A feedforward compensation active disturbance rejection controller based on a scheduling signal and its design method

Abstract

The present invention discloses a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof, aiming at solving the problem of poor control quality of large-inertia processes during frequent operation under variable working conditions in a large range. The active disturbance rejection controller includes a feedforward controller, a feedback controller, a compensation module and an extended state observer. By introducing a scheduling signal, variable parameter design and real-time adjustment are respectively performed on the feedforward controller, the feedback controller, the compensation module and the extended state observer, and the dynamic model information of the controlled process under variable working conditions is utilized in this process, so that the adaptability of the active disturbance rejection controller to large inertia and variable working conditions can be improved. The control system has a simple structure and a concise tuning method, and has good engineering application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial automation, and particularly to a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof. Background Art

[0002] Active Disturbance Rejection Control (ADRC) is an advanced control method that combines classical PID control with modern control theory. The earliest ADRC is a non-linear controller, which consists of a tracking differentiator, a non-linear combination, and an extended state observer. However, the non-linear ADRC has a complex structure and difficult controller parameter tuning, so the more commonly used one is the linear ADRC. The basic structure of the linear ADRC includes two parts: an Error-based Linear Function (ELF) and an Extended State Observer (ESO). Compared with other advanced control algorithms, the linear ADRC does not depend on the accurate model of the controlled object, and has the advantages of simple structure, convenient tuning, good disturbance rejection performance, and strong robustness. In recent years, it has been applied and developed in the field of industrial process control.

[0003] However, when the linear ADRC is applied to the automatic control of large thermal processes, it mainly faces two problems. One is that when the inertia and lag of the controlled process are large, the observation effect of the ESO becomes poor, resulting in an unsatisfactory control effect of the ADRC. The other is that when the working conditions of the controlled process change frequently in a large range, the control performance of the ADRC designed according to the rated working conditions deteriorates. Patent document CN107703746A proposes to use the linear combination of the derivatives of the set value as the feedforward control quantity of the ADRC, which can improve the tracking ability when the set value changes rapidly. Wang You et al.'s "Design of Linear Active Disturbance Rejection Controller for High-Order Large Inertia Systems" (Control and Decision, March 2022) proposes an ADRC control structure and parameter tuning method that uses model information for compensation, which improves the control effect of the ADRC on large inertia processes. However, for solving the problems existing in the above thermal process control, that is, when the inertia of the controlled process is large and the dynamic characteristics change significantly with the working conditions, the improvement of the control effect of the above methods is limited. Summary of the Invention

[0004] The present invention provides a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof, aiming to solve the problem of poor control quality of large-inertia processes during frequent operation under wide-range variable working conditions. By introducing a scheduling signal and utilizing the dynamic model information of the controlled process under variable working conditions, variable parameter design and real-time adjustment are respectively performed on the feedforward controller, feedback controller, compensation module, and extended state observer, which can improve the adaptability of the active disturbance rejection controller to large inertia and variable working conditions.

[0005] The present invention is realized through the following technical solutions.

[0006] One aspect of the present invention provides a feedforward compensation active disturbance rejection controller based on a scheduling signal, including a feedforward controller, a feedback controller, a compensation module, and an extended state observer.

[0007] The feedforward controller is: u Q (t) = F1(Q(t)), where u Q (t) is the feedforward control quantity, Q(t) is the scheduling signal, and F1(·) is the feedforward function.

[0008] The feedback controller is: where u C (t) is the output of the feedback controller, r(t) is the set value, z i (t) (i = 1, 2,..., m + 1) is the output of the extended state observer, and b0(t) are adjustable parameters and change with the change of the scheduling signal Q(t).

[0009] The output u C (t) of the feedback controller can be used as the input of the compensation module.

[0010] The compensation module is: u TF (t) = F2(u C (t), T F2 (t), p), where u TF (t) is the output of the compensation module, F2(·) is the compensation function, T F2 (t) and p are adjustable parameters, and T F2 (t) changes with the change of the scheduling signal Q(t).

[0011] The output u TF (t) of the compensation module can be used as the input of the extended state observer.

[0012] The output of the feedback controller and the output of the feedforward controller constitute the control law of the active disturbance rejection controller, which is: u(t) = u Q (t) + u C(t), where u(t) is the control quantity.

