A linear active disturbance rejection controller and its design method and parameter tuning method

Abstract

The application discloses a linear active disturbance rejection controller and a design method and a parameter setting method thereof, the design method constructs a gain parameter considering the influence of the order of a controlled object on the overshoot in the step response of the controller, introduces the gain parameter in a linear error feedback control law, dynamically adjusts the error component between the output of a linear tracking differentiator and the output of a linear extended state observer, thereby configuring the zero point of a forward channel of a system, i.e. the zero point of a closed-loop system, thereby reducing the overshoot. The input of a linear error feedback control law in the linear active disturbance rejection controller of the application is provided with a gain parameter, the input of the linear error feedback control law, the gain parameter dynamically adjusts the error component between the output of the linear tracking differentiator and the output of the linear extended state observer, thereby configuring the zero point of the forward channel of the system, i.e. the zero point of the closed-loop system, thereby reducing the overshoot.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology, and particularly relates to a linear active disturbance rejection controller and its design and parameter tuning methods. Background Technology

[0002] With the rapid development of industrial automation technology, the requirements for the anti-disturbance capability and dynamic response performance of control systems are becoming increasingly stringent. Active Disturbance Rejection Control (ADRC) technology has attracted widespread attention due to its ability to estimate system state in real time and suppress disturbances. Among them, the linear tracking differentiator (LTD), as an important component of ADRC, has the ability to extract smooth derivative signals through filtering, overcoming the noise amplification problem in traditional differentiating methods.

[0003] Although ADRC control strategies perform excellently in engineering applications, traditional high-order linear ADRC systems based on the bandwidth parameter tuning method still suffer from closed-loop step response overshoot in practical use. This overshoot is unacceptable for certain process controls, such as temperature control which requires preventing over-temperature, as over-temperature can affect the lifespan of metal pipes; and for some precision controls, overshoot can lead to product defects. Some researchers have improved upon the traditional bandwidth parameter tuning method of ADRC by incorporating linear error feedback control... Change to In the formula, u0 is the output of the linear error feedback control law; v i k is the i-th output of the linear tracking differentiator; i The parameters of the linear error feedback control law are z. i v1 is the i-th output of the linear extended state observer; v2 is the 1-th output of the linear tracking differentiator. Although this improvement solves the overshoot problem, it sacrifices the speed of the ADRC controller.

[0004] Since it is difficult to balance the suppression of overshoot and response speed, an improved solution is urgently needed to enhance the robustness and dynamic performance of the system while maintaining control accuracy. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a linear active disturbance rejection controller and its design and parameter tuning methods.

[0006] The technical solution of the present invention is as follows:

[0007] A design method for a linear active disturbance rejection controller, the linear active disturbance rejection controller comprising a linear tracking differentiator, a linear error feedback control law, and a linear extended state observer; the design method includes:

[0008] The gain parameter considering the influence of the order of the controlled object on the overshoot in the step response of the controller is constructed;

[0009] The gain parameter is introduced into the linear error feedback control law, and the input of the linear error feedback control law is the difference between the output of the linear tracking differentiator multiplied by the gain parameter and the output of the linear extended state observer.

[0010] Further, the expression of the linear error feedback control law is

[0011]

[0012] In the formula, u0 is the output of the linear error feedback control law; u is the input of the controlled object; b0 is the control amount gain of the controlled object; v i is the i-th output of the linear tracking differentiator, i=1, 2, …, n; z i is the i-th output of the linear extended state observer, i=1, 2, …, n+1; k i is the parameter of the linear error feedback control law, satisfying s n +k1s n-1 +…+k n-1 s+k n =(s+ω c ) n , where ω c is the bandwidth of the linear error feedback law; λ i is the gain coefficient corresponding to the i-th output of the linear tracking differentiator.

[0013] Further, the gain parameter satisfies the following constraint:

[0014]

[0015] In the formula, λ i is the gain coefficient corresponding to the i-th output of the linear tracking differentiator, i=1, 2, …, n, and n is the order of the controlled object.

