A method and system for anti-saturation self-disturbance rejection control and quantitative parameter setting

Abstract

The present invention provides an anti-saturation self-disturbance control and quantitative parameter setting method and system, the method includes the following steps: a class of actual industrial systems are described by a high-order inertial system; the expected dynamic equation of the closed-loop system is designed; the next calculation step value of the compensation algorithm input is obtained based on the current value of the feedforward and the hand operator output; the next two calculation step values ​​of the compensation algorithm output are further calculated; the tracking value of the next three calculation step values ​​of the high-order inertial system output and the total disturbance is obtained by the extended state observer algorithm; the next four calculation step values ​​of the hand operator input are obtained by the control law algorithm; the next five calculation step values ​​of the hand operator output are obtained by updating the hand operator input; and the values ​​are sent to the actuator to adjust the opening of the actuator. The present invention can quantitatively calculate the parameters of the proposed self-disturbance control and has a strong anti-saturation ability, and can achieve a satisfactory control effect.

Description

Technical Field

[0001] The present invention relates to the field of industrial control, and in particular to an anti-saturation self-disturbance rejection control and quantitative parameter setting method and system. 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. Wherein 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 meaning of each parameter in the above formula is: 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 to 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 systems, there are standard ADRC algorithms and improved ADRC algorithms (such as CN108287466B, an improved ADRC method for a class of high-order systems). Among them, the standard ADRC algorithm is effective in controlling high-order inertial systems. When the anti-interference performance is strong, the tracking performance is poor, and when the tracking performance is strong, the anti-interference performance is poor. Although the existing improved anti-interference control algorithm can achieve a good balance between tracking and anti-interference performance, it has the following problems:

[0005] 1) Parameter tuning relies on trial and error, lacking a quantitative parameter tuning method that takes tracking into account while ensuring robustness and lacks anti-interference performance;

[0006] 2) The problems of amplitude saturation and rate saturation of the actuator are not well solved. That is, when the actuator has serious amplitude saturation or rate saturation, the control effect will be significantly reduced, and there is a lack of simple and effective anti-saturation methods. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of the existing technology. For a class of high-order inertial industrial systems, an anti-saturation auto-disturbance rejection control and quantitative parameter setting method and system are provided. By improving the control quantity, an anti-saturation auto-disturbance rejection control algorithm is realized; by designing the expected dynamic equation of the closed-loop system, the parameters of an anti-saturation auto-disturbance rejection control algorithm can be directly calculated, the parameters of the proposed anti-saturation auto-disturbance rejection control algorithm can be quantitatively calculated, and the closed-loop system control effect after adjustment is guaranteed to be ideal, providing support for the wide application of the anti-saturation auto-disturbance rejection control algorithm in solving a class of high-order inertial industrial systems.

[0008] The present invention proposes an anti-saturation auto-disturbance rejection control and quantitative parameter setting method, comprising the following steps:

[0009] Step 1: A class of controlled actual industrial systems is described using a high-order inertial system. The mathematical expression is:

[0010]

[0011] Among them, 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 represents the differential operator, K represents the gain, T represents the time constant, represents the nth order, and n≥3;

[0012] Step 2: Design the expected dynamic equation of the closed-loop system for a class of actual industrial systems controlled in step 1. The mathematical expression is:

[0013]

[0014] Among them, G d (s) is the transfer function of the expected dynamic equation of the closed-loop system, λ is an adjustable factor, 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];

[0015] Step 3, based on the current value u of the feedforward quantity f (k) and the current value u output by the handheld operator out (k) Get the next calculation step value u of the compensation algorithm input ma (k+1),u ma The calculation formula for (k+1) is:

[0016] u ma (k+1)=u out (k)-u f (k);

[0017] Step 4: Input the next calculation step value u of the compensation algorithm obtained in step 3ma (k+1) The next two calculation step values ​​u of the compensation algorithm output are calculated by the compensation algorithm. cp (k+2), the mathematical expression of the compensation algorithm is:

[0018]

[0019] Among them, the output of the compensation algorithm U cp (s) In the next two calculation steps, the numerical value and input U ma (s) In the next calculation step, the numerical value is u cp (k+2) and u ma (k+1) represents the calculation step sequence;

