of comprehensive robustness, obtaining the time constant of the low-pass filter in the compensation channel by establishing a monotonically decreasing amplitude curve of the time-delay ADRC open-loop Bode diagram.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of thermal power generation, and particularly relates to a thermal process ADRC design method with time delay robustness. BACKGROUND

[0002] In the current background of fast response of thermal power units to grid load instructions, the process variables of time delay control systems in the thermal production link of power plants are affected by many disturbances and uncertainties, causing the controlled variables of the process to deviate from the set value, affecting the efficiency and economy of the thermal power generation process, and even threatening the safe operation of the unit. Active disturbance rejection control (ADRC) can estimate the difference between the controlled process and the nominal model in real time by observing the input and output signals, and feedback it to the input signal in time, so compared with the traditional PID control based on error adjustment, it can improve and enhance the suppression ability of the control system to unknown disturbances. For the time delay link in the thermal process, an additional time delay compensation structure is usually introduced to avoid the asynchronous behavior of the observer signal caused by time delay in ADRC, so as to ensure the control performance. The current time delay compensation structure is usually input time delay compensation (for short, time delay ADRC, see Zhao S, Gao Z. Modified active disturbance rejection control for time-delay systems [J]. ISA transactions, 2014, 53(4): 882-888), that is, an artificial time delay module is added in the control signal channel of the observer to ensure simple structure while realizing accurate estimation of the disturbance signal.

[0003] Although the current time-delay ADRC design for thermal process (see Southeast University. A parameter tuning method and controller for self-disturbance-rejection time-delay controller of thermal process: CN202011384756.2[P]. 2022-05-24.) improves the control performance, its time-delay robustness is far lower than that of the traditional PID, generally only about 20%, and cannot guarantee stability within the nominal time delay range. This characteristic makes it particularly cautious when applied to the current thermal process with changing conditions, because the time delay of most thermal processes is a comprehensive representation of material transfer, signal transmission and high-order inertia approximation, and any change in any link will cause the time delay to change, resulting in strong uncertainty of the time delay. In order to enhance the time-delay robustness, i.e. to widen the accommodation range of uncertain time delay, the general method is to further conserve the parameters of the time-delay ADRC, thereby sacrificing more control performance. For the time-delay ADRC based on the traditional extended state observer (ESO), this weak time-delay robustness feature is difficult to avoid, on the one hand, a higher observer bandwidth is needed to ensure closed-loop stability, and on the other hand, when the observer bandwidth is high to a certain extent, the time-delay robustness will drop sharply. SUMMARY

[0004] The purpose of the present application is to provide a thermal time-delay process ADRC design method, which decouples the conflict between system time-delay robustness and closed-loop stability by improving the control structure, and develops a parameter tuning rule that is clear and intuitive and has a characterization of nominal stability and time-delay robustness according to the low-order transfer function model widely used in thermal time-delay processes. Using the method of the present application can reduce the parameter tuning burden of the thermal time-delay process ADRC while maintaining the advantages of the current thermal time-delay process ADRC, achieving superior control performance while ensuring strong time-delay robustness.

[0005] To achieve the purpose of the application, the technical solutions adopted by the present application are as follows:

[0006] Step 1: Establish a transfer function model of a commonly used first-order inertia time-delay process in thermal processes.

[0007] Step 2: Establish a time-delay ADRC structure based on model information driving, mainly introducing transfer function model information in the observer, adding a set value proportional gain in the set value channel, and adding an inertia filter with unit gain in the disturbance compensation channel.

[0008] Step 3: Based on the time-delay ADRC structure established in step 2, obtain the proportional gain with the expected closed-loop dynamic characterization and the corresponding observer bandwidth tuning rule through low-frequency approximation.

[0009] Step 4: The control parameters of the ADRC system are scaled according to the transfer function model established in step 1, and the default adjustment parameters of the proportional gain and the observation bandwidth are set in this form.

[0010] Step 5: The equivalent two-degree-of-freedom transformation is performed on the closed-loop system, the nominal stability of the ADRC system is analyzed based on the double-track method, and the nominal stability domain of the control parameters is obtained.

[0011] Step 6: Within the nominal stability domain obtained in step 4, according to the regularization rule of the ADRC scaling parameters and the requirement of comprehensive robustness, the time constant of the low-pass filter in the compensation channel is obtained by establishing the open-loop Bode diagram of the time-delay ADRC with a monotonically decreasing amplitude curve.

