ADRC control system based on intelligent variable bandwidth expansion state observer and advanced internal model control system

Abstract

The invention discloses an ADRC control system and an advanced internal model control system based on an intelligent variable bandwidth extended state observer, and compared with other internal model control methods needing to establish an accurate internal model, the internal model of the control system is obtained based on standard dynamics Gcl (s) given by the ADRC. A new and practical solution is provided for the internal model control design of a complex nonlinear system; the modeling process of the control system is simplified, and the method can be expanded to other control methods needing to establish accurate models; according to the method, the observation phase lag problem and the noise sensitivity problem of an existing observer are solved, the design process is simple, and application and popularization in engineering are facilitated. According to the method, an internal model in traditional internal model control is replaced by standard dynamics given by ADRC, and a new and practical solution is provided for design of an internal model controller of a complex nonlinear system.

Description

Technical Field

[0001] The present invention belongs to the field of advanced control, and in particular relates to a design method of an ADRC control system based on an intelligent variable bandwidth extended state observer and a design method of an advanced internal model control system, as well as an ADRC control system and an advanced internal model control system based on an intelligent variable bandwidth extended state observer obtained by design. Background Art

[0002] With the development of science and technology, the application of automatic control technology in production and life is becoming more and more extensive. The use of automatic control technology can greatly reduce the demand for manpower. At present, my country's automatic control technology has been widely used in many fields, but compared with some developed countries, it still has a large room for development. Therefore, combined with the current form and future development trend of automatic control technology, it is urgent to continue to study new control methods to further improve control performance and reduce costs.

[0003] According to the degree of reliance on the model, existing control methods can be divided into three categories: 1. Methods that rely on minimal model information, such as PID control; 2. Methods that rely on partial model information, such as Active Disturbance Rejection Control (ADRC), fuzzy control and sliding mode control; 3. Methods that rely on more model information, such as feedback linearization control, internal model control (IMC) and model reference adaptive control. For PID control, although it is simple and easy to use, it passively eliminates errors and its performance is limited in the presence of uncertainty and / or interference. Although fuzzy control and sliding mode control are suitable for complex nonlinear systems and can achieve ideal performance, the rule formulation of fuzzy control is subjective, and sliding mode control has the problem of control signal jitter. For control methods that rely on more model information, although the control effect is better, the high reliance on model information limits their application.

[0004] In the presence of uncertainty and interference, the active disturbance rejection controller ADRC based on the extended state observer (ESO) is not only easy to implement, but also can achieve satisfactory performance. In addition, if an accurate internal model can be obtained, IMC can also achieve the desired performance. ADRC can be explained under the framework of two-degree-of-freedom IMC. The combination of ADRC and IMC has continued to attract attention in recent years and has been applied in many fields. Invention Patent No. 2019112412522 provides a variable bandwidth active disturbance rejection control method, which uses the estimated error of the system output to dynamically adjust the observer bandwidth (referred to as: SESO-based PD controller). There is still a phase lag problem, which needs to be further optimized. And the prior art also has the following problems:

[0005] 1. For IMC, even if combined with ADRC, there is still the problem of high cost of obtaining accurate internal models;

[0006] 2. Although ESO, the core of ADRC, can effectively estimate constant disturbances, it cannot accurately estimate time-varying disturbances and has the problem of observation phase lag. Especially in the case of high-frequency total interference, the performance will be further deteriorated;

[0007] 3. Under a fixed observer bandwidth, the ESO cannot accurately reconstruct the total disturbance whose frequency is not within its bandwidth. Summary of the invention

[0008] In view of the deficiencies in the prior art, the present invention provides a design method for an ADRC control system based on an intelligent variable bandwidth extended state observer and a design method for an advanced internal model control system, as well as an ADRC control system and an advanced internal model control system based on an intelligent variable bandwidth extended state observer obtained by design.

