Improved active-disturbance-rejection control method based on pre-compensation and quantification parameter setting

Abstract

The invention provides an improved active-disturbance-rejection control method based on pre-compensation and quantitative parameter setting, and the method comprises the steps: designing a pre-compensation structure, enabling the designed pre-compensation structure and an original high-order inertial system to be equivalent to a new high-order inertial system, and designing an expected dynamic equation of a closed-loop system; based on the current value output by the new high-order inertial system, obtaining a compensation value of the next calculation step sequence of the new high-order inertial system through a compensation algorithm; obtaining the tracking values of the next two calculation step sequence values of the output of the new high-order inertial system and the received total disturbance through an extended state observer algorithm; obtaining the next three calculation step sequence values of the improved active-disturbance-rejection control algorithm based on pre-compensation through a control law algorithm; determining a dynamic equation of a closed-loop system, and quantitatively calculating a parameter setting formula; updating a quantitative calculation parameter setting formula; and substituting the parameters obtained by quantitative calculation into the control loop to obtain the next four calculation step sequence numerical values of the updated control quantity, thereby realizing the control quantity adjustment of the closed-loop system.

Description

Technical Field

[0001] The invention relates to the field of industrial control, and in particular to an improved auto-disturbance rejection control method based on pre-compensation and quantitative parameter setting. Background Art

[0002] The ADRC algorithm has been widely used and paid attention to due to its simple structure, tracking and anti-interference performance, strong robustness, etc. The ADRC algorithm, especially the first-order ADRC algorithm, has been successfully applied in aerospace systems, motor systems, microgrid systems and robotic systems.

[0003] However, in typical industrial process control such as chemical process and thermal power generation process, there is a kind of large lag process, such as denitrification system and main steam pressure system in thermal power generation, which are generally described by high-order inertial system. Where s, K, T and n represent the differential operator, the gain of the high-order inertial system, the time constant of the high-order inertial system, and the order of the high-order inertial system, respectively, and n≥3, Y(s) and U(s) are the output and input of the high-order inertial system, respectively; taking the denitrification system as an example, the meanings of the parameters in the above formula are: the output Y(s) is the output value of the nitrogen oxide concentration of the denitrification system, the input U(s) is the ammonia injection amount of the denitrification system, the gain coefficient K refers to the amplification factor of the high-order system on the input value, and the input value is the change in the nitrogen oxide concentration of the denitrification system corresponding to 1 ton of ammonia injection, and the time constant T refers to the time required for the system response to reach 63.2% of the steady-state value.

[0004] For the above high-order inertial system, the Chinese patent application with publication number CN108287466A proposes an improved automatic disturbance rejection control algorithm and a standard automatic disturbance rejection control algorithm. The process is as follows: Figure 1 As shown: the actual controlled object is described by a high-order system with a first-order inertia link in series; the input value of the previous calculation step of the high-order system is compensated by a compensation algorithm to obtain the compensation value of the current calculation step; the output value of the current calculation step of the high-order system and the compensation value of the current calculation step are subjected to ESO calculation to obtain the tracking value of the output value of the next calculation step of the high-order system and the tracking value of the first-order derivative of the output value, and then the input values ​​of the next two calculation steps of the high-order system are obtained, and at the same time, the high-order system adjusts the change amount of the actuator in real time according to the calculation results. Although this invention can better balance the tracking ability and anti-interference ability of the closed-loop system and has good control quality, it still has the following problems:

[0005] 1) Parameter tuning relies on trial and error, and there is a lack of quantitative parameter tuning methods that take into account both tracking and anti-interference performance while ensuring robustness.

[0006] 2) When the controlled object is a high-order inertial system, there is still room for improvement in the control effect of the closed-loop system. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide an improved auto-disturbance rejection control method based on pre-compensation and quantitative parameter tuning for a class of high-order inertial industrial systems. By designing the expected dynamic equation of the closed-loop system for the new controlled object after the pre-compensation structure is compensated, the parameters of the proposed improved auto-disturbance rejection control algorithm based on pre-compensation can be quantitatively calculated, and the control effect of the closed-loop system after tuning is ideal, providing support for the wide application of the improved auto-disturbance rejection control algorithm based on pre-compensation in solving a class of high-order inertial industrial systems.