[0012] Further, in step 1, the transfer function model of the commonly used first-order inertial time-delay process in thermal process is established as follows:

[0013]

[0014] In the formula, u, y are control variables (input of the controlled process) and controlled variables (output of the controlled process) respectively, K is the steady-state gain; T is the time constant and T > 0; e -Ls is the time delay, L is the time delay, and s is the Laplace operator.

[0015] Further, in step 2, the designed time-delay ADRC structure is as shown in Figure 1 The designed time-delay ADRC structure includes a proportional feedback link and an observation compensation link; the proportional feedback link performs the tracking task of the set value, and the observation compensation link suppresses the lumped disturbance composed of model uncertainty and unknown external disturbance;

[0016] The low-order form of the extended state observer (Model-driven Extended State Observer, MESO) is used under the premise of introducing model information, which is as follows:

[0017]

[0018] In the formula, a0 = 1 / T, b0 = K / T are the converted parameters of the transfer function model, z(t) is an auxiliary variable, is an estimated variable of the lumped disturbance signal, ω o is the observer bandwidth, and the MESO structure is as shown in Figure 2As shown, combined with formula (2), the output of the observer MESO structure is the superposition of the auxiliary variable and the controlled variable after gain change, and the auxiliary variable is the superposition and integration of the variable itself, the controlled variable and the control variable after time delay processing after gain change.

[0019] The expression of the disturbance estimation variable generated by the above observer structure in the frequency domain is:

[0020]

[0021] The disturbance signal estimated by the observer is introduced into a low-pass filter G f (s) = 1 / (1+T f s), and the disturbance estimation signal after observation reconstruction is obtained

[0022] Under the above observation reconstruction structure, the overall control expression of the ADRC is:

[0023]

[0024] In the formula, r is a set value variable, k p is a proportional feedback gain parameter. Compared with the traditional proportional feedback form k p r-k p y, the application uses an additional gain form (k p +a0) r in the set value channel.

[0025] Further, in step 3, an inertia time delay model with unit gain is used as the expected closed-loop dynamic:

[0026]

[0027] In the formula, T c is the expected closed-loop time constant. The application shapes the closed-loop dynamic of the time delay ADRC system into the above expected dynamic by formulating a proportional gain setting rule. The closed-loop dynamic of the time delay ADRC system can be obtained by bringing the reconstructed disturbance expression into the control action:

[0028]

[0029] The time delay term e -Ls in the denominator of the above formula is approximated as 1-Ls, and the closed-loop dynamic can be approximated as

[0030]

[0031] Comparing the formula with the expected closed-loop dynamic, if the proportional gain adjustment satisfies 1-k p L=T c(a0+k p If we can approximate G, then we can obtain G. cl (s)≈e -Ls / 1+T c s

[0032] Therefore, the proportional gain tuning rule with the desired closed-loop dynamic characterization can be obtained as follows:

[0033]

[0034] The observer bandwidth is typically set to 10 times the closed-loop bandwidth. Although the closed-loop bandwidth of a time-delay control system does not exist, this invention introduces the desired closed-loop dynamics for parameter design, which allows the bandwidth of the desired dynamics to be 1 / T. c For reference, the formula for tuning the observer bandwidth is:

[0035]

[0036] Furthermore, in step 4, the parameters of the time-delay ADRC control system are scaled as follows:

[0037]

[0038] Where s′, τ, τ c , τ f ,λ,k′ p Let represent the scaled Laplacian operator, model time constant, desired closed-loop time constant, observation reconstruction filter time constant, observer bandwidth, and proportional gain, respectively. The scaled control parameter tuning rules (8) and (9) become:

[0039]

[0040] After obtaining the transfer function model of the controlled object, only by adjusting τ c The aforementioned control parameters can then be obtained. For the purposes of this invention, this parameter is set to a default value.

[0041] τ c =1 (12)

[0042] This means that the desired closed-loop time constant should be equal to the time delay. After obtaining the nominal stable range of this parameter, its value can be further adjusted based on performance and robustness requirements.