[0016] Further, the gain parameter satisfies the following constraint: so that the system closed-loop zero point is configured at -ω c .

[0017] Further, the gain parameter satisfies the following constraint: so that the system closed-loop zero point is configured at -ω c / ε, where ε is the zero point coefficient.

[0018] Further, the value range of the zero point coefficient ε is ε>1.

[0019] A linear active disturbance rejection controller, comprising a linear tracking differentiator, a linear error feedback control law with variable parameters and a linear extended state observer; wherein the input of the linear tracking differentiator is v0, and the output is v i , i = 1, 2, …, n;

[0020] The input u of the controlled object is multiplied by b0 gain as the first input signal of the linear extended state observer;

[0021] The output y of the controlled object is as the second input signal of the linear extended state observer;

[0022] The output of the linear extended state observer is z i , i = 1, 2, …, n+1;

[0023] The input e of the linear error feedback control law with variable parameters is i = λ i · v i -z i , i = 1, 2, …, n, λ i is the gain parameter of the input component of the linear error feedback control law;

[0024] The output u0 of the linear error feedback control law with variable parameters is subtracted from the (n+1)th output component z n+1 of the extended state observer and multiplied by 1 / b0 gain to obtain the input u of the controlled object.

[0025] Further, the expression of the controlled object is

[0026]

[0027] In the formula, y is the output of the controlled object; x is the state variable of the controlled object; f is a function about the state variable x; d is an external disturbance;

[0028] The expression of the linear extended state observer is

[0029]

[0030] In the formula, β i is the polynomial coefficient of the linear extended state observer, satisfying s n+1 + β1s n + … + β n s + β n+1 = (s + ω0) n+1 , wherein, ω o is the bandwidth of the linear extended state observer;

[0031] The expression of the linear tracking differentiator is

[0032]

[0033] In the formula, v0 is the input signal; r is the parameter of the linear extended tracking differentiator, r = ω o .

[0034] Based on the above-described design method for linear active disturbance rejection controllers, a parameter tuning method for a second-order linear active disturbance rejection controller is presented. This second-order linear active disturbance rejection controller is designed for delay-free second-order objects. The method for controlling includes:

[0035] Step 1) Let the bandwidth ω of the linear error feedback law be... c With the bandwidth ω of the extended state observer o The ratio is equal to the parameter λ, that is Set the value of parameter λ, and let the bandwidth of the second-order linear active disturbance rejection controller based on the linear error feedback control law with variable parameters be ω. a ω a satisfy

[0036] Step 2) Calculate the bandwidth ω according to the parameter tuning formula of the second-order linear active disturbance rejection controller described below. a and the control quantity gain b0 of the controlled object: ω a =1 / T, b0=K / T 2 Then based on obtaining ω c and ω o With λ and ω a The relationship between the bandwidth ω of the linear error feedback law is used to obtain the bandwidth ω. c With the bandwidth ω of the extended state observer o :

[0037]

[0038] Step 3) Set the gain parameter of the second-order linear active disturbance rejection controller to configure the zero point of the forward path of the control system, i.e. the zero point of the closed-loop system.

[0039] Step 4) Using the calculated ω c ω o The system automatically controls b0 and the set gain parameters to complete parameter tuning.

[0040] Furthermore, the method for setting the gain parameter in step 3) includes:

[0041] Set the initial values ​​for the first gain parameter λ1 of the first input in the linear error feedback control law with corresponding variable parameters and the second gain parameter of the second input in the linear error feedback control law with corresponding variable parameters: In the formula, epsilon is a zero point coefficient;

[0042] Take epsilon = 1 as the initial value and gradually increase to epsilon = 1.68, and take the value of the gain parameter meeting the preset overshoot requirement in the gradual increase process as the final setting value of the gain parameter.

[0043] An electronic device, the electronic device comprising a memory and a processor, the memory storing a computer program, the processor being configured to invoke and run the computer program stored in the memory to execute the method according to any one of the preceding method.