[0013] In the above technical solution, the extended state observer is:

[0014]

[0015] where y(t) is the controlled quantity, and β i (t) (i = 1, 2,..., m + 1) are the adjustable parameters of the extended state observer, which change with the scheduling signal Q(t), and b0(t) is the adjustable parameter of the feedback controller.

[0016] In the above technical solution, the transfer function of the compensation function (i.e., the frequency domain form of the compensation function) is:

[0017]

[0018] where F2(s) is the transfer function of the compensation function, U TF (s) and U C (s) are the Laplace transforms of the outputs u TF (t) and u C (t) of the compensation module and the feedback controller respectively, p is the order of the transfer function of the compensation function, T F2 (t) and p are both adjustable parameters, and the value of T F2 (t) changes with the scheduling signal Q(t).

[0019] Another aspect of the present invention provides a design method for a feedforward compensation active disturbance rejection controller based on a scheduling signal, including the following steps:

[0020] S1. Select the scheduling signal Q(t) according to the variable working condition characteristics of the controlled process, and obtain the functional relationship between the scheduling signal Q(t) and the feedforward control quantity through design calculation or on-site experiment;

[0021] S2. Find the inverse function according to the functional relationship between the scheduling signal Q(t) and the feedforward control quantity to obtain the feedforward function F1(·); calculate the feedforward control quantity u Q (t) = F1(Q(t)) based on the feedforward function and the scheduling signal;

[0022] S3. Obtain the variable working condition dynamic information of the controlled process;

[0023] S4. Design the compensation module and its compensation function F2(·), and use the variable working condition dynamic information obtained in S3 to obtain the output u TF (t) = F2(u C (t), T F2 (t), p) of the compensation module, where F2(·) is the compensation function, uC (t) is the output of the feedback controller, T F2 (t) and p are adjustable parameters;

[0024] Design an extended state observer. The output of the compensation module can be used as the input of the extended state observer to obtain the output z of the extended state observer i (t) (i = 1, 2, …, m + 1);

[0025] S6. Design a feedback controller and calculate the feedback control quantity u C (t):

[0026] where r(t) is the set value, and b0(t) are adjustable parameters;

[0027] S7. Form the control law of the active disturbance rejection controller, and obtain the control quantity of the active disturbance rejection controller through the feedforward control quantity and the feedback control quantity:

[0028] u(t) = u Q (t) + u C (t).

[0029] In the above technical solution, the selection of the scheduling signal Q(t) simultaneously satisfies the following two conditions:

[0030] (1) It can characterize the variable working condition characteristics of the controlled process;

[0031] (2) It has a designable functional relationship with the feedforward control quantity.

[0032] According to one embodiment, the method for obtaining the variable working condition dynamic information of the controlled process in step S3 includes:

[0033] According to the nonlinearity of the controlled process, divide the variable working condition range of the controlled process into q segments, obtain the dynamic information of each segment and represent it by the transfer function (high-order linear function) of the controlled process as:

[0034]

[0035] where s is the Laplace operator, Y(s) and U(s) are the Laplace transforms of y(t) and u(t) respectively, the subscript γ2 (γ2 = 1, 2, …, q) is the working condition number, G p,γ2 (s) is the transfer function of the controlled process under the working condition γ2, K γ2 is the system gain under the working condition γ2, T γ2 is the time constant under the working condition γ2, and n is the order of the transfer function of the controlled process.

[0036] In the above technical solution, the transfer function of the compensation function is designed as:

[0037]

[0038] where F2(s) is the transfer function of the compensation function F2(·), U TF (s) and U C (s) are the Laplace transforms of u TF (t) and u C (t) respectively, and T F2 (t) and p are adjustable parameters.

[0039] In the above technical solution, the adjustable parameter T F2 (t) is designed as:

[0040] T F2 (t) = γ (t) = F Tγ (Q(t), {Q r2}, {T γ2}), (γ2 = 1, 2,..., q),

[0041] where {T γ2} is the time constant under each working condition in the dynamic information of variable working conditions, {Q r2} is the scheduling signal value under each working condition, Q(t) is the scheduling signal, and F Tγ (·) is a linear or nonlinear function; T γ (t) is the output of the function, representing the time constant corresponding to the scheduling signal Q(t).

[0042] In the above technical solution, the adjustable parameter p of the compensation function is designed as: p = n - m. Where n is the order of the transfer function of the controlled process, and m is the order of the feedback controller.