[0008] The first aspect of the present invention provides an improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting, comprising the following steps:

[0009] (1) A class of actual industrial systems is described using a high-order inertial system; a pre-compensation structure is designed, and the designed pre-compensation structure and the original high-order inertial system are equivalent to a new high-order inertial system; the expected dynamic equations of the closed-loop system are designed for the equivalent new high-order inertial system;

[0010] (2) Based on the current value of the output of the equivalent new high-order inertial system, compensation is performed through a compensation algorithm to obtain a compensation value of the next calculation step of the new high-order inertial system;

[0011] Through the extended state observer algorithm, the equivalent new high-order inertial system output and the tracking values ​​of the next two calculation step values ​​of the total disturbance are obtained;

[0012] The numerical values ​​of the next three calculation steps of the improved active disturbance rejection control algorithm based on precompensation are obtained through the control law algorithm;

[0013] (3) Approximate the partial transfer function of the improved active disturbance rejection control algorithm based on precompensation as an integral link; determine the dynamic equation of the closed-loop system, and quantitatively calculate the parameter setting formula of the improved active disturbance rejection control algorithm based on precompensation;

[0014] (4) adjusting the relationship between the gain amplification factor after compensation and the corresponding changed parameters through linear fitting, and updating the quantitative calculation parameter setting formula of the improved active disturbance rejection control algorithm based on pre-compensation;

[0015] (5) By substituting the parameters obtained by quantitative calculation into the control loop, the values ​​of the next four calculation steps of the updated control quantity are obtained, and the control quantity of the closed-loop system is adjusted, thereby achieving the adjustment of the output of the controlled object.

[0016] Based on the above, the mathematical expression for describing a type of controlled actual industrial system using a high-order inertial system is:

[0017]

[0018] Wherein, the output Y(s) and input U(s) of the high-order inertial system are represented by y(k) and u(k) in each calculation step, k represents the calculation step, s, K, T and n represent the differential operator, the gain of the high-order inertial system, the time constant of the high-order inertial system, and the order of the high-order inertial system, respectively, and n≥3;

[0019] For the above-mentioned actual industrial system, the mathematical expression of the designed pre-compensation structure is:

[0020]

[0021] Among them, T p is the time constant of the compensated high-order inertial system, and T p ∈[0.3,0.5]T;

[0022] The combination of the pre-compensation structure and the original high-order inertial system is equivalent to the expression of the new high-order inertial system:

[0023]

[0024] The expected dynamic equation of the closed-loop system designed for the equivalent new high-order inertial system is:

[0025]

[0026] Among them, G d (s) is the transfer function of the expected dynamic equation of the closed-loop system, λ is the adjustable factor of the expected dynamic equation, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves. The value range of λ is [0.5,1.5].

[0027] Based on the above, step (2) is:

[0028] The current input value u(k) of the equivalent new high-order inertial system is compensated by the compensation algorithm to obtain the compensation value u of the next calculation step cp (k+1), the compensation algorithm used is:

[0029]

[0030] Among them, the output of the compensation algorithm U cp (s) and input U(s) are respectively used as u in the next calculation step cp (k+1) and u(k+1), k represents the calculation step sequence;

[0031] The next calculation step value y(k+1) output by the high-order inertial system and the next calculation step value u output by the compensation algorithm are obtained. cp (k+1) jointly use the extended state observer algorithm for real-time estimation and compensation calculation to obtain the tracking value z1(k+2) of the next two calculation step values ​​y(k+2) output by the high-order inertial system and the tracking value z2(k+2) of the two calculation steps under the total disturbance;

[0032] The extended state observer algorithm for z1(k+2) and z2(k+2) is as follows,

[0033]

[0034] Where b0 is the calculation coefficient, h is the sampling step, and the value range of h is [0.001, 100]; β1 and β2 are the gains of the extended state observer. The gain of the observer obtained by the parameter bandwidth method is:

[0035]

[0036] Among them, ω o represents the bandwidth of the extended state observer algorithm, ω o The larger the value, the stronger the observation ability of the extended state observer algorithm. o The smaller the value, the weaker the observation ability of the extended state observer algorithm. o The value range of is [0.01,100];

[0037] The obtained tracking value z2(k+2) of the two calculation steps under the total disturbance of the high-order inertial system and the tracking value z1(k+2) of the next two calculation step values ​​y(k+2) of the high-order inertial output are combined with the two calculation step values ​​r(k+2) under the set value of a class of controlled actual industrial systems, and the next three calculation step values ​​u(k+3) of the improved active disturbance rejection control algorithm based on pre-compensation are obtained through the control law algorithm;

[0038] u(k+3) is calculated by the following formula:

[0039]

[0040] Among them, k p is the control gain of the active disturbance rejection control, u0(k+2) is the two calculation step values ​​of the virtual control quantity of the improved active disturbance rejection control algorithm based on pre-compensation, and k represents the calculation step.