[0020] Step 5: Based on the expected dynamic equation in step 2, use the next two calculation step values ​​y(k+2) of the output of the controlled object in step 1 and the next two calculation step values ​​u of the compensation algorithm output obtained in step 4. cp (k+2) Design an extended state observer algorithm to obtain the tracking value z1(k+3) of the next three calculation step values ​​output by the high-order inertial system and the tracking value z2(k+3) of the three calculation steps under the total disturbance;

[0021] The extended state observer algorithm for z1(k+3) and z2(k+3) is as follows:

[0022]

[0023] Where, h is the sampling period, and the value range of h is [0.001,100];

[0024] l1, l2 and b0 are the parameters to be adjusted in the implementation of ADRC, which are calculated by the following formula:

[0025]

[0026] Among them, ρ represents the magnification of b0, and the value range of ρ is [0.5,105); 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]; e is the natural exponent, and the value of e is 2.718281; k fw is the feedforward weight coefficient, k fw The value range of is [0,1);

[0027] Step 6: Combine the tracking value z2(k+3) of the three calculation steps under the total disturbance of the high-order inertial system obtained in step 5 and the tracking value z1(k+3) of the next three calculation step values ​​y(k+3) of the high-order inertial output with the three calculation step values ​​r(k+3) of the set value of a class of controlled actual industrial system and the next three calculation step values ​​u of the feedforward quantity. f (k+3), the next four calculation step values ​​u are obtained by the control law algorithm input by the hand operator in (k+4);

[0028] u in (k+4) is calculated by the following formula:

[0029]

[0030] or

[0031]

[0032] Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula:

[0033]

[0034] Step 7: Enter the next three calculation step values ​​u entered by the handheld operator in (k+3) is updated to the next four calculation step sequence values ​​u of the hand operator input obtained in step 6 in (k+4) and sent to the handheld operator to obtain the next five calculation step sequence values ​​u output by the handheld operator out (k+5);

[0035] The next five calculation step values ​​u output by the handheld operator out (k+5) is sent to the actuator to adjust the opening of the actuator, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

[0036] The characteristics and beneficial effects of the present invention are:

[0037] The present invention proposes an anti-saturation auto-disturbance rejection control and quantitative parameter setting method, which retains the existing improved auto-disturbance rejection control algorithm while taking into account the tracking ability and anti-disturbance ability of this type of high-order inertial system, has a strong ability to resist actuator amplitude saturation and rate saturation, and can obtain the parameters that need to be adjusted through quantitative calculation without adding new setting parameters and ensuring robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a structural block diagram of the anti-saturation automatic disturbance rejection control and quantitative parameter setting system in Example 1 of the present invention.

[0039] Figure 2 These are the implementation steps of the anti-saturation auto-disturbance rejection control and quantitative parameter setting method according to Embodiment 1 of the present invention.

[0040] Figure 3 It 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 there is no actuator amplitude saturation and rate saturation.

[0041] Figure 4 It 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 actuator amplitude saturation and rate saturation exist. DETAILED DESCRIPTION

[0042] Various exemplary embodiments of the present invention will be described in detail below in conjunction with specific embodiments. The description of the exemplary embodiments is merely illustrative and is not intended to be any limitation on the present invention and its application or use. The present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to make the present invention thorough and complete and to fully express the scope of the present invention to those skilled in the art. It should be noted that unless otherwise specifically stated, the relative arrangement of the components and steps described in these embodiments should be interpreted as being merely exemplary and not as a limitation.

[0043] All terms (including technical terms or scientific terms) used in the present invention have the same meanings as those understood by ordinary technicians in the field to which the present invention belongs, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries should be interpreted as having meanings consistent with their meanings in the context of the relevant technology, and should not be interpreted in an idealized or extremely formal sense, unless explicitly defined herein.

[0044] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0045] The following is further described in detail with reference to the accompanying drawings and specific embodiments.