[0043] In the above technical solution, the time-domain form of the output u TF (t) of the compensation module is:

[0044]

[0045] where ΔT is the calculation period and k is the discrete time sequence.

[0046] In the above technical solution, the extended state observer is designed as:

[0047]

[0048] where y(t) is the controlled quantity, β i(t) (i = 1, 2, …, m + 1) are adjustable parameters of the extended state observer, which change with the scheduling signal Q(t), and b0(t) is an adjustable parameter of the feedback controller.

[0049] In the above technical solution, the adjustable parameter β of the extended state observer i (t) (i = 1, 2, …, m + 1) can be selected in the following manner:

[0050]

[0051] where ω o (t) is the bandwidth of the state observer, where T γ (t) is the time constant corresponding to the scheduling signal Q(t).

[0052] In the above technical solution, the adjustable parameter of the feedback controller is designed as:

[0053]

[0054] where m is the order of the feedback controller, ω c (t) is the bandwidth of the feedback controller, and T γ (t) changes with the scheduling signal Q(t).

[0055] In the above technical solution, the adjustable parameter b0(t) of the feedback controller is designed as:

[0056]

[0057] where T γ (t) and K γ (t) both change with the scheduling signal Q(t).

[0058] where K γ (t) is calculated according to the following formula:

[0059] K γ (t) = F Kγ (Q(t), {Q r2}, {K γ2},

[0060] where {K γ2} are the time constants under each working condition in the dynamic information of the controlled process under variable working conditions, {Q r2} are the scheduling signal values under each working condition, Q(t) is the scheduling signal, and F Kγ (·) is a linear or nonlinear function; K γ (t) is the output of the function, representing the system gain corresponding to the scheduling signal Q(t).

[0061] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0062] For a large-inertia controlled process with frequent variable operating conditions, the present invention proposes a feedforward compensation active disturbance rejection controller based on a scheduling signal and its design method. The adjustable parameters of the feedforward controller, feedback controller, compensation module, and extended state observer are adjusted in real time using the scheduling signal, and the dynamic model information of the controlled process under variable operating conditions is utilized to improve the adaptability of the active disturbance rejection control to large inertia and variable operating conditions. The control system has a simple structure and a concise tuning method, and has good engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings.

[0064] Figure 1 It is a schematic structural diagram of the feedforward compensation active disturbance rejection controller based on a scheduling signal according to an embodiment of the present invention.

[0065] Figure 2 It is a schematic diagram for comparing the controlled variable curves under rated operating conditions provided in Embodiment 1 of the present invention.

[0066] Figure 3 It is a schematic diagram for comparing the control variable curves under rated operating conditions provided in Embodiment 1 of the present invention.

[0067] Figure 4 It is a schematic diagram for comparing the controlled variable curves under variable operating conditions provided in Embodiment 1 of the present invention.

[0068] Figure 5 It is a schematic diagram for comparing the control variable curves under variable operating conditions provided in Embodiment 1 of the present invention.

[0069] Figure 6 It is a schematic diagram for comparing the controlled variable curves during load increase and decrease provided in Embodiment 2 of the present invention.

[0070] Figure 7 It is a schematic diagram for comparing the control variable curves during load increase and decrease provided in Embodiment 2 of the present invention.

[0071] In the figure:

[0072] r(t) is the set value, y(t) is the controlled variable, u c (t) is the feedback control variable, u Q (t) is the feedforward control variable, u(t) is the control variable, u TF(t) is the output of the compensation module, and z1(t) ~ z m+1 (t) is the output of the extended state observer, and Q(t) is the scheduling signal. Specific implementation mode

[0073] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0074] In addition, terms such as "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. In the description of the following embodiments, "a plurality" means more than two, unless otherwise specifically defined.

[0075] A feedforward compensation active disturbance rejection controller based on a scheduling signal provided by the present invention is applicable to the active disturbance rejection control of a controlled process (or a controlled object), and includes a feedforward controller, a feedback controller, a compensation module, and an extended state observer. The control system (referred to as the system) of the present invention includes the active disturbance rejection controller and the controlled process to which it is applied. As Figure 1 shown, to solve the problem of poor control quality when a large-inertia process operates under frequent variable working conditions in a large range, in the design of the active disturbance rejection controller of the present invention, a scheduling signal is introduced and the dynamic model information of the controlled process under variable working conditions is utilized to perform variable parameter design and real-time adjustment on the feedforward controller, the feedback controller, the compensation module, and the extended state observer respectively, improving the adaptability of the active disturbance rejection controller to large inertia and variable working conditions.