[0009] The specific technical solutions of the present invention are as follows:

[0010] A design method of an ADRC control system based on an intelligent variable bandwidth extended state observer comprises the following steps:

[0011] S1: Based on the mathematical model of the n-th order controlled object, the internal uncertainty and external disturbance of the controlled object are regarded as the total disturbance f and used as the state variables of the system. The mathematical model of the controlled object is expressed as an extended state equation, a linear extended state observer with fixed bandwidth is constructed, and the observer bandwidth ω is set according to the bandwidth parameterization method. o and the gain of the extended state observer L = [β 1 ,β 2 ,…β n ,β n+1 ] T ;

[0012] S2: Output variable z based on the extended state observer 1 ,z 2 ,...z n , design state feedback control law u 0 =k 1 (rz 1 )-k 2 z 2 -…k n z n , and set the controller bandwidth ω according to the bandwidth parameterization method c ,ω c >0, and then design the controller gain k i(i=1,2,…n); r is the set value;

[0013] S3: Estimation of the total disturbance z by the integrated extended state observer n+1 and the state feedback control law u 0 , design control law u=(u 0 -z n+1 ) / b 0 ; b 0 is the adjustable controller gain;

[0014] S4: Let ω' o =ω o +η|z n+1 -f|, construct an intelligent variable bandwidth extended state observer, and estimate the deviation |z with the total disturbance n+1 -f| is used as the adjustment basis to dynamically adjust the bandwidth of the observer. The bandwidth of the intelligent variable bandwidth expansion state observer is expressed as follows:

[0015]

[0016] Where f = y (n) -b 0 u,y (n) is the nth-order differential of the output of the controlled object, which can be extracted by the tracking differentiator; b 0 is the adjustable controller gain, u is the input of the controlled object; η is the telescopic factor, which is used to adjust the bandwidth range of the observer, η>0;

[0017] The adaptive variable gain of the bandwidth parameterization configuration is as follows:

[0018]

[0019] S5: The intelligent variable bandwidth linear expansion observer is designed as follows:

[0020]

[0021] S6: Based on the output of the intelligent variable bandwidth extended state observer, the control law is adjusted accordingly:

[0022]

[0023] Among them, z 1SBW ,z 2SBW ,…z iSBW ,…z (n+1)SBW is the output of the intelligent variable bandwidth extended state observer;

[0024] S7: Use the ADRC control system based on intelligent variable bandwidth extended state observer to complete the control of the n-order controlled object and adjust the controller parameter ω o ,ωc , b 0 and η make the system work normally until the desired control effect is achieved.

[0025] A design method for an advanced internal model control system based on an intelligent variable bandwidth extended state observer comprises the following steps:

[0026] S8: ADRC control system based on intelligent variable bandwidth extended state observer designed based on the above method. When the extended state observer is reasonably designed, that is, z n+1 ≈f, the controlled object can be simplified to an n-order integral system y (n) =u 0 -z n+1 +f≈u 0 ; The closed-loop transfer function of the n-th order ADRC without zeros can be obtained, that is, the standard closed-loop ADRC system dynamics G cl (s):

[0027]

[0028] Among them, k i (i=1,2,…n) is the controller gain;

[0029] S9: Based on the standard closed-loop ADRC system dynamics G cl (s), and design the internal model controller G by combining the following formula c (s), internal model G m (s) and filter f c (s):

[0030]

[0031] f c (s) = 1 / (1 + αs) n

[0032] Where n is the order of the controlled object, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics. Compared with the standard closed-loop ADRC system dynamics G cl (s), where

[0033] S10: The internal model controller based on the intelligent variable bandwidth extended state observer completes the control of the controlled object and adjusts the controller parameters α, ω o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0034] The design method of ADRC control system based on intelligent variable bandwidth extended state observer, for the second-order ADRC controller, includes the following steps:

[0035] S1: Establish a mathematical model of the second-order controlled object and obtain the model parameters of the controlled object through model identification; for the second-order controlled object, the mathematical model is:

[0036]

[0037] Among them, u is the control input of the system; y is the output of the system; is the first-order differential of the system output y; is the uncertainty inside the system; ω is the external disturbance; b is the gain of the controlled object;

[0038] The internal uncertainty and external disturbance of the controlled object are regarded as the total disturbance and as the state variables of the system. The mathematical model of the controlled object is expressed as an extended state equation.