[0043] Furthermore, in step 5, a two-degree-of-freedom transformation is performed on the ADRC system based on the parameter scaling rule, such as... Figure 3 As shown, the equivalent feedback controller and the transferred function of the controlled object are as follows:

[0044]

[0045] Thus in the nominal case, based on the scaled parameter form of the closed-loop characteristic equation 1 + G c (s')G p (s') = 0 is:

[0046]

[0047] Based on the dual locus method, the regulation parameter τ c can be obtained, and the stable region of τ c is as follows:

[0048]

[0049] where ω * is the solution of the equation in ω * = τ tan(ω * ) in (0, π).

[0050] Further, in step 6, the open-loop transfer function G ol (s') of the time-delay ADRC system is:

[0051]

[0052] In the control system without time-delay compensation, in the nominal stable region of the regulation parameter, the Nyquist curve of the open-loop transfer function of the system generally only crosses the unit circle once, and the phase margin and the gain cross frequency ω gc of the open-loop system are formed at the crossing point. According to the phase relationship between the crossing point and the critical point, the corresponding maximum time-delay increment maxΔl + can be expressed as:

[0053]

[0054] Since the only crossing point will only surround the critical point when the time delay increases, only the maximum time-delay increment is considered, and the time-delay margin in the parameter scaling form is then expressed as:

[0055] d m = (0, 1 + maxΔl + ) (19)

[0056] For the time-delay ADRC system studied in the present application, without introducing observation reconstruction, the Nyquist curve of the open-loop transfer function will cross the unit circle multiple times, forming multiple crossing points, and further having multiple sets of phase margin and gain cross frequency ω gc , such as Figure 4Besides, the crossing point will pass through the critical point when the time delay increases and decreases, so not only the maximum time delay increment, but also the maximum time delay decrement should be considered. The crossing points are arranged in the order from 1, and the maximum increments and decrements of the time delay are calculated as shown below:

[0057]

[0058] In the formula, i is the order number of the crossing point, k is a non-negative integer, if k=0, i=1, indicating that it only crosses once. The time delay margin of the system is represented as:

[0059] d m =(1-maxΔl - ,1+maxΔl + ) (21)

[0060] It can be seen that the unstable time delay point appears in the nominal time delay range of the control system. This is mainly due to the introduction of time delay compensation, the time delay term appears in the denominator of the open-loop transfer function of the time delay ADRC system, which destroys the original monotonic decay characteristic. The present application adjusts again by introducing an observation reconstruction filter to ensure that the open-loop transfer function only crosses the unit circle once.

[0061] The Nyquist curve is converted into the Bode diagram as shown in Figure 5 , through the experiment of different time delay models under the scaling parameter, it is found that when the time constant of the observation reconstruction filter satisfies τ f ≥0.4, for the default adjustment parameter τ c =1, it can be ensured that the open-loop transfer function Bode diagram of the control system of the time delay object only crosses the 0dB line once in the range of τ∈(0.05,2), that is, the Nyquist curve only crosses the unit circle once. Therefore, in order to not sacrifice too much performance, the time constant of the observation reconstruction filter is set as follows by default

[0062] τ f =0.4 (22)

[0063] Therefore, for the time delay ADRC system designed by the present application, after obtaining the transfer function of the controlled object, the control parameter values can be automatically calculated and obtained according to the above default recommendations, which is very convenient for practical application.

[0064] The present application provides an ADRC design method for a thermal time delay process, which has the following technical effects:

[0065] 1) Without increasing the complexity of the control structure, the contradiction between system stability and time delay robustness is decoupled by appropriate structural improvement on the basis of maintaining the original characteristics of the time delay ADRC;

[0066] 2) Through strict theoretical analysis, the parameter stable range is determined and the intuitive setting rule is formulated, so that all controller parameters can be determined after the transfer function of the thermal time-delay object is obtained, and the parameter setting process is simplified;

[0067] 3) The control system has expected closed-loop tracking dynamics and good disturbance suppression performance, and compared with the traditional time-delay ADRC, the stability of the control system in the nominal time-delay range is ensured, the time-delay margin is improved, and the time-delay robustness is enhanced. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 The overall structure of the time-delay ADRC system of the application is shown in the figure;

[0069] Figure 2 The structure of the model information-based extended state observer MESO of the application is shown in the figure;

[0070] Figure 3 The equivalent two-degree-of-freedom structure of the time-delay ADRC system of the application is shown in the figure;

[0071] Figure 4 The open-loop transfer function Nyquist curve of the system without observation reconstruction of the application is shown in the figure;

[0072] Figure 5 The open-loop transfer function Bode diagram of the system with observation reconstruction under different time delays of the application is shown in the figure;

[0073] Figure 6 The comparative response diagram of the application and the current time-delay ADRC when the time delay of the controlled object changes is shown in the figure;

[0074] Figure 7 The performance comparison diagram of the application and the PI control based on the SIMC rule tuning under the nominal condition is shown in the figure. DETAILED DESCRIPTION

[0075] The application is further described below in combination with the accompanying drawings of the specification.