[0076] The control law of the active disturbance rejection controller constructed by the present invention, that is, the control quantity of the active disturbance rejection controller is obtained through the feedforward control quantity and the feedback control quantity: u(t) = u Q (t) + u C (t).

[0077] S1. Select the scheduling signal

[0078] Select the scheduling signal Q(t) according to the variable working condition characteristics of the controlled process, and obtain the functional relationship between the scheduling signal Q(t) and the feedforward control quantity through design calculation or on-site experiment.

[0079] The scheduling signal Q(t) can be selected according to the physical working mechanism of the controlled process, and the following two conditions need to be satisfied simultaneously:

[0080] (1) It can characterize the variable operating condition characteristics of the controlled process, that is, it can characterize the expected operating conditions during the variable load process of the controlled process. For example, the power generation load command of a thermal power unit.

[0081] (2) It has a designable functional relationship with the feedforward control quantity. For example, when taking the power generation load command of a thermal power unit as the scheduling signal and the basic coal feeding quantity as the preset feedforward control quantity, the functional relationship between the power generation load command and the basic coal feeding quantity can be obtained in advance through design calculations or on-site experiments.

[0082] S2. Design the feedforward function and the feedforward controller

[0083] The feedforward function F1(·) can be a linear function or a non-linear function, and is designed according to the physical relationship between the feedforward control quantity and the scheduling signal. The role of the feedforward controller is that when the scheduling signal changes and thus the expected operating conditions of the controlled process change, the control quantity can change rapidly according to the change of the scheduling signal Q(t), accelerating the response process of the control system.

[0084] The feedforward control quantity of the feedforward controller is: u Q (t) = F1(Q(t)).

[0085] The feedforward function F1(·) can be obtained by finding the inverse function according to the functional relationship between the scheduling signal Q(t) and the feedforward control quantity.

[0086] According to what is described in the above step S1, the functional relationship between the feedforward control quantity and the scheduling signal within the variable operating condition range can be obtained through design calculations or on-site experiments, that is, the feedforward function F1(·) can be determined by finding the inverse function. For example, if Q(t) = F1 f (u(t)) is obtained from a steady-state experiment, then the feedforward function F1(·) can be designed, and the feedforward control quantity (the output of the feedforward controller) can be obtained, where Q(t) is the scheduling signal, and k f is an adjustable parameter representing the strength of the feedforward effect.

[0087] S3. Obtain the variable operating condition dynamic information of the controlled process

[0088] According to the non-linearity of the controlled process, its variable operating condition range is divided into q segments, and the dynamic information of each segment is represented by a linear high-order transfer function, that is, the transfer function of the controlled process, which is:

[0089]

[0090] where s is the Laplace operator, Y(s) and U(s) are the Laplace transforms of y(t) and u(t) respectively, the subscript γ2 (γ2 = 1, 2,..., q) is the operating condition number, and F p,γ2(s) is the controlled process transfer function of the controlled process under operating condition γ2, K γ2 is the system gain under operating condition γ2, T γ2 is the time constant under operating condition γ2, and n is the order of the controlled process transfer function.

[0091] S4, design the compensation module and compensation function

[0092] The role of the compensation module and compensation function is to generate a dynamic compensation effect that matches the dynamic characteristics of the controlled process and send it into the extended state observer when the system operating condition changes and the scheduling signal changes, reducing the state observation error and improving the control effect of the controller on the large inertia process.

[0093] The design of the compensation function F2(·) is based on the variable operating condition dynamic information of the controlled process obtained above and can be expressed in frequency domain or time domain form.

[0094] The frequency domain form of the compensation function, i.e., the transfer function, is:

[0095]

[0096] where F2(s) is the transfer function of the compensation function, U TF (s) and U C (s) are the Laplace transforms of u TF (t) and u C (t) respectively, and T F2 (t) and p are adjustable parameters.

[0097] The output u TF (t) of the compensation module in time domain form is:

[0098]

[0099] where ΔT is the calculation period and k is the discrete time sequence.