[0044] A computer readable storage medium, the computer readable storage medium storing a computer program, the computer program being executed by a processor to implement the steps of the method according to any one of the preceding method.

[0045] Compared with the prior art, the present application has the following beneficial effects:

[0046] The present application proposes a linear active disturbance rejection controller and a design method and parameter tuning method thereof, the design method constructs a gain parameter considering the influence of the order of the controlled object on the overshoot in the step response of the controller, and introduces the gain parameter in the linear error feedback control law, dynamically adjusts the error component between the output of the linear tracking differentiator and the output of the linear extended state observer, thereby configuring the zero point of the forward channel of the system, i.e. the zero point of the closed-loop system, thereby reducing the overshoot.

[0047] The input of the linear error feedback control law in the linear active disturbance rejection controller of the present application is provided with a gain parameter, and the input e of the linear error feedback control law i = lambda i ·v i -z i The gain parameter dynamically adjusts the error component between the output of the linear tracking differentiator and the output of the linear extended state observer, thereby configuring the zero point of the forward channel of the system, i.e. the zero point of the closed-loop system, thereby reducing the overshoot.

[0048] The tuning method of the linear active disturbance rejection controller of the present application has reasonable debugging rules, is more suitable for debugging sites, and is specific in theoretical guidance, avoiding the problem of fuzzy parameter tuning process caused by the experience tuning method.

[0049] The present application has wide applicability in the field of industrial process control, especially in complex dynamic environments such as energy and power, automation equipment, petrochemical industry, metal smelting and intelligent driving, and shows significant technical advantages. By improving the robustness and dynamic response performance of the control system, the present application can effectively cope with various disturbances and uncertainties, providing reliable protection for high-precision control and stable operation of the above-mentioned industries. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 System block diagram of LADRC control system based on variable parameter linear state feedback control law;

[0051] Figure 2 System block diagram of LADRC control system based on variable parameter linear state feedback control law (system order is two);

[0052] Figure 3 Effect diagram of closed loop response curve of non-delay controlled object using the control system and parameter tuning method of the application;

[0053] Figure 4 Step response curve diagram corresponding to the process that the value of controller parameter λ2 is increased from 0.5 to 0.84. DETAILED DESCRIPTION

[0054] The application will be further clarified by the following embodiments and drawings, which should not be considered as limiting the scope of the application. After reading the application, those skilled in the art will be able to modify various equivalent forms of the application, which are within the scope of the appended claims.

[0055] Embodiment one:

[0056] The embodiment provides a design method of a linear active disturbance rejection controller, the linear active disturbance rejection controller comprising a linear tracking differentiator, a linear error feedback control law and a linear extended state observer; the design method comprises:

[0057] Based on the bandwidth parameter tuning method, a gain parameter considering the influence of the order of the controlled object on the overshoot of the step response of the controller is constructed;

[0058] The gain parameter is introduced into the linear error feedback control law, so that the input of the linear error feedback control law is the difference between the product of the output value of the linear tracking differentiator and the gain parameter and the output of the linear extended state observer, and the error component between the output of the linear tracking differentiator and the output of the linear extended state observer is dynamically adjusted, thereby configuring the zero point of the forward channel of the system, i.e. the zero point of the closed loop system.

[0059] Further, the above bandwidth parameter tuning method is a method for simplifying parameter tuning by adjusting the bandwidth (ω o ) of the linear extended state observer and the bandwidth (ω c ) of the linear error feedback control law, which can be found in the prior art document entitled "Scaling and bandwidth-parameterization based controller tuning". In the bandwidth parameter tuning method, the expression of the linear error feedback control law is On this basis, researchers have made improvements, and changed to But the improvement although solves the overshoot problem, but sacrifices the rapidity of ADRC controller.