[0046] Example 1

[0047] like Figure 1As shown, this embodiment provides an anti-saturation auto-disturbance rejection control and quantitative parameter setting system, including: a controlled actual industrial system, a compensation calculator for performing compensation algorithm calculations, a control law calculator for performing control law calculations, and an extended state observer for performing extended state observer algorithm calculations; the control law calculator, the compensation calculator, the extended state observer, and the actual controlled industrial system are communicatively connected to implement the anti-saturation auto-disturbance rejection control and quantitative parameter setting method.

[0048] like Figure 2 As shown, the anti-saturation automatic disturbance rejection control and quantitative parameter setting method, the process includes the following steps:

[0049] S1: A type of coal-fired unit denitrification system is described using a high-order inertial system, and the mathematical expression is:

[0050]

[0051] Among them, 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 represents the differential operator, K represents the gain, T represents the time constant, represents the nth order, and n≥3.

[0052] S2: Design the expected dynamic equation of the closed-loop system for a class of actual industrial systems controlled in step S1. The mathematical expression is:

[0053]

[0054] Among them, G d (s) is expressed as the transfer function of the expected dynamic equation of the closed-loop system, λ is an adjustable factor, 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].

[0055] S3: Based on the current value u of the feedforward quantity f (k) and the current value u output by the handheld operator out (k) Get the next calculation step value u of the compensation algorithm input ma (k+1),u ma The calculation formula for (k+1) is:

[0056] u ma (k+1)=u out (k)-u f (k).

[0057] S4: Input the next calculation step value u of the compensation algorithm obtained in step S3 ma(k+1) The next two calculation step values ​​u of the compensation algorithm output are calculated by the compensation algorithm. cp (k+2), the mathematical expression of the compensation algorithm is:

[0058]

[0059] Among them, the output of the compensation algorithm U cp (s) In the next two calculation steps, the numerical value and input U ma (s) In the next calculation step, the numerical value is u cp (k+2) and u ma (k+1), where k represents the calculation step sequence.

[0060] S5: Based on the expected dynamic equation in step S2, the output of the controlled object in step S1 in the next two calculation step values ​​y(k+2) and the next two calculation step values ​​u of the compensation algorithm output obtained in step S4 are converted into cp (k+2) Design an extended state observer algorithm to obtain the tracking value z1(k+3) of the next three calculation step values ​​output by the high-order inertial system and the tracking value z2(k+3) of the three calculation steps under the total disturbance;

[0061] The extended state observer algorithm for z1(k+3) and z2(k+3) is as follows,

[0062]

[0063] Where h is the sampling period, and the value range of h is [0.001,100];

[0064] l1, l2 and b0 are the parameters to be adjusted in the implementation of ADRC, which are calculated by the following formula:

[0065]

[0066] Among them, ρ represents the magnification of b0, and the value range of ρ is [0.5,105); 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]; e is the natural exponent, and the value of e is 2.718281; k fw is the feedforward weight coefficient, k fw The value range of is [0,1).

[0067] S6: Combine the tracking value z2(k+3) of the three calculation steps under the total disturbance of the high-order inertial system obtained in step S5 and the tracking value z1(k+3) of the next three calculation step values ​​y(k+3) of the high-order inertial output, with the three calculation step values ​​r(k+3) under the set value of a class of controlled actual industrial systems, and with the next three calculation step values ​​u of the feedforward quantity f (k+3), the next four calculation step values ​​u are obtained by the control law algorithm input by the hand operator in (k+4);

[0068] u in (k+4) can be calculated by the following formula:

[0069]

[0070] or

[0071]

[0072] Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula:

[0073]

[0074] S7: Enter the next three calculation step values ​​u entered by the handheld operator in (k+3) is updated to the next four calculation step sequence values ​​u of the hand operator input obtained in step 106 in (k+4) and sent to the handheld operator to obtain the next five calculation step sequence values ​​u output by the handheld operator out (k+5);

[0075] The next five calculation step values ​​u output by the handheld operator out (k+5) is sent to the actuator to adjust the opening of the actuator, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

[0076] Example 2

[0077] This embodiment takes the main steam pressure control in a thermal system as an example to illustrate the technical superiority of the present invention:

[0078] S21: The denitration system of coal-fired units is described by a high-order inertial system, and the mathematical expression is:

[0079]

[0080] Among them, 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 represents the differential operator, K represents the gain, T represents the time constant, n represents the order, and n≥3; in the coal-fired unit denitrification system in this embodiment, K=-0.2, T=100 and n=4.