[0100] The adjustable parameters in the compensation function are T F2 (t) and p. In the present invention, the selection method is as follows:

[0101] T F2 (t) varies with the scheduling signal Q(t) with the aim of matching the variation law of the dynamic characteristics of the controlled process with the operating condition, thereby reducing the order of the equivalent observed object of the extended state observer and improving the state observation effect. Therefore, the real-time value of T F2 (t) is determined according to the variable operating condition dynamic information of the controlled process and the scheduling signal, i.e.:

[0102] T F2 (t) = T γ (t) = F Tγ (Q(t),{Qr2 ,{T γ2}), (γ2 = 1, 2, …, q)

[0103] Among them, {T γ2} is the time constant under each working condition in the variable working condition dynamic information, {Q r2} is the scheduling signal value under each working condition, Q(t) is the scheduling signal, F Tγ (·) is a linear or nonlinear function, T γ (t) is the output of the function, representing the time constant corresponding to the scheduling signal Q(t).

[0104] The selection of the adjustable parameter p depends on the order of the active disturbance rejection controller adopted. If the order of the controlled process is n and the order of the active disturbance rejection controller is m, then the order of the extended state observer is m + 1, and the order p of the compensation module should be taken as: p = n - m. In this way of selection, the states not included in the compensation module can all be observed by the extended state observer.

[0105] S5. Design the extended state observer

[0106] The time domain form of the extended state observer is as follows:

[0107]

[0108] β i (t) (i = 1, 2, …, m + 1) are the adjustable parameters of the extended state observer, and b0(t) is the adjustable parameter of the feedback controller, both of which change with the scheduling signal Q(t).

[0109] In the programmable control system, the extended state observer is discretized by the Euler method, and its expression is as follows:

[0110]

[0111] Among them, ΔT represents the calculation period, and k represents the discrete time sequence.

[0112] The adjustable parameters β i (t) (i = 1, 2, …, m + 1) are selected in the following way:

[0113]

[0114] Among them, ω o (t) is the bandwidth of the extended state observer, Among them, T γ (t) is the time constant corresponding to the scheduling signal Q(t).

[0115] S6. Design the feedback controller

[0116] The feedback control quantity is calculated by the feedback controller based on the set value and the output of the extended state observer:

[0117]

[0118] where u C (t) is the feedback control quantity, r(t) is the set value of the control system, z i (t) (i = 1, 2, …, m + 1) is the output of the said extended state observer, and b0(t) are adjustable parameters of the feedback controller, both of which vary with the scheduling signal Q(t). Among them can be calculated according to the bandwidth parameterization method based on the controller bandwidth ω c (t), or can be determined by an optimization algorithm or on-site tests. b0(t) is an estimated value of the high-order gain of the controlled process and varies with the scheduling signal Q(t). The role of the feedback controller is that when the operating condition changes or a disturbance occurs, the feedback controller can adjust the control quantity according to the set value and the output of the extended state observer, cancel the observed total disturbance and finally eliminate the control deviation.

[0119] The adjustable parameters of the said feedback controller are designed as:

[0120]

[0121] where m is the order of the feedback controller, ω c (t) is the feedback controller bandwidth, T γ (t) varies with the scheduling signal Q(t).

[0122] The adjustable parameter b0(t) of the said feedback controller is designed as:

[0123]

[0124] where T γ (t) and K γ (t) both vary with the scheduling signal Q(t).

[0125] K γ (t) is calculated according to the following formula:

[0126] K γ (t) = K Kγ (Q(t), {Q r2}, {K γ2})

[0127] where {K γ2} are the time constants under each operating condition in the dynamic information of the controlled process under variable operating conditions, {Q r2} is the scheduling signal value under each working condition, Q(t) is the scheduling signal, and F Kγ (·) is a linear or non-linear function, and K γ (t) is the output of the function, representing the system gain corresponding to the scheduling signal Q(t).

[0128] For simplicity of use, the function F Kγ (·) and F Tγ (·) can be taken as linear interpolation functions.

[0129] Then, the control quantity of the feedforward compensation active disturbance rejection controller based on the scheduling signal is the sum of the feedforward control quantity and the feedback control quantity, that is:

[0130] u(t) = u Q (t) + u C (t).

[0131] The following uses two simulation examples as embodiments to illustrate the control effect of the present invention.

[0132] Embodiment 1: Under the rated working condition, the transfer function of the main steam pressure controlled object of a coal-fired unit is:

[0133]

[0134] When the working condition changes, the time constant T varies between 30 and 50.