[0041] Based on the above, step (3) is:

[0042] Based on the designed pre-compensation structure, the transfer function G from U0(s) to Y(s) is obtained EP (s), the mathematical expression is:

[0043]

[0044] Among them, ΔK and ΔT represent the uncertainty of the high-order inertial system;

[0045] The relationship between the output Y(s) and the control quantity U(s) is expressed mathematically as follows:

[0046]

[0047] Among them, U cp (s) represents the output of the compensation algorithm;

[0048] Perform Laplace transform on the relationship between output Y(s) and control quantity U(s):

[0049]

[0050] in, is the gain after compensation, is the total disturbance of the system after compensation;

[0051] make Substitute the transfer function G from u0(s) to y(s) EP (s) expression, that is:

[0052]

[0053] Based on the transfer function G obtained after Laplace transformation EP (s), according to the final value theorem, we get the following:

[0054]

[0055] The transfer function G EP (s) is approximately the following integral link:

[0056]

[0057] in,

[0058] Based on the designed control law and transfer function G EP The approximate transfer function of (s) is used to obtain the equivalent closed-loop dynamic equation of the compensated high-order inertial system, and its mathematical expression is:

[0059]

[0060] in, The time constant of the dynamic equation is expressed by Indicates T p The desired system is designed in combination with the dynamics of n, where λ represents the adjustable factor of the expected dynamic equation;

[0061] Based on the described compensated high-order inertial system expression, the time constant of the dynamic equation is as follows:

[0062]

[0063] The expression of the proportional coefficient in the feedback control law is obtained:

[0064]

[0065] Among them, ω c is the feedback control law bandwidth;

[0066] By selecting λ, combining the expression of the described high-order inertial system, and the quantitative parameter calculation formula, the parameters of the active disturbance rejection control algorithm are calculated, and the quantitative parameter tuning expression is:

[0067]

[0068] Based on the above, b0 is adjusted to Therefore, it is necessary to p Make corresponding adjustments to ensure that the closed-loop system has satisfactory control performance; based on a large number of simulations, by adjusting different γ = [0.5, 0.7, 0.9, 1.0, 1.5, 1.8, 2.0, 2.2, 2.5, 3.0], we get k p The scaling factor of is ρ = [0.65, 0.80, 0.95, 1.00, 1.25, 1.40, 1.50, 1.60, 1.70, 2.00]; for b o and k p The corresponding relationship between the proportional factors is used to fit the function, and the function expression is:

[0069] ρ(γ)=0.518γ+0.451,γ>0;

[0070] By adjusting b o The coefficient γ of k p The proportional factor ρ(γ) is combined with the expression of the high-order inertial system described and the quantitative parameter calculation formula to calculate the parameters of the active disturbance rejection control algorithm. The quantitative parameter tuning expression is rewritten as:

[0071]

[0072] Based on the above, step (5) is:

[0073] Substitute the parameters of the improved anti-disturbance control algorithm based on pre-compensation obtained in step (4) into the control loop to obtain the next four calculation step values ​​u(k+4) of the updated control quantity, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

[0074] The second aspect of the present invention provides an improved active disturbance rejection control system based on pre-compensation and quantitative parameter setting, characterized in that it comprises: a high-order inertial system, a pre-compensation structure for being equivalent to the original high-order inertial system as a new high-order inertial system, a compensation calculator for performing compensation algorithm calculation, a control law calculator for performing feedback control law calculation, and an extended state observer for performing extended state observer algorithm calculation;

[0075] The control law calculator, the compensation calculator, the extended state observer and the new high-order inertial system are communicatively connected to implement the improved auto-disturbance rejection control method based on pre-compensation and quantitative parameter setting.

[0076] A third aspect of the present invention provides a device, comprising:

[0077] one or more processors;

[0078] A memory for storing one or more programs, which, when executed by the one or more processors, enables the one or more processors to perform the improved active disturbance rejection control method based on pre-compensation and quantitative parameter tuning as described above.

[0079] A first aspect of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the improved active disturbance rejection control method based on pre-compensation and quantitative parameter tuning as described above.

[0080] The characteristics and beneficial effects of the present invention are:

[0081] The improved ADRC design based on pre-compensation and the quantitative parameter setting method proposed in the present invention retain the existing improved ADRC algorithm while taking into account the tracking ability and anti-interference ability of this type of high-order inertial system. At the same time, the parameters that need to be adjusted can be obtained through quantitative calculation without adding new setting parameters and under the premise of ensuring robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 This is a structural block diagram of an existing improved active disturbance rejection control algorithm.

[0083] Figure 2 It is an algorithm structure block diagram of the improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting of the present invention.

[0084] Figure 3These are the implementation steps of the improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting of the present invention.

[0085] Figure 4 The figure is a comparison diagram of the set value, the output value of the method of the present invention and the output value of the comparison method when the controlled object is a high-order inertial system. DETAILED DESCRIPTION

[0086] The present invention proposes an improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting, which is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0087] Example 1

[0088] The present invention proposes an improved automatic disturbance rejection control design based on precompensation and a quantitative parameter setting method, the structure of which is as follows: Figure 2 As shown, the process is as follows Figure 3 The steps shown include:

[0089] 101: A class of actual industrial systems is described using a high-order inertial system, and the mathematical expression is:

[0090]

[0091] The output Y(s) and input U(s) of the high-order inertial system are represented by y(k) and u(k) respectively in each calculation step, k represents the calculation step, s, K, T and n represent the differential operator, the gain of the high-order inertial system, the time constant of the high-order inertial system, and the order of the high-order inertial system respectively, and n≥3.