[0060] The application introduces the gain parameter in the linear error feedback control law, dynamically adjusts the error component between the output of the linear tracking differentiator and the output of the linear extended state observer, thereby configures the zero point of the forward channel of the system, and the expression of the linear error feedback control law of the application is:

[0061]

[0062] In the formula, u0 is the output of the linear error feedback control law; u is the input of the controlled object; b0 is the control amount gain of the controlled object; v i is the i-th output of the linear tracking differentiator, i=1, 2,..., n; z i is the i-th output of the linear extended state observer, i=1, 2,..., n+1; k i is the parameter of the linear error feedback control law, and satisfies s n +k1s n-1 +…+k n-1 s+k n =(s+ω c ) n , Wherein, ω c is the bandwidth of the linear error feedback law; λ i is the gain coefficient corresponding to the i-th output of the linear tracking differentiator.

[0063] Embodiment two:

[0064] The embodiment is further designed on the basis of embodiment one, and in the example, the gain parameter satisfies the following constraint:

[0065]

[0066] In the formula, λ i is the gain coefficient corresponding to the i-th output of the linear tracking differentifier, i=1, 2,..., n, and n is the order of the controlled object.

[0067] Embodiment three:

[0068] The embodiment is further designed on the basis of embodiment one, and in the example, the gain parameter satisfies the following constraint: So that the system closed-loop zero point is configured at-ω c , that is, (s+ω c ) n -s n is changed to (s+ω c )n-1 .

[0069] Embodiment four:

[0070] The embodiment is further designed on the basis of embodiment one, and in the embodiment, the gain parameter satisfies the following constraint: so that the system closed-loop zero point is configured at -ω c / ε, that is, (s+ω c ) n -s n is changed to (s+εω c ) n-1 , wherein ε is a zero point coefficient, so that the closed-loop step response satisfies that the maximum overshoot is not more than 5%.

[0071] Embodiment five:

[0072] The embodiment is further designed on the basis of embodiment four, and in the embodiment, the value range of the zero point coefficient ε is ε>1.

[0073] Embodiment six:

[0074] The embodiment provides a linear active disturbance rejection controller, which is obtained by the design method of the linear active disturbance rejection controller of any one of the above embodiments, as shown in the following formula (1), the linear active disturbance rejection controller comprises a linear tracking differentiator (also referred to as “LTD”), a variable parameter linear error feedback control law (also referred to as “LSEF”), and a linear extended state observer (also referred to as “LESO”). Figure 1

[0075] Wherein, the input of the linear tracking differentiator is v0, and the output is v i , i=1, 2, …, n;

[0076] The input u of the controlled object is multiplied by b0 to obtain a gain as a first input signal of the linear extended state observer;

[0077] The output y of the controlled object is taken as a second input signal of the linear extended state observer;

[0078] The output of the linear extended state observer is z i , i=1, 2, …, n+1;

[0079] The input parameter of the variable parameter linear error feedback control law is variable, the linear error feedback control law in the embodiment is also referred to as the variable parameter linear error feedback control law, and specifically, e i =λ i ·v i -z i , i=1, 2, …, n, λ i is a gain parameter of the linear error feedback control law input component, that is, a weight factor; ​

[0080] The output u0 of the variable parameter linear error feedback control law and the (n+1)th dimension output component z of the extended state observer n+1 The difference is taken and multiplied by the 1 / b0 gain to obtain the input u of the controlled object.

[0081] Further, the expression of the n-order controlled object in this example is

[0082]

[0083] In the formula, y is the output of the controlled object; x is the state variable of the controlled object; f is a function related to the state variable x; d is the external disturbance;

[0084] The expression of the linear extended state observer is

[0085]

[0086] In the formula, β i is the polynomial coefficient of the linear extended state observer, satisfying s n+1 +β1s n +…+β n s+β n+1 =(s+ω0) n+1 , wherein, ω o is the bandwidth of the linear extended state observer;

[0087] The expression of the linear tracking differentiator is

[0088]

[0089] In the formula, v0 is the input signal; r is the parameter of the linear extended tracking differentiator, r=ω o .