[0076] The application provides a thermal time-delay process ADRC design method, and the specific implementation manner is as follows.

[0077] Step 1) For the thermal time-delay controlled process studied, the following frequency-domain first-order transfer function model is obtained through process mechanism simplification analysis or field step response dynamic test:

[0078]

[0079] In the formula, u and y are respectively a control variable (input of the controlled process) and a controlled variable (output of the controlled process), K is a steady-state gain, T is a time constant and T>0, e -Lsis the time delay, L is the time delay amount, and s is a Laplace operator. Further, the transfer function model is converted into a time-domain state space equation form as follows:

[0080]

[0081] where a0=1 / T, b0=K / T are parameters converted from the transfer function model, and d is a process disturbance variable.

[0082] Step 2) a time-delay ADRC structure as shown in Figure 1 is established, and a model-driven extended state observer (MESO) in a reduced-order form is used under the premise of introducing model information, and the structure is as shown in Figure 2 Based on the state space equation of the controlled process, the corresponding MESO state space equation is as follows:

[0083]

[0084] where z is an auxiliary variable, is an estimated variable of the lumped disturbance d, and ω o is an observer bandwidth parameter, and the expression of the estimated signal produced by the above observer structure in the frequency domain is as follows:

[0085]

[0086] A low-pass type observation reconstruction filter G f (s) = 1 / (1+T f s) is introduced, and the disturbance estimated variable is further processed, and the disturbance estimated variable after observation reconstruction is obtained as

[0087]

[0088] where T f is a filter time constant to be designed. Under the above observation reconstruction structure, the expression of the control variable of the ADRC is as follows:

[0089]

[0090] where r is a set value variable, and k p is a proportional feedback gain parameter. Compared with the traditional proportional feedback form k p r-k p y, the application uses an additional gain form, i.e., (k p +a0)r, in the set value channel.

[0091] Step 3) Establish the following inertia time-delay model with unit gain as the expected closed-loop dynamic:

[0092]

[0093] where T c is the expected closed-loop time constant. The present application shapes the closed-loop tracking dynamic of the time-delay ADRC system into the above expected mode by formulating the proportional gain tuning rule. By substituting the restructured disturbance expression into the control variable expression, the closed-loop dynamic of the time-delay ADRC system can be obtained as:

[0094]

[0095] The time-delay term in the denominator of the above expression can be approximated as 1-L0s in the low frequency range, and the closed-loop dynamic can be approximated as

[0096]

[0097] By comparing this expression with the expected closed-loop dynamic, it can be known that if the adjusted proportional gain satisfies 1-k p L=T c (a0+k p ), then the G cl (s)≈e -Ls / 1+T c s can be approximately obtained.

[0098] Therefore, the proportional gain tuning rule with the expected closed-loop dynamic representation can be obtained as:

[0099]

[0100] The observer bandwidth is usually formulated as 10 times of the closed-loop bandwidth. Although the closed-loop bandwidth of the time-delay control system does not exist, since the present application introduces the expected closed-loop dynamic for parameter design, the bandwidth of the expected dynamic, i.e., the inverse of the closed-loop time constant 1 / T c , can be taken as a reference, and thus the tuning formula of the observer bandwidth is:

[0101]

[0102] Step 4) The scaling form of the parameters of the time-delay ADRC control system is as follows:

[0103]

[0104] where s′, τ, τ c , τ f , λ, k′ prespectively, denote the scaled Laplacian operator, the model time constant, the desired closed-loop time constant, the observation reconstruction filter time constant, the observer bandwidth and the proportional gain, respectively. The scaled control parameter tuning rules (10) (11) become

[0105]

[0106] After obtaining the transfer function model of the controlled object, only by adjusting τ c , the above control parameters can be obtained. For the present application, the parameter is set as

[0107] τ c = 1 (14)

[0108] That is, the desired closed-loop time constant is equal to the time delay. After obtaining the nominal stable range of the parameter, the parameter value can be further adjusted in combination with the performance and robustness requirements.