[0092] 102: For a type of actual industrial system controlled in step 101, a pre-compensation structure is designed, and the mathematical expression is:

[0093]

[0094] Among them, T p is the time constant of the compensated high-order inertial system, and T p ∈[0.3,0.5]T. At this time, the combination of the pre-compensation structure and the high-order inertial system is equivalent to a new high-order inertial system, and its expression is:

[0095]

[0096] 103: For the new high-order inertial system after equivalent in step 102, design the expected dynamic equation of the closed-loop system, the mathematical expression is:

[0097]

[0098] Among them G d(s) is the transfer function of the expected dynamic equation of the closed-loop system, λ is the adjustable factor of the expected dynamic equation, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves; the value range of λ is [0.5,1.5].

[0099] 104: Compensate the current input value u(k) of the new high-order inertial system after the equivalent in step 102 by using the compensation algorithm to obtain the compensation value u for the next calculation step. cp (k+1), the mathematical expression of the compensation algorithm is:

[0100]

[0101] Among them, the output of the compensation algorithm U cp (s) and input U(s) are respectively used as u in the next calculation step cp (k+1) and u(k+1), where k represents the calculation step order.

[0102] 105: Based on the expected dynamic equation in step 103, the next calculation step value y(k+1) of the high-order inertial system output and the next calculation step value u of the compensation algorithm output obtained in step 104 are calculated. cp (k+1) The extended state observer algorithm ESO is used together for real-time estimation and compensation calculation to obtain the tracking value z1(k+2) of the two calculation step values ​​y(k+2) under the output of the high-order inertial system and the tracking value z2(k+2) of the two calculation step values ​​under the total disturbance;

[0103] The extended state observer algorithm for z1(k+2) and z2(k+2) is as follows,

[0104]

[0105] Where b0 is the calculation coefficient, h is the sampling step, and the value range of h is [0.001, 100]; β1 and β2 are the gains of the observer. The gain of the observer obtained by the parameter bandwidth method is:

[0106]

[0107] Among them, ω o represents the bandwidth of the extended state observer algorithm, ω o The larger the value, the stronger the observation ability of the extended state observer algorithm. o The smaller the value, the weaker the observation ability of the extended state observer algorithm. o The value range is [0.01,100].

[0108] 106: The tracking value z2(k+2) of the two calculation steps under the total disturbance of the high-order inertial system obtained in step 105 and the tracking value z1(k+2) of the next two calculation step values ​​y(k+2) of the high-order inertial output are combined with the two calculation step values ​​r(k+2) under the set value of a class of controlled actual industrial systems, and the next three calculation step values ​​u(k+3) of the improved active disturbance rejection control algorithm based on pre-compensation are obtained through the control law algorithm;

[0109] u(k+3) can be calculated by the following formula:

[0110]

[0111] Among them, k p is the control gain of the active disturbance rejection control, u0(k+2) is the two calculation step sequence values ​​under the virtual control quantity of the active disturbance rejection control algorithm designed by the present invention, and k represents the calculation step sequence.

[0112] 107: Combined with the compensation algorithm designed in step 104, the transfer function G from U0(s) to Y(s) is obtained. EP (s), the mathematical expression is:

[0113]

[0114] Among them, ΔK and ΔT represent the uncertainty of the high-order inertial system;

[0115] The relationship between the output Y(s) and the control quantity U(s) is expressed mathematically as follows:

[0116]

[0117] Among them, U cp (s) represents the output of the compensation algorithm;

[0118] Furthermore, the relationship between the output Y(s) and the control quantity U(s) is Laplace transformed, that is,

[0119]

[0120] in, is the gain after compensation, is the total disturbance of the system after compensation;

[0121] make Substitute the transfer function G from u0(s) to y(s) EP (s) expression, that is:

[0122]

[0123] 108: Based on the transfer function G obtained after Laplace transformEP (s), according to the final value theorem, we can get the following:

[0124]

[0125] The transfer function G EP (s) is approximately the following integral link:

[0126]

[0127] in,

[0128] 109: Based on the control law and transfer function G designed in step 106 EP The approximate transfer function of (s) is used to obtain the equivalent closed-loop dynamic equation of the compensated high-order inertial system, and its mathematical expression is:

[0129]

[0130] in, Denotes the time constant of the dynamic equation. Indicates T p The desired system is designed by combining the dynamics of n, where λ represents the adjustable factor of the expected dynamic equation. The larger the λ, the slower the closed-loop system moves, and the smaller the λ, the faster the closed-loop system moves. In order to balance control performance and robustness, λ∈[0.5,1.5] is recommended.