[0081] S22: Design the expected dynamic equation of the closed-loop system, the mathematical expression is:

[0082]

[0083] 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=0.9 for the denitration system of the coal-fired unit.

[0084] S23: Based on the current value u of the feedforward quantity f (k) and the current value u output by the handheld operator out (k) Get the next calculation step value u of the compensation algorithm input ma (k+1),u ma The calculation formula for (k+1) is:

[0085] u ma (k+1)=u out (k)-u f (k).

[0086] S24: Input the next calculation step sequence value u of the compensation algorithm obtained in step S23 ma (k+1) The next two calculation step values ​​u of the compensation algorithm output are calculated by the compensation algorithm. cp (k+2), the mathematical expression of the compensation algorithm is:

[0087]

[0088] Among them, the output of the compensation algorithm U cp (s) In the next two calculation steps, the numerical value and input U ma (s) In the next calculation step, the numerical value is u cp (k+2) and u ma (k+1), where k represents the calculation step sequence.

[0089] S25: Based on the expected dynamic equation in step S22, the output of the controlled object in step S21 in the next two calculation step values ​​y(k+2) and the next two calculation step values ​​u of the compensation algorithm output obtained in step S24 are calculated. cp(k+2) Design an extended state observer algorithm to obtain the tracking value z1(k+3) of the next three calculation step values ​​output by the high-order inertial system and the tracking value z2(k+3) of the three calculation steps under the total disturbance;

[0090] The extended state observer algorithm for z1(k+3) and z2(k+3) is as follows,

[0091]

[0092] Wherein, h is the sampling period, h = 0.2;

[0093] l1, l2 and b0 are the parameters to be adjusted in the implementation of ADRC, which are calculated by the following formula:

[0094]

[0095] Where, ρ represents the magnification of b0, ρ = 1, b0 = -0.0020; 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 =0.3; e is the natural exponent, the value is 2.718281; k fw is the feedforward weight coefficient, k fw =0.

[0096] S26: Combine the tracking value z2(k+3) of the three calculation steps under the total disturbance of the high-order inertial system obtained in step S25 and the tracking value z1(k+3) of the next three calculation step values ​​y(k+3) of the high-order inertial output, with the three calculation step values ​​r(k+3) under the set value of a class of controlled actual industrial systems, and with the next three calculation step values ​​u of the feedforward quantity f (k+3), the next four calculation step values ​​u are obtained by the control law algorithm input by the hand operator in (k+4);

[0097] u in (k+4) is calculated by the following formula:

[0098]

[0099] Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula:

[0100]

[0101] S27: Enter the next three calculation step values ​​u entered by the handheld operatorin (k+3) is updated to the next four calculation step sequence values ​​u obtained from the hand operator input in step S26 in (k+4) and sent to the handheld operator to obtain the next five calculation step sequence values ​​u output by the handheld operator out (k+5);

[0102] The next five calculation step values ​​u output by the handheld operator out (k+5) is sent to the actuator to adjust the opening of the actuator, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

[0103] Figure 3 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 there is no actuator amplitude saturation and rate saturation; Figure 4 It is a comparison diagram of the set value, the output value of the method of the present invention and the output value of the comparative method (patent CN108287466B) when the actuator amplitude saturation and rate saturation exist; the parameters of the improved ADRC algorithm in patent CN108287466B are: K = -0.2, T = 100, n = 4, b0 = -0.0020, ω o = 0.3 and k p =0.0113; the solid line, the box line and the dotted line are the set value of the denitrification system, the output value of the method of the present invention and the output value of the comparative method (patent CN108287466B), respectively.

[0104] The specific simulation process is as follows: at the beginning of the simulation, the system is in a steady state, the set value is changed from 0 to 1 at 100s, the closed loop is disturbed by the control quantity at 2000s, and the value changes from 0 to -1 until a steady state is reached at 4000s. Through simulation, it can be seen that when there is no actuator amplitude saturation and rate saturation, the method of the present invention and the comparative method can take into account the tracking ability and anti-interference ability of the system, and have relatively fast tracking ability and strong anti-interference ability. When there is actuator amplitude saturation (amplitude limit is ±5.2) and rate saturation (rate limit is ±0.1), the method of the present invention can still take into account the tracking ability and anti-interference ability of the system, and has relatively fast tracking ability and strong anti-interference ability. The control effect of the comparative method is significantly reduced, and the tracking still does not reach a steady state at 2000s.