[0109] Step 5) Perform a two-degree-of-freedom transformation on the ADRC system as shown in Figure 3 , obtain the equivalent feedback controller based on parameter scaling and the transfer function of the controlled object as follows:

[0110]

[0111] Therefore, in the nominal case, the closed-loop characteristic equation 1 + G c (s') G p (s') = 0 is:

[0112]

[0113] Based on the double trajectory method, the stable region of the adjustment parameter τ c is as follows:

[0114]

[0115] where ω * is the solution of the equation in (0, π) at ω * = τ tan (ω * ).

[0116] Step 6) Establish the open-loop transfer function G ol (s') of the time-delay ADRC system as shown in Figure 3 :

[0117]

[0118] In the control system without time delay compensation, the Nyquist curve of the open-loop transfer function of the system generally only crosses the unit circle once in the nominal stable region of the adjustment parameters, and the crossing point forms the phase margin of the open-loop system and the gain cross frequency ω gc . According to the phase relationship between the crossing point and the critical point, the corresponding maximum time delay increment maxΔl + may be expressed as:

[0119]

[0120] Since the only crossing point only surrounds the critical point when the time delay increases, only the maximum time delay increment is considered, and the time delay margin in the parameter scaling form is then expressed as:

[0121] d m =(0,1+maxΔl + ) (21)

[0122] For the time delay ADRC system studied in the present application, without introducing observation reconstruction, the Nyquist curve of the open-loop transfer function will cross the unit circle multiple times, forming multiple crossing points, and then having multiple sets of phase margins and gain cross frequencies ω gc . Moreover, when the time delay increases and decreases, the crossing point will pass through the critical point, so not only the maximum time delay increment but also the maximum time delay decrement should be considered. Taking τ=1 as an example, Figure 4 the Nyquist curve of the open-loop transfer function of the time delay ADRC without observation reconstruction is shown, which crosses the unit circle 5 times. The crossing points are arranged in the order of 1 according to the crossing order, and the corresponding maximum time delay increment and decrement are calculated as follows:

[0123]

[0124] In the formula, i is the sequential number of the crossing point. In this case of multiple crossings, the time delay margin based on parameter scaling is expressed as:

[0125] d m =(1-maxΔl - ,1+maxΔl + ) (23)

[0126] As can be seen, the nominal time delay range (0, 1) of the control system under parameter scaling appears unstable time delay points. This is mainly due to the introduction of time delay compensation, the time delay term appears in the denominator of the open-loop transfer function of the time delay ADRC system, resulting in the amplification of the amplitude in the mid-frequency band. The present application adjusts again by introducing an observation reconstruction filter to suppress the influence of time delay on the amplitude of the open-loop transfer function in the mid-frequency band, that is, to ensure that the open-loop transfer function only crosses the unit circle once.

[0127] The view angle is converted from the Nyquist curve to the Bode plot Figure 5 The Nyquist curve crosses the unit circle once, which means that the amplitude-frequency curve in the Bode plot crosses the 0dB line only once. It is found that when the time constant of the observation reconstruction filter satisfies τ f ≥ 0.4, for the default adjustment parameter τ c = 1, the amplitude-frequency characteristic of the Bode plot of the open-loop transfer function of the control system of the time-delay object in the range of τ ∈ (0.05, 2) can be guaranteed to cross the 0dB line only once, i.e., the Nyquist curve crosses the unit circle only once. Therefore, in order to guarantee not too much performance sacrifice, the time constant of the observation reconstruction filter is set as follows by default

[0128] τ f = 0.4 (24)

[0129] Therefore, for the time-delay ADRC system designed in the present application, after obtaining the transfer function of the controlled object, the control parameter values can be automatically calculated and obtained according to the above default recommendation, which is very convenient for practical application. The default value of the closed-loop adjustment parameter τ c is τ c = 1, and if it is necessary to further adjust the value of τ c , the time constant of the observation reconstruction filter should also be adjusted. The specific principle is as follows: when τ c is increased, the robustness of the system will be increased, at this time, τ f can be kept unchanged, or the value of τ f can be appropriately reduced to guarantee the disturbance suppression performance; when τ c is reduced, the robustness of the system will be reduced, at this time, the value of τ f should be increased to guarantee the time-delay robustness.