[0135] To illustrate the control effect of the present invention, first, the method of the present invention is adopted and k f = 0 is used for design, and it is compared with the conventional ADRC, the ADRC with set value feedforward in Comparative Example 1 (Patent Document CN107703746A), and the compensated ADRC in Comparative Example 2 (Wang You et al., Design of Linear Active Disturbance Rejection Controller for High-Order Large Inertia Systems, Control and Decision, March 3, 2022, https: / / doi.org / 10.13195 / j.kzyjc.2021.1576).

[0136] Take the order of the feedback controller as m = 2. According to the design method of the present invention, the order of the extended state observer is m + 1 = 3, and the order of the compensation function is n - m = 3. Under the rated working condition, take the time constant T F2 of the compensation function as 50, the controller bandwidth as 0.02, the extended state observer bandwidth as 1, and the control parameters as b0 = 1.12×10 -5 , β1 = 3, β2 = 3, β3 = 1, k1 = 4×10 -4 , k2 = 0.04. Under the rated working condition, design the traditional ADRC and the ADRC in Comparative Example 1, with the controller bandwidth of 0.02, the extended state observer bandwidth of 0.2, and the control parameter b0 = 2.0158×10-4 , β1 = 0.6, β2 = 0.12, β3 = 0.008, k1 = 4×10 -4 , k2 = 0.04. Simulate the control effects of the above three methods.

[0137] Figure 2 are the setpoint step response and disturbance response curves under rated conditions. At 1000 seconds, a unit step change occurs in the setpoint, and at 5000 seconds, a step disturbance with an amplitude of 0.5 occurs in the input of the controlled process. It can be seen from the curves that when there is a step change in the setpoint, the compensated ADRC designed by the present invention can reach the setpoint faster and without overshoot compared with the conventional ADRC and the ADRC with setpoint feedforward in Comparative Example 1. When a disturbance occurs in the input of the controlled process, the ADRC designed by the present invention can eliminate the influence of the disturbance faster, and at the same time, the dynamic deviation is also the smallest.

[0138] Figure 3 is the curve of the control quantity change under rated conditions. It can be seen that the control quantity change of the compensated ADRC designed by the present invention is faster and smoother. The control quantity of the ADRC in Comparative Example 1 fluctuates too much instantaneously during the setpoint step response, while the control quantity of the conventional ADRC is significantly slower.

[0139] Figure 4 are the comparison curves of the setpoint step response and disturbance response when the working condition changes to T = 30. Here, a second-order compensated ADRC of Comparative Example 2 is added, and its parameters are the same as those of the ADRC of the present invention under rated conditions, but do not change with the working condition. It can be seen that due to the control parameters of the variable-parameter ADRC with compensation designed by the present invention changing with the working condition, the controlled quantity can reach the new setpoint faster and more smoothly and without overshoot; the setpoint tracking of the ADRC with compensation in Comparative Example 2 is slightly slower, and the response speeds of the ADRC with setpoint feedforward in Comparative Example 1 and the conventional ADRC are the slowest. At the same time, when a disturbance occurs, the disturbance rejection capabilities of the ADRC of the present invention and the ADRC of Comparative Example 2 are comparable, and both can eliminate the influence of the disturbance faster, and at the same time, the dynamic deviation is also smaller.

[0140] Figure 5 is the comparison curve of the control quantity when the working condition changes to T = 30. It can be seen that the change of the control quantity of the ADRC of the present invention is both rapid and smooth compared with the other three methods, that is, it will not cause an impact on the actuator and can act in time, showing good engineering applicability.

[0141] It should be noted that in the above simulations, the second-order compensation active disturbance rejection controller (ADRC) designed by the present invention based on the scheduling signal does not set a feedforward function. Therefore, the curve comparison reflects the control effect of the compensation ADRC based on the scheduling signal. It can be seen from the simulation comparison results that the ADRC designed by the present invention is faster, more stable, and has no overshoot in setpoint tracking compared with the compensation ADRC in Comparative Example 2, the conventional ADRC, and the ADRC with setpoint feedforward in Comparative Example 1. It can also eliminate the influence of disturbances faster and has a smaller dynamic deviation, showing the excellent performance of the method of the present invention.

[0142] Embodiment 2: For a main steam pressure loop of a coal-fired unit, the controlled variable is the main steam pressure, the control variable is the coal feed rate, and the transfer function is in the form of a high-order inertia:

[0143]

[0144] where n = 5. The load, coal feed rate, main steam pressure under each steady-state condition, and the model parameters K γ2 and T γ2 of the controlled process under this condition are shown in the following table.