[0131] 110: Based on the compensated high-order inertial system expression described above, the time constant of the dynamic equation is as follows:

[0132]

[0133] The expression of the proportional coefficient in the feedback control law is obtained:

[0134]

[0135] Among them, ω c is the feedback control law bandwidth.

[0136] 111: By selecting λ, combining the expression of the described high-order inertial system, and the quantitative parameter calculation formula, the parameters of the active disturbance rejection control algorithm are calculated, and the quantitative parameter tuning expression is:

[0137]

[0138] 112: Considering that in order to adapt to the actual industrial system requirements, b0 can be adjusted to Therefore, it is necessary to pMake corresponding adjustments to ensure that the closed-loop system has satisfactory control performance; based on a large number of simulations, by adjusting different γ = [0.5, 0.7, 0.9, 1.0, 1.5, 1.8, 2.0, 2.2, 2.5, 3.0], we get k p The scaling factor of is ρ = [0.65, 0.80, 0.95, 1.00, 1.25, 1.40, 1.50, 1.60, 1.70, 2.00]; for b o and k p The corresponding relationship between the proportional factors is used to fit the function, and the function expression is:

[0139] ρ(γ)=0.518γ+0.451, γ>0.

[0140] 113: By adjusting b o The coefficient γ of k p The proportional factor ρ(γ) is combined with the expression of the high-order inertial system described and the quantitative parameter calculation formula to calculate the parameters of the active disturbance rejection control algorithm. The quantitative parameter tuning expression is rewritten as:

[0141]

[0142] 114: Substitute the parameters of the improved anti-disturbance control algorithm based on pre-compensation obtained in step 113 into the control loop to obtain the next four calculation step values ​​u(k+4) of the updated control quantity, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

[0143] Example 2

[0144] In order to illustrate the technical superiority of the present invention, this embodiment takes the main steam pressure control in a thermal system as an example for explanation:

[0145] 101: The denitrification system of coal-fired units is described by a high-order inertial system, and the mathematical expression is:

[0146]

[0147] The output Y(s) and input U(s) of the high-order inertial system are represented by y(k) and u(k) in each calculation step, respectively, k represents the calculation step, s, K, T and n represent the differential operator, the gain of the high-order inertial system, the time constant of the high-order inertial system, the order of the high-order inertial system, respectively, and n≥3; in the denitrification system of the coal-fired unit in this embodiment, K=-0.2, T=100 and n=4.

[0148] 102: For the denitration system of the coal-fired unit in step 101, a pre-compensation structure is designed, and the mathematical expression is:

[0149]

[0150] Among them, T p is the time constant of the compensated high-order inertial system, and T p ∈[0.3,0.5]T. T of the coal-fired unit denitrification system in this embodiment p =0.4T=40; at this time, the combination of the pre-compensation structure and the high-order inertial system is equivalent to a new high-order inertial system, and its expression is:

[0151]

[0152] 103: For the new high-order inertial system after equivalent in step 102, design the expected dynamic equation of the closed-loop system, the mathematical expression is:

[0153]

[0154] Among them G d (s) represents the transfer function of the expected dynamic equation of the closed-loop system, λ represents the adjustable factor of the expected dynamic equation, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves; in this embodiment, λ=0.95 for the denitration system of the coal-fired unit.

[0155] 104: Compensate the current input value u(k) of the new high-order inertial system after the equivalent in step 102 by using the compensation algorithm to obtain the compensation value u for the next calculation step. cp (k+1), the mathematical expression of the compensation algorithm is:

[0156]

[0157] Among them, the output of the compensation algorithm U cp (s) and input U(s) are respectively used as u in the next calculation step cp (k+1) and u(k+1), where k represents the calculation step order.

[0158] 105: Based on the expected dynamic equation in step 103, the next calculation step value y(k+1) of the high-order inertial system output and the next calculation step value u of the compensation algorithm output obtained in step 104 are calculated. cp (k+1) The extended state observer algorithm ESO is used together for real-time estimation and compensation calculation to obtain the tracking value z1(k+2) of the two calculation step values ​​y(k+2) under the output of the high-order inertial system and the tracking value z2(k+2) of the two calculation step values ​​under the total disturbance;

[0159] The extended state observer algorithm for z1(k+2) and z2(k+2) is as follows,

[0160]

[0161] Wherein, b0 is the calculation coefficient, h is the sampling step length, and h=0.2 for the denitration system of the coal-fired unit in this embodiment; β1 and β2 are the gains of the observer, and the gain of the observer obtained by the parameter bandwidth method is:

[0162]

[0163] Among them, ω o represents the bandwidth of the extended state observer algorithm, ω o The larger the value, the stronger the observation ability of the extended state observer algorithm. o The smaller the value, the weaker the observation ability of the extended state observer algorithm. o The value range of is [0.01,100]; in this embodiment, the ω of the denitration system of the coal-fired unit o =0.15.