[0130] Control effect simulation example: consider the transfer function model of the secondary current of the high-frequency power supply of the final-stage electric field and the smoke dust at the outlet of the dry-type electrostatic precipitator in the coal-fired power plant environmental protection island coal-fired flue gas dry-type electrostatic precipitation process:

[0131]

[0132] In the formula, C d is the smoke dust concentration at the outlet of the dry-type electrostatic precipitator, with the unit of mg / Nm 3 , and C d is the high-frequency secondary current of the final-stage electric field, with the unit of mA. The model parameters of the process are K = -0.0015, T = 62.05, and L = 27, from which the control parameters of the time-delay ADRC designed in the present application can be calculated as follows:

[0133]

[0134] The set value step response comparison is performed between the time delay ADRC designed in the present application and the time delay ADRC designed in the current thermal process when the time delay of the controlled object changes by ±25%, as shown in Figure 6 It can be found that the output of the controlled object of the time delay ADRC designed in the present application remains stable whether the uncertain time delay increases or decreases by 25% of the nominal time delay, while the current time delay ADRC has an unstable phenomenon of divergence of the output of the controlled object.

[0135] The set value step response comparison is performed between the time delay ADRC designed in the present application and the PI control after tuning of the famous SIMC rule in the nominal case, and a constant disturbance is added at 200 seconds, and the result is shown in Figure 7 Since the same closed-loop tracking time constant is used for tuning, it can be found that the time delay ADRC designed in the present application has the same tracking performance as the tuned PI, but the disturbance suppression capability is greatly enhanced.

[0136] The primary task of most thermal processes is to stabilize the controlled variable at the set value under the variable working condition of the unit, so the suppression performance of the disturbance and uncertainty is mainly concerned. Based on the above implementation process and simulation examples, it can be known that the present application has achieved superior effects in the two aspects, so the time delay ADRC provided in the present application has the basis and potential to improve the control performance of the thermal process.

[0137] The above embodiments are only preferred embodiments of the present application, and are not a limitation on the technical solutions of the present application. Any technical solutions that can be realized on the basis of the above embodiments without creative labor shall be considered to fall within the protection scope of the patent of the present application.

Claims

1. A thermal process with time delay ADRC design method with time delay robustness, characterized in that, The method comprises the following steps: Step 1: establishing a transfer function model of a first-order inertia time-delay process of a thermal process; Step 2: establishing a time-delay ADRC structure based on model information driving, including introducing the transfer function model information in an observer, adding a set value proportional gain in a set value channel, and adding an inertia filter with unit gain in a disturbance compensation channel; Step 3: based on the time-delay ADRC structure established in step 2, obtaining a proportional gain with a desired closed-loop dynamic characteristic and a corresponding observer bandwidth setting rule through low-frequency approximation; Step 4: scaling the control parameters of the ADRC system according to the transfer function model established in step 1, and setting default adjustment parameters of the proportional gain and the observer bandwidth; Step 5: performing equivalent two-degree-of-freedom transformation on the closed-loop system, analyzing the nominal stability of the ADRC system based on a double-track method, and obtaining a nominal stability domain of the control parameters; Step 6: within the nominal stability domain obtained in step 4, according to the regularization rule of the ADRC scaling parameters and the demand for comprehensive robustness, obtaining the time constant of the low-pass filter in the compensation channel by establishing a time-delay ADRC open-loop Bode diagram with a monotonously decreasing amplitude curve.

2. The design method of a thermal process with time delay and robustness according to claim 1, characterized in that, In step 1, the transfer function model is as follows: where K is a steady state gain; T is a time constant and T > 0; e -Ls is a time delay element, L is a time delay amount, and s is a Laplace operator.

3. The design method of a thermal process with time delay and robustness according to claim 1, characterized in that, In step 2, a low-order form of the extended state observer MESO is used under the premise of introducing the model information, and is specifically as follows: where: u, y are control variable and controlled variable, respectively, a0=1 / T, b0=K / T are the parameters converted from the transfer function model, z(t) is an auxiliary variable, is the estimated variable of the lumped disturbance signal, ω o is the observer bandwidth; The expression form of the disturbance estimation variable generated by the observer MESO structure in the frequency domain is as follows: The disturbance signal estimated by the observer MESO is introduced into a low-pass filter G f (s) = 1 / (1 + T f s), the disturbance estimate signal after reconstruction by the observer is obtained Under the structure of the observation reconstruction, the overall control expression of the ADRC is as follows: where: r is a setpoint variable, k p is a proportional feedback gain parameter; an additional gain form is used in the setpoint channel, i.e., (k p + a0) r.