[0090] Embodiment Seven

[0091] The embodiment provides a parameter setting method of a second-order linear active disturbance rejection controller designed based on the design method of the linear active disturbance rejection controller in the above-described embodiment one, the second-order linear active disturbance rejection controller performing control on a second-order object without delay, and the method comprises the following steps.

[0092] Step 1) setting the ratio of the bandwidth ω c of the linear error feedback law to the bandwidth ω o of the extended state observer to be equal to the parameter λ, that is, Setting the value of the parameter λ, in this example, λ=0.1, and setting the bandwidth of the second-order linear active disturbance rejection controller based on the variable parameter linear error feedback control law to be ω a , ω a satisfying ​

[0093]

[0094] Step 2) Calculate the bandwidth ω of the second-order linear active disturbance rejection controller according to the parameter tuning formula as follows: a and the control quantity gain b0 of the controlled object: ω a = 1 / T, b0 = K / T 2 , and then obtain ω c and ω o based on the relationship between λ and ω a , and obtain the bandwidth ω c of the linear error feedback law and the bandwidth ω o of the extended state observer:

[0095]

[0096] Step 3) Set the gain parameters of the second-order linear active disturbance rejection controller to configure the zero points of the forward channel of the control system, i.e., the zero points of the closed-loop system.

[0097] Step 4) Perform automatic control with the calculated ω c , ω o , b0 and the set gain parameters to complete parameter tuning.

[0098] Further, the setting method of the gain parameters in Step 3) includes:

[0099] Set the initial values of the first gain parameter λ1 corresponding to the first input of the linear error feedback control rate of the variable parameter and the second gain parameter corresponding to the second input of the linear error feedback control rate of the variable parameter: In the formula, ε is the zero point coefficient;

[0100] Take ε = 1 as the initial value and gradually increase it to ε = 1.68, and take the value of the gain parameter that meets the preset overshoot requirement in the gradual increase process as the final setting value of the gain parameter.

[0101] Further, for the controlled object in Figure 2 , the controlled object is a second-order object to obtain the steady-state gain K and the inertia time constant of the controlled object; set the bandwidth ω c of the linear error feedback law and the bandwidth ω o of the extended state observer in the ratio of λ, i.e. Set the bandwidth ω a of the LADRC control system based on the linear state feedback control law of the variable parameter, which satisfies and further deduce According to the controlled object, the LADRC parameter tuning formula is as follows: ω a = 1 / T, b0 = K.

[0102] For n-order non-delayed object, the n-order improved linear active disturbance rejection controller can be designed according to the method of the application, and the parameter setting method can refer to the 2-order control process.

[0103] Embodiment eight:

[0104] The electronic device includes a memory and a processor, the memory stores a computer program, and the processor is used to call and run the computer program stored in the memory to execute the method of any one of the above embodiments.

[0105] The computer readable storage medium stores a computer program, and the computer program is executed by the processor to realize the steps of any one of the above embodiments.

[0106] Application embodiment one:

[0107] This example describes the principle of the linear active disturbance rejection controller designed by the design method of the application. For n-order linear ADRC, after expansion, u=G v (s)v0-G y (s)y, and the closed-loop transfer function combined with the control object is

[0108] The poles of the closed-loop transfer function are the roots of the closed-loop characteristic equation 1+G y (s)G(s)=0.

[0109] The closed-loop stability is only related to G y (s) and is irrelevant to G v (s). Let

[0110] D1=s n+1 +β1s n +…+β n s+β n+1 =(s+ω o ) n+1

[0111] D2=s n +k n s n-1 +…+k2s+k1=(s+ω c ) n

[0112] D1D2=D3s n+1 +D4

[0113] Then

[0114] Assuming that a linear tracking differentiator (also referred to as "LTD") is used in the standard ADRC, then where linear extended tracking differentiator parameter r = ω o

[0115]

[0116] In particular, when n = 2, there are

[0117] D1 = (s + ω o ) 3 , D2 = (s + ω c ) 2

[0118]

[0119] Assuming a second-order object

[0120]

[0121] It can be proved that the absolute value of the real part of the closed-loop transfer function pole is near ω c (ω c ≤ ω o ), but there is a zero point equal to -ω c / 2, so it is known that the step response of the closed-loop system has overshoot.