[0164] 106: The tracking value z2(k+2) of the two calculation steps under the total disturbance of the high-order inertial system obtained in step 105 and the tracking value z1(k+2) of the next two calculation step values ​​y(k+2) of the high-order inertial output are combined with the two calculation step values ​​r(k+2) under the set value of a class of controlled actual industrial systems, and the next three calculation step values ​​u(k+3) of the improved active disturbance rejection control algorithm based on pre-compensation are obtained through the control law algorithm;

[0165] u(k+3) can be calculated by the following formula:

[0166]

[0167] Among them, k p is the control gain of the active disturbance rejection control, u0(k+2) is the two calculation step sequence values ​​under the virtual control quantity of the active disturbance rejection control algorithm designed by the present invention, and k represents the calculation step sequence.

[0168] 107: Combined with the compensation algorithm designed in step 104, the transfer function G from U0(s) to Y(s) is obtained. EP (s), the mathematical expression is:

[0169]

[0170] Among them, ΔK and ΔT represent the uncertainty of the high-order inertial system;

[0171] The relationship between the output Y(s) and the control quantity U(s) is expressed mathematically as follows:

[0172]

[0173] Among them, U cp (s) represents the output of the compensation algorithm;

[0174] Furthermore, the relationship between the output Y(s) and the control quantity U(s) is Laplace transformed, that is,

[0175]

[0176] in, is the gain after compensation, is the total disturbance of the system after compensation;

[0177] make Substitute the transfer function G from u0(s) to y(s) EP (s) expression, that is:

[0178]

[0179] 108: Based on the transfer function G obtained after Laplace transform EP (s), according to the final value theorem, we can get the following:

[0180]

[0181] The transfer function G EP (s) is approximately the following integral link:

[0182]

[0183] Among them, the denitration system of the coal-fired unit in this embodiment

[0184] 109: Based on the control law and transfer function G designed in step 106 EP The approximate transfer function of (s) is used to obtain the equivalent closed-loop dynamic equation of the compensated high-order inertial system, and its mathematical expression is:

[0185]

[0186] in, Denotes the time constant of the dynamic equation. Indicates T p The system required for the dynamic design of n is designed, where λ represents the adjustable factor of the expected dynamic equation, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves; λ=0.95 for the denitration system of the coal-fired unit in this embodiment.

[0187] 110: Based on the compensated high-order inertial system expression described above, the time constant of the dynamic equation is as follows:

[0188]

[0189] The expression of the proportional coefficient in the feedback control law is obtained:

[0190]

[0191] Among them, the denitration system of the coal-fired unit in this embodiment

[0192] 111: By selecting λ = 0.95, combining the expression of the described high-order inertial system and the quantitative parameter calculation formula, the parameters of the active disturbance rejection control algorithm are calculated, and the quantitative parameter tuning expression is:

[0193]

[0194] 112: Considering that in order to adapt to the actual industrial system requirements, b0 can be adjusted to Therefore, it is necessary to p Make corresponding adjustments to ensure that the closed-loop system has satisfactory control performance. Based on a large number of simulations, by adjusting different γ=[0.5, 0.7, 0.9, 1.0, 1.5,1.8, 2.0, 2.2, 2.5, 3.0], we get k p The scaling factor of is ρ = [0.65, 0.80, 0.95, 1.00, 1.25, 1.40, 1.50, 1.60, 1.70, 2.00]; for b o and k p The corresponding relationship between the proportional factors is linearly fitted, and the function expression is:

[0195] ρ(γ)=0.518γ+0.451,γ>0;

[0196] In this embodiment, the denitrification system of the coal-fired unit The error caused by the fitting function can be eliminated by adjusting the parameter λ.

[0197] 113: By adjusting b o The coefficient γ of k p The proportional factor ρ(γ) is combined with the expression of the high-order inertial system described and the quantitative parameter calculation formula to calculate the parameters of the active disturbance rejection control algorithm. The quantitative parameter tuning expression is rewritten as:

[0198]

[0199] 114: Substitute the parameters of the improved anti-disturbance control algorithm based on pre-compensation obtained in step 113 into the control loop to obtain the next four calculation step values ​​u(k+4) of the updated control quantity, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

[0200] Figure 4 When the controlled object is a high-order inertial system, the set value, the output value of the method of this embodiment and the output value of the comparison method are compared; the parameters of the comparison method (the improved active disturbance rejection control algorithm in the Chinese invention patent application with publication number CN108287466A) are: K = -0.2, T = 100, n = 4, b0 = -0.0020, ω o = 0.3 and k p =0.0113; the dotted line, solid line and double-strike line are the set value of the denitrification system, the output value of the method of this embodiment and the output value of the comparative method respectively.

[0201] The specific simulation process is as follows: at the beginning of the simulation, the system is in a steady state, at 100s the set value is changed from 0 to 1, at 2000s the closed loop is disturbed by the control quantity, from 0 to -1, until a steady state is reached at 4000s. It can be seen from the simulation that when the controlled object is a high-order inertial system, the method of this embodiment has faster tracking capability and stronger anti-interference capability than the comparative method, such as Figure 4 shown.