4. The design method of a thermal process with time delay and robustness according to claim 1, characterized in that, In step 3, the inertia time-delay model with unit gain is used as the desired closed-loop dynamic: In the formula: T c is the desired closed loop time constant; By formulating the proportional gain setting rule, the closed-loop dynamic of the time-delay ADRC system is shaped into the above-mentioned desired closed-loop dynamic; the reconstructed disturbance expression is brought into the control action, and the closed-loop dynamic of the time-delay ADRC system is as follows: The time delay term e in the denominator of the above equation -Ls Approximating 1-Ls, the closed-loop dynamics can be approximated as... Comparing this equation with the desired closed loop dynamics, if the proportional gain is adjusted to satisfy 1 - k p L = T c (a0+ k p ), then it can be approximated that G cl (s) ≈ e -Ls / 1 + T c s Therefore, the proportional gain setting rule with the desired closed-loop dynamic characteristic is as follows: The observer bandwidth is set to 10 times the closed-loop bandwidth, and the parameters are designed to introduce the desired closed-loop dynamics, with the bandwidth of the desired closed-loop dynamics 1 / T c As a reference, the tuning formula for the observer bandwidth is thus:

5. The design method of a thermal process with time delay and robustness according to claim 1, characterized in that, In step 4, the scaling form of the control parameters of the time-delay ADRC system is as follows: where s', τ, τ c , λ, k' f , λ, k' p represent the scaled Laplacian operator, the model time constant, the desired closed loop time constant, the observation reconstruction filter time constant, the observer bandwidth and the proportional gain, respectively. The scaling control parameter setting rule formula (8), (9) should be changed to: After obtaining the transfer function model of the controlled object, only by adjusting τ c The control parameters can be obtained. The parameter τ c is set to default: τ c = 1 (12).

6. The design method of a thermal process with time delay and robustness according to claim 1, characterized in that, In step 5, based on the parameter scaling rule, the ADRC system is subjected to two-degree-of-freedom transformation, and the equivalent feedback controller and the transfer function of the controlled object are as follows: In the nominal case, the closed loop characteristic equation 1 + G c (s') G p (s') = 0 is: Based on the double trajectory method, the stable region of the adjusting parameter τ c is as follows: where ω * is the solution of the equation * = - tan(ω * ) in (0, π).

7. The design method of a thermal process with time delay and robustness according to claim 1, characterized in that, In step 6, the open-loop Bode diagram of the time-delay ADRC system corresponds to the open-loop transfer function G ol (s') is: In the control system without time delay compensation, the Nyquist curve of the open-loop transfer function of the system only crosses the unit circle once in the nominal stable region of the adjustment parameters, and the crossing point forms the phase margin of the open-loop system and the gain cross-over frequency ω gc ; according to the phase relationship between the crossing point and the critical point, the corresponding maximum time delay increment maxΔl + is represented as: Since the unique crossing point only surrounds the critical point when the time delay increases, only the maximum time delay increment is considered, and the time delay margin under the parameter scaling form is as follows: d m = (0, 1 + maxΔl + ) (19) When the time delay increases and decreases, the crossing point will pass through the critical point, so not only the maximum time delay increment but also the maximum time delay decrement should be considered; the crossing points are arranged in the order from 1, and the corresponding maximum time delay increment and decrement are calculated as follows: In the formula, i is the order number of the crossing point, k is a non-negative integer, if k=0, i=1, indicating that the system only crosses once, and the time delay margin of the system is as follows: d m = (1 - maxΔl - ,1+maxΔl + ) (21) The time constant of the observation reconstruction filter is set as follows to ensure that the performance is not sacrificed too much: The Nyquist curve is converted into the Bode plot. Through the test of different time delay models with scaling parameters, it is obtained that when the time constant of the observation reconstruction filter satisfies τ f ≥ 0.4, for the default adjustment parameter τ c = 1, the open-loop transfer function Bode plot magnitude-frequency characteristics of the control system of the time delay object are ensured to cross the 0dB line only once, i.e. the Nyquist curve crosses the unit circle only once when τ ∈ (0.05, 2). ​ τ f = 0.4 (22) After obtaining the transfer function of the controlled object, the control parameter values are automatically calculated according to the default recommendations described above.

Images