[0122] In fact, if the ADRC can completely compensate for internal and external disturbances, the object will be transformed into an integral series type, and the closed-loop transfer function under ideal conditions must be Its step response will certainly overshoot when n ≥ 2.

[0123] The linear active disturbance rejection controller of the application modifies the n-order LTD and the linear feedback control law to where Thus, the improved satisfies the zero point -ω c .

[0124] Still aiming at the above-mentioned second-order object

[0125]

[0126] D1 = (s + ω o ) 3 , D2 = (s + ω c ) 2

[0127]

[0128] Therefore

[0129] ​​​

[0130] make get Application Example 2:

[0131] This embodiment is for the following: Figure 2 The second-order time-delay-free model shown The linear active disturbance rejection controller and its parameter tuning method proposed in this invention were used for simulation verification. The simulation employed a fixed-step Euler method with a step size of 0.01. This example also selected the standard ADRC and... The open-loop response curve is compared with that of the LADRC control system based on the linear state feedback control law with variable parameters.

[0132] Given system parameters T = 1 and K = 1, and since τ = 0, take... Get And by setting λ = 0.1, we can obtain... The controller's variable parameters are λ1 = 1 and λ2 = 0.5.

[0133] The step response curve obtained from the operation is as follows: Figure 3 As shown, the standard ADRC maintains Under the premise that the overshoot is about 10%, which is much higher than that of the improved ADRC, the results show that the control effect is significantly improved after the improvement, proving the necessity of the present invention, that is, solving the overshoot problem of the standard ADRC in the absence of time delay.

[0134] Furthermore, by setting the values ​​of ε to 1, 1.2, 1.4 and 1.68 respectively, we obtain the values ​​of λ2 to be 0.5, 0.6, 0.7 and 0.84 respectively, in order to verify the effect of different values ​​of parameter ε on the overshoot.

[0135] The simulation used the Euler method with a fixed step size of 0.01. The resulting step response curve is shown below. Figure 4 As shown, the results indicate that as the value of the controller parameter ε increases from 1 to 1.68, the overshoot of the response curve also increases. When ε = 1.68, the overshoot reaches exactly 5%. Therefore, the value of parameter ε in the LADRC control system based on the variable parameter linear state feedback control law is 1 ≤ ε ≤ 1.68.

[0136] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of designing a linear active disturbance rejection controller, characterized in that, The linear active disturbance rejection controller comprises a linear tracking differentiator, a linear error feedback control law and a linear extended state observer; the design method comprises: a gain parameter considering the influence of the order of the controlled object on the overshoot in the step response of the controller is constructed; the gain parameter is introduced into the linear error feedback control law, so that the input of the linear error feedback control law is the difference between the product of the output value of the linear tracking differentiator and the gain parameter and the output of the linear extended state observer; the expression of the linear error feedback control law is where u0 is the output of the linear error feedback control law; u is the input of the controlled object; b0 is the control quantity gain of the controlled object; v i is the i-th output of the linear tracking differentiator, i = 1, 2, …, n; z i is the i-th output of the linear extended state observer, i = 1, 2, …, n + 1; k i is the parameter of the linear error feedback control law, satisfying s n + k1s n-1 + … + k n-1 s + k n = (s + ω c ) n , where ω c is the bandwidth of the linear error feedback control law; λ i is the gain coefficient corresponding to the i-th output of the linear tracking differentiator.

2. The method for designing a linear active disturbance rejection controller according to claim 1, wherein, the gain parameter satisfies the following constraint: In the formula, λ i is the gain coefficient corresponding to the i-th output of the linear tracking differentiator, i = 1, 2, …, n, and n is the order of the controlled object.