[0202] Example 3

[0203] This embodiment provides an improved active disturbance rejection control based on pre-compensation and quantitative parameter setting, including: a high-order inertial system, a pre-compensation structure for being equivalent to an original high-order inertial system as a new high-order inertial system, a compensation calculator for performing compensation algorithm calculation, a control law calculator for performing feedback control law calculation, and an extended state observer for performing extended state observer algorithm calculation;

[0204] The control law calculator, the compensation calculator, the extended state observer and the new high-order inertial system are communicatively connected to implement the improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting described in Example 1.

[0205] For the specific implementation method of this embodiment, please refer to an improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting, which will not be described in detail here.

[0206] As another embodiment of the present invention, there is provided a device, comprising:

[0207] one or more processors;

[0208] A memory for storing one or more programs, which, when executed by the one or more processors, enables the one or more processors to perform the improved active disturbance rejection control method based on pre-compensation and quantitative parameter tuning as described above.

[0209] As another embodiment of the present invention, a computer-readable storage medium storing a computer program is provided, wherein when the program is executed by a processor, the improved auto-disturbance rejection control method based on pre-compensation and quantitative parameter adjustment as described is implemented.

Claims

1. An improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting, characterized in that: The following steps are involved: (1) A class of actual industrial systems is described using a high-order inertial system; a pre-compensation structure is designed, and the designed pre-compensation structure and the original high-order inertial system are equivalent to a new high-order inertial system; the expected dynamic equations of the closed-loop system are designed for the equivalent new high-order inertial system; (2) Based on the current value of the output of the equivalent new high-order inertial system, compensation is performed through a compensation algorithm to obtain a compensation value of the next calculation step of the new high-order inertial system; Through the extended state observer algorithm, the equivalent new high-order inertial system output and the tracking values ​​of the next two calculation step values ​​of the total disturbance are obtained; The numerical values ​​of the next three calculation steps of the improved active disturbance rejection control algorithm based on precompensation are obtained through the control law algorithm; (3) Approximate the partial transfer function of the improved active disturbance rejection control algorithm based on precompensation as an integral link; determine the dynamic equation of the closed-loop system, and quantitatively calculate the parameter setting formula of the improved active disturbance rejection control algorithm based on precompensation; (4) adjusting the relationship between the gain amplification factor after compensation and the corresponding changed parameters through linear fitting, and updating the quantitative calculation parameter setting formula of the improved active disturbance rejection control algorithm based on pre-compensation; (5) By substituting the parameters obtained by quantitative calculation into the control loop, the values ​​of the next four calculation steps of the updated control quantity are obtained, and the control quantity of the closed-loop system is adjusted, thereby achieving the adjustment of the output of the controlled object.

2. The improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting according to claim 1 is characterized in that: The mathematical expression for describing a type of controlled actual industrial system using a high-order inertial system is: Wherein, the output Y(s) and input U(s) of the high-order inertial system are represented by y(k) and u(k) in each calculation step, k represents the calculation step, s, K, T and n represent the differential operator, the gain of the high-order inertial system, the time constant of the high-order inertial system, and the order of the high-order inertial system, respectively, and n≥3; For the above-mentioned actual industrial system, the mathematical expression of the designed pre-compensation structure is: Among them, T p is the time constant of the compensated high-order inertial system, and T p ∈[0.3,0.5]T; The combination of the pre-compensation structure and the original high-order inertial system is equivalent to the expression of the new high-order inertial system: The expected dynamic equation of the closed-loop system designed for the equivalent new high-order inertial system is: Among them, G d (s) is the transfer function of the expected dynamic equation of the closed-loop system, λ is the adjustable factor of the expected dynamic equation, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves. The value range of λ is [0.5,1.5].