[0145] Load 0 99 165 250 330 Coal feeding rate 70 70 115 168 220 Main steam pressure 0 9.5 13 16.5 19 <![CDATA[K γ2 > 0.1357 0.1357 0.1130 0.0982 0.0864 <![CDATA[T γ2 > 400 300 250 220 200

[0146] To illustrate the control effect of the present invention, a feedforward compensation active disturbance rejection controller based on the scheduling signal is designed according to the method of the present invention, and the order of the controller is taken as m = 1. Taking the load command as the scheduling signal Q(t), referring to the model information and steady state under each condition, taking k f = 0.5, the feedforward controller is designed as follows:

[0147]

[0148] According to the variable-condition dynamic information of the controlled process, the compensation function is determined to be a 4th-order inertia link, and its form is as follows:

[0149]

[0150] where the time constant of the compensation function changes with the scheduling signal as follows:

[0151]

[0152] The extended state observer is designed to be second-order, and its observer bandwidth ω o (t) changes with the scheduling signal:

[0153]

[0154] The adjustable parameters of the extended state observer change with ω o (t):

[0155]

[0156] The bandwidth ω of the feedback controller c (t) and the adjustable parameters vary with the scheduling signal as follows:

[0157]

[0158] k p (t) = ω c (t)

[0159]

[0160] The simulation calculation period is ΔT = 0.2 s. The working condition value first decreases in segments and then increases in segments, with a change rate of 0.055 per second, and the set value follows the change of the working condition. At the same time, to compare and illustrate the beneficial effects of the present invention, a compensation ADRC based on the scheduling signal with k f = 0 (i.e., without feedforward) and a compensation ADRC without the scheduling signal in Comparative Example 2 are also designed, and the controller order is taken as 1. When the load changes, the curves of the controlled variable and the control variable obtained by simulation are respectively shown in Figure 6 and Figure 7 .

[0161] From Figure 6 it can be seen that: The feedforward compensation ADRC based on the scheduling signal of the present invention can quickly and smoothly track the change of the set value in both the high load section, the medium load section and the low load section, and the adjustment time is significantly faster than the other two control methods. When k f = 0, the control parameters of the compensation ADRC based on the scheduling signal without feedforward can change with the load, so it shows a relatively consistent and stable control effect under different working conditions. However, since there is no feedforward controller and it relies entirely on the feedback action for adjustment, the response speed is significantly slower than that of the feedforward compensation auto-disturbance rejection controller based on the scheduling signal. For the compensation ADRC without the scheduling signal in Comparative Example 2, the controlled variable can relatively smoothly track the change of the set value in the high load section, but due to the absence of a signal scheduling mechanism and the control parameters not changing with the working condition, there is a significantly larger overshoot in the low load section. Based on the above comparison results, it can be seen that when the working condition changes greatly, the feedforward compensation ADRC designed by the present invention based on the scheduling signal can show a relatively consistent and satisfactory control effect under each load, demonstrating excellent working condition adaptability and excellent control effect.

[0162] From Figure 7 the curve of the control variable change, it can be seen that the control variable of the ADRC of the present invention is also fast and stable under each working condition, so it has very good engineering application prospects.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A feedforward compensation active disturbance rejection controller based on a scheduling signal, which can be applied to the automatic control of a thermal process, is characterized in that It includes a feedforward controller, a feedback controller, a compensation module, and an extended state observer; The feedforward controller is: u Q (t) = F1(Q(t)), where u Q (t) is the feedforward control quantity, Q(t) is the scheduling signal, and F1(·) is the feedforward function; The selection of the scheduling signal Q(t) simultaneously satisfies the following two conditions: (1) It can characterize the variable operating condition characteristics of the controlled process; (2) It has a designable functional relationship with the feedforward control quantity; The feedback controller is as follows: where u C (t) is the output of the feedback controller, r(t) is the setpoint, and z i (t) (i = 1, 2, …, m + 1) are the outputs of the extended state observer, and b0(t) are adjustable parameters that vary with the scheduling signal Q(t); m is the order of the feedback controller; The compensation module is: u TF (t) = F2(u C (t), T F2 (t), p), where u TF (t) is the output of the compensation module, F2(·) is the compensation function, u C (t) is the output of the feedback controller, T F2 (t) and p are adjustable parameters, T F2 (t) changes with the scheduling signal Q(t); the output u TF (t) of the compensation module is used as the input of the extended state observer; The output of the feedback controller and the output of the feedforward controller constitute the control law of the active disturbance rejection controller, which is: u(t) = u Q (t) + u C (t), where u(t) is the control variable.