Claims

1. An anti-saturation auto-disturbance rejection control and quantitative parameter setting method, characterized in that: The following steps are involved: Step 1: A class of controlled actual industrial systems is described using a high-order inertial system. The mathematical expression is: Among them, 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 represents the differential operator, K represents the gain, T represents the time constant, n represents the order, and n≥3; Step 2: Design the expected dynamic equation of the closed-loop system for a class of actual industrial systems controlled in step 1. The mathematical expression is: Among them, G d (s) is the transfer function of the expected dynamic equation of the closed-loop system, λ is an adjustable factor, 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]; Step 3, based on the current value u of the feedforward quantity f (k) and the current value u output by the handheld operator out (k) Get the next calculation step value u of the compensation algorithm input ma (k+1),u ma The calculation formula for (k+1) is: in ma (k+1)=u out (k)-u f (k); Step 4: Input the next calculation step value u of the compensation algorithm obtained in step 3 ma (k+1) The next two calculation step values ​​u of the compensation algorithm output are calculated by the compensation algorithm. cp (k+2), the mathematical expression of the compensation algorithm is: Among them, the output of the compensation algorithm U cp (s) In the next two calculation steps, the numerical value and input U ma (s) In the next calculation step, the numerical value is u cp (k+2) and u ma (k+1) represents the calculation step sequence; Step 5, based on the expected dynamic equation in step 2, use the output of the controlled object in step 1 in the next two calculation step values ​​y(k+2) and the next two calculation step values ​​of the compensation algorithm output obtained in step 4 u cp (k+2) Design an extended state observer algorithm to obtain the tracking value z1(k+3) of the next three calculation step values ​​output by the high-order inertial system and the tracking value z2(k+3) of the three calculation steps under the total disturbance; The extended state observer algorithm for z1(k+3) and z2(k+3) is as follows: Where, h is the sampling period, and the value range of h is [0.001,100]; l1, l2 and b0 are the parameters to be adjusted in the implementation of ADRC, which are calculated by the following formula: Among them, ρ represents the magnification of b0, and the value range of ρ is [0.5,105); 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]; e is the natural exponent, and the value of e is 2.718281; k fw is the feedforward weight coefficient, k fw The value range of is [0,1); Step 6: Combine the tracking value z2(k+3) of the three calculation steps under the total disturbance of the high-order inertial system obtained in step 5 and the tracking value z1(k+3) of the next three calculation step values ​​y(k+3) of the high-order inertial output with the three calculation step values ​​r(k+3) of the set value of a class of controlled actual industrial system and the next three calculation step values ​​u of the feedforward quantity. f (k+3), the next four calculation step values ​​u are obtained by the control law algorithm input by the hand operator in (k+4); u in (k+4) is calculated by the following formula: or Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula: Step 7: Enter the next three calculation step values ​​u entered by the handheld operator in (k+3) is updated to the next four calculation step sequence values ​​u of the hand operator input obtained in step 6 in (k+4) and sent to the handheld operator to obtain the next five calculation step sequence values ​​u output by the handheld operator out (k+5); The next five calculation step values ​​u output by the handheld operator out (k+5) is sent to the actuator to adjust the opening of the actuator, so as to adjust the control quantity of the closed-loop system and thus adjust the output of the controlled object.

2. An anti-saturation auto-disturbance rejection control and quantitative parameter setting system, characterized in that: include: The actual industrial system being controlled, a compensation calculator for performing compensation algorithm calculations, a control law calculator for performing control law calculations, and an extended state observer for performing extended state observer algorithm calculations; The control law calculator, the compensation calculator, the extended state observer and the actual industrial system being controlled are communicatively connected to implement the anti-saturation self-disturbance rejection control and quantitative parameter setting method described in claim 1.

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