3. The improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting according to claim 2 is characterized in that: Step (2) is: The current input value u(k) of the equivalent new high-order inertial system is compensated by the compensation algorithm to obtain the compensation value u of the next calculation step cp (k+1), the compensation algorithm used is: Among them, the output of the compensation algorithm U cp (s) and input U(s) are respectively used as u in the next calculation step cp (k+1) and u(k+1), k represents the calculation step sequence; The next calculation step value y(k+1) output by the high-order inertial system and the next calculation step value u output by the compensation algorithm are obtained. cp (k+1) jointly use the extended state observer algorithm for real-time estimation and compensation calculation to obtain the tracking value z1(k+2) of the next two calculation step values ​​y(k+2) output by the high-order inertial system and the tracking value z2(k+2) of the two calculation steps under the total disturbance; The extended state observer algorithm for z1(k+2) and z2(k+2) is as follows, Where b0 is the calculation coefficient, h is the sampling step, and the value range of h is [0.001, 100]; β1 and β2 are the gains of the extended state observer. The gain of the observer obtained by the parameter bandwidth method is: Among them, ω o represents the bandwidth of the extended state observer algorithm, ω o The larger the value, the stronger the observation ability of the extended state observer algorithm. o The smaller the value, the weaker the observation ability of the extended state observer algorithm. o The value range of is [0.01,100]; The obtained tracking value z2(k+2) of the two calculation steps under the total disturbance of the high-order inertial system and the tracking value z1(k+2) of the next two calculation step values ​​y(k+2) of the high-order inertial output are combined with the two calculation step values ​​r(k+2) under the set value of a class of controlled actual industrial systems, and the next three calculation step values ​​u(k+3) of the improved active disturbance rejection control algorithm based on pre-compensation are obtained through the control law algorithm; u(k+3) is calculated by the following formula: Among them, k p is the control gain of the active disturbance rejection control, u0(k+2) is the two calculation step values ​​of the virtual control quantity of the improved active disturbance rejection control algorithm based on pre-compensation, and k represents the calculation step.

4. The improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting according to claim 2 is characterized in that: Step (3) is: Based on the designed pre-compensation structure, the transfer function G from U0(s) to Y(s) is obtained EP (s), the mathematical expression is: Among them, ΔK and ΔT represent the uncertainty of the high-order inertial system; The relationship between the output Y(s) and the control quantity U(s) is expressed mathematically as follows: Among them, U cp (s) represents the output of the compensation algorithm; Perform Laplace transform on the relationship between output Y(s) and control quantity U(s): in, is the gain after compensation, is the total disturbance of the system after compensation; make Substitute the transfer function G from u0(s) to y(s) EP (s) expression, that is: Based on the transfer function G obtained after Laplace transformation EP (s), according to the final value theorem, we get the following: The transfer function G EP (s) is approximately the following integral link: in, Based on the designed control law and transfer function G EP The approximate transfer function of (s) is used to obtain the equivalent closed-loop dynamic equation of the compensated high-order inertial system, and its mathematical expression is: in, The time constant of the dynamic equation is expressed by Indicates T p The desired system is designed in combination with the dynamics of n, where λ represents the adjustable factor of the expected dynamic equation; Based on the described compensated high-order inertial system expression, the time constant of the dynamic equation is as follows: The expression of the proportional coefficient in the feedback control law is obtained: Among them, ω c is the feedback control law bandwidth; By selecting λ, combining the expression of the described high-order inertial system, and the quantitative parameter calculation formula, the parameters of the active disturbance rejection control algorithm are calculated, and the quantitative parameter tuning expression is:

5. The improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting according to claim 4 is characterized in that: b0 is adjusted to γ>0, so k p Make corresponding adjustments to ensure that the closed-loop system has satisfactory control performance; based on a large number of simulations, by adjusting different γ = [0.5, 0.7, 0.9, 1.0, 1.5, 1.8, 2.0, 2.2, 2.5, 3.0], we get k p The scaling factor of is ρ = [0.65, 0.80, 0.95, 1.00, 1.25, 1.40, 1.50, 1.60, 1.70, 2.00]; for b o and k p The corresponding relationship between the proportional factors is used to fit the function, and the function expression is: ρ(γ)=0.518γ+0.451,γ>0; By adjusting b o The coefficient γ of k p The proportional factor ρ(γ) is combined with the expression of the high-order inertial system described and the quantitative parameter calculation formula to calculate the parameters of the active disturbance rejection control algorithm. The quantitative parameter tuning expression is rewritten as:

6. The improved active disturbance rejection control method based on pre-compensation and quantitative parameter setting according to claim 5 is characterized in that: Step (5) is: Substitute the parameters of the improved anti-disturbance control algorithm based on pre-compensation obtained in step (4) into the control loop to obtain the next four calculation step values ​​u(k+4) of the updated control quantity, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

7. An improved active disturbance rejection control system based on pre-compensation and quantitative parameter setting, characterized in that: include: A high-order inertial system, a pre-compensation structure for converting the original high-order inertial system into a new high-order inertial system, a compensation calculator for calculating a compensation algorithm, a control law calculator for calculating a feedback control law, and an extended state observer for calculating an extended state observer algorithm; The control law calculator, the compensation calculator, the extended state observer and the new high-order inertial system are communicatively connected to implement the improved auto-disturbance rejection control method based on pre-compensation and quantitative parameter setting as described in any one of claims 1-6.

8. A device, characterized in that include: one or more processors; A memory for storing one or more programs, which, when executed by the one or more processors, enables the one or more processors to execute the improved auto-disturbance rejection control method based on pre-compensation and quantitative parameter adjustment as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the program is executed by a processor, the improved active disturbance rejection control method based on pre-compensation and quantitative parameter adjustment as described in any one of claims 1 to 6 is implemented.

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