2. The active disturbance rejection controller according to claim 1, characterized in that, The extended state observer is: where y(t) is the controlled variable, and β i (t) (i = 1, 2, …, m + 1) are the adjustable parameters of the extended state observer, which change with the scheduling signal Q(t), and b0(t) is the adjustable parameter.

3. The active disturbance rejection controller according to claim 1, characterized in that, The transfer function of the compensation function is: where s is the Laplace operator; F2(s) is the transfer function of the compensation function, U TF (s) and U C (s) are the Laplace transforms of the outputs u TF (t) and u C (t) of the compensation module and the feedback controller respectively, T F2 (t) and p are adjustable parameters, and the value of the said T F2 (t) varies with the scheduling signal Q(t).

4. A design method of a feedforward compensation active disturbance rejection controller based on a scheduling signal as described in any one of claims 1 to 3, characterized in that, It includes: S1, Select the scheduling signal Q(t) according to the variable operating condition characteristics of the controlled process, and obtain the functional relationship between the scheduling signal Q(t) and the feedforward control quantity through design calculation or on-site experiment; S2. Obtain the inverse function according to the functional relationship between the scheduling signal Q(t) and the feedforward control quantity, and get the feedforward function F1(·); calculate the feedforward control quantity u Q (t) = F1(Q(t)); S3, Obtain the variable operating condition dynamic information of the controlled process; S4. Design a compensation module and a compensation function F2(·), and use the variable-condition dynamic information obtained in S3 to obtain the output u of the compensation module TF (t) = F2(u C (t), T F2 (t), p), where F2(·) is the compensation function, and u C (t) is the output of the feedback controller, and T F2 (t) and p are adjustable parameters; S5. Design an extended state observer, where the output of the compensation module can be used as the input of the extended state observer to obtain the output z of the extended state observer i (t) (i = 1, 2, …, m + 1); m is the order of the feedback controller; S6. Design a feedback controller to calculate the feedback control quantity u C (t): where r(t) is the set value, and b0(t) are adjustable parameters; S7, Construct the control law of the active disturbance rejection controller, and obtain the control quantity of the active disturbance rejection controller through the feedforward control quantity and the feedback control quantity: u(t) = u q (t) + u C (t).

5. The design method according to claim 4, characterized in that The selection of the scheduling signal Q(t) simultaneously satisfies the following two conditions: (1) It can characterize the variable operating condition characteristics of the controlled process; (2) It has a designable functional relationship with the feedforward control quantity.

6. The design method according to claim 4, characterized in that The method for obtaining the variable operating condition dynamic information of the controlled process includes: According to the nonlinearity of the controlled process, divide the variable operating condition range of the controlled process into q segments, obtain the dynamic information of each segment and represent it through the transfer function of the controlled process as: where s is the Laplace operator, Y(s) and U(s) are the Laplace transforms of y(t) and u(t) respectively, the subscript γ2 (γ2 = 1, 2, …, q) is the operating condition number, and G p,γ2 (s) is the transfer function of the controlled process under the operating condition γ2, and K γ2 is the system gain under the operating condition γ2, T γ2 is the time constant under the operating condition γ2, and n is the order.

7. The design method according to claim 4, characterized in that The transfer function of the compensation function is: Among them, F2(s) is the transfer function of the compensation function F2(·), U TF (s) and U C (s) are the Laplace transforms of u TF (t) and u C (t) respectively, and T F2 (t) and p are adjustable parameters.

8. The design method according to claim 4, characterized in that, The output u TF (t) in the time domain is as follows: Where, ΔT is the calculation period, k is the discrete time sequence; p is an adjustable parameter.

9. The design method according to claim 4, characterized in that, The extended state observer is designed as: where y(t) is the controlled variable, and β i (t) (i = 1, 2, … m + 1) are adjustable parameters that change with the scheduling signal Q(t), and b0(t) is an adjustable parameter.

10. The design method according to claim 4, wherein The adjustable parameters of the feedback controller are as follows: where m is the order of the feedback controller, and t c (t) is the bandwidth of the feedback controller, and T γ (t) varies with the scheduling signal Q(t).

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