3. The method for designing a linear active disturbance rejection controller according to claim 1, wherein, The gain parameters satisfy the following constraints: such that the system closed-loop zero is configured at -ω c .

4. The method for designing a linear active disturbance rejection controller according to claim 1, wherein, The gain parameters satisfy the following constraint: such that the system closed-loop zero is configured at -ω c / ε, where ε is a zero coefficient.

5. The method for designing a linear active disturbance rejection controller according to claim 4, wherein, the value range of the zero point coefficient ε is ε>1.

6. A linear active disturbance rejection controller characterized by, The linear tracking differentiator, the linear error feedback control rate with variable parameters and the linear extended state observer are included; wherein the input of the linear tracking differentiator is v0, and the output is v i , i = 1, 2, …, n; the input u of the controlled object is multiplied by b0 to be used as the first input signal of the linear extended state observer; the output y of the controlled object is used as the second input signal of the linear extended state observer; The output of the linear extended state observer is z i , i = 1, 2, …, n + 1; the input e of the linear error feedback control law of the variable parameter i = λ i · v i - z i , i = 1, 2, …, n, λ i is a gain parameter of the input component of the linear error feedback control law; The output u0 of the linear error feedback control law of the variable parameter is multiplied by the (n+1)th dimension output component z of the extended state observer n+1 The difference is multiplied by the 1 / b0 gain to obtain the input u of the controlled object.

7. The linear active disturbance rejection controller according to claim 6, characterized in that the expression of the controlled object is wherein y is the output of the controlled object; x is the state variable of the controlled object; f is a function related to the state variable x; and d is an external disturbance; the expression of the linear extended state observer is where β i are polynomial coefficients of the linear extended state observer, satisfying s n+1 + β1s n + … + β n s + β n+1 = (s + ω0) n+1 where ω0 i = 1, 2, …, n + 1; ω o is the bandwidth of the linear extended state observer; the expression of the linear tracking differentiator is where v0 is an input signal; r is a parameter of the linear extended tracking differentiator, r = ω o .

8. A parameter tuning method of a second order linear active disturbance rejection controller designed based on the design method of the linear active disturbance rejection controller according to claim 1, the second order linear active disturbance rejection controller being for a second order object without delay is controlled, characterized in that the method comprises: Step 1) Set the ratio of the bandwidth ω of the linear error feedback law to the bandwidth ω of the extended state observer equal to the parameter λ, i.e. c Step 2) Set the ratio of the bandwidth ω of the linear error feedback law to the bandwidth ω of the extended state observer equal to the parameter λ, i.e. o Step 3) Set the value of the parameter λ and set the bandwidth ω of the second order linear active disturbance rejection controller based on the variable parameter linear error feedback control law to be ω a , ω a ​​ Step 2) Calculate the bandwidth ω of the second order linear active disturbance rejection controller according to the parameter tuning formula as follows a and the control quantity gain b0 of the controlled object: ω a = 1 / T, b0 = K / T 2 , and then obtain the bandwidth ω of the linear error feedback law based on ω c and ω o and the relationship between λ and ω a c and the bandwidth ω of the extended state observer: o : ​ Step 3) setting the gain parameter of the second-order linear active disturbance rejection controller to configure the zero point of the forward channel of the control system, i.e. the zero point of the closed-loop system; Step 4) Automatic control is completed with the calculated ω c , ω o , b0 and the set gain parameters.

9. The parameter tuning method of a linear active disturbance rejection controller according to claim 8, wherein, the setting method of the gain parameter in the step 3) comprises: The first gain parameter λ1 of the first path input in the linear error feedback control rate corresponding to the variable parameter and the initial value of the second gain parameter of the second path input in the linear error feedback control rate corresponding to the variable parameter are set: In the formula, ε is a zero point coefficient. taking ε=1 as the initial value and gradually increasing it to ε=1.68, and taking the value of the gain parameter meeting the preset overshoot requirement in the gradual increasing process as the final setting value of the gain parameter.

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