[0039]

[0040] Among them, x 1 =y(t), The total disturbance is expressed as b 0 is the adjustable controller gain;

[0041] S2: Based on the extended state equation, a fixed bandwidth extended state observer is constructed:

[0042]

[0043] And set the observer bandwidth ω according to the bandwidth parameterization method o ,ω o >0, and then design the observer gain L=[β 1 ,β 2 ,β 3 ];

[0044] Among them, z 1 is the estimate of the system output y; z 2 is the estimate of the differential of the system output y; z 3 is the estimate of the total disturbance;

[0045] S3: Output variable z based on the extended state observer 1 ,z 2 , design PD controller u 0 =k 1 (rz 1 )-k 2 z 2, and set the PD controller bandwidth ω according to the bandwidth parameterization method c ,ω c >0, and then design the PD controller gain k 1 ,k 2 ;

[0046] S4: Estimation of the total disturbance z by the integrated extended state observer 3 and the PD controller output u 0 , generate control output u according to the control law;

[0047]

[0048] in, r is the set value;

[0049] S5: Let ω' o =ω o +η|z 3 -f|, construct an intelligent variable bandwidth extended state observer, and estimate the deviation |z with the total disturbance 3 -f| is used as the adjustment basis to dynamically adjust the bandwidth of the observer. The bandwidth of the intelligent variable bandwidth expansion state observer is expressed as follows:

[0050]

[0051] in, is the second-order differential of the output of the controlled object, which can be extracted by the tracking differentiator; b 0 is the adjustable controller gain, u is the input of the controlled object; η is the telescopic factor, which is used to adjust the bandwidth range of the observer, η>0;

[0052] The adaptive variable gain of the bandwidth parameterization configuration is as follows:

[0053]

[0054] S6: Design an intelligent variable bandwidth extended state observer and adjust the control law accordingly;

[0055]

[0056] Among them, z 1SBW ,z 2SBW ,z 3SBW is the output of the intelligent variable bandwidth extended state observer; η>0 is the scaling factor, which is used to adjust the variation range of the observer bandwidth.

[0057] Accordingly, the control law is adjusted as follows:

[0058]

[0059] S7, ADRC control system based on intelligent variable bandwidth extended state observer completes the control of the second-order controlled object and adjusts the controller parameter ω o ,ω c , b 0 and η, so that the system can work normally until the desired control effect is achieved.

[0060] The design method of an advanced internal model control system based on an intelligent variable bandwidth extended state observer includes the following steps:

[0061] S8: Using the above ADRC control system based on intelligent variable bandwidth extended state observer, for the second-order ADRC controller, ignoring the estimation deviation of the extended state observer for the total disturbance, the second-order controlled object can be equivalent to an integral series type, that is, the standard closed-loop ADRC system dynamics G cl (s):

[0062]

[0063] S9: Based on the standard closed-loop ADRC system dynamics G cl (s) Design the internal model controller G based on the following formula c (s), internal model

[0064] G m (s) and filter f c (s):

[0065]

[0066] f c (s) = 1 / (1 + αs) 2

[0067] Where n is the order of the controlled object, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics. Compared with the standard closed-loop ADRC system dynamics G cl The deviation between (s),

[0068] S10: The internal model controller based on the intelligent variable bandwidth extended state observer completes the control of the controlled object and adjusts the controller parameters α, ω o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0069] Further, in step S10, when adjusting the controller parameters, at a given adjustment time t s , when the error tolerance range is ±5%, the initial value of the filter parameter α can be determined by the following formula:

[0070] t s =3.5α

[0071] Further, in step S10, when adjusting the controller parameters, under the given overshoot σ%, the PD controller bandwidth ω c The initial value of can be determined by the following formula:

[0072]

[0073] The n-th order ADRC control system is obtained by adopting the design method of the ADRC control system based on the intelligent variable bandwidth extended state observer.

[0074] By adopting the above-mentioned design method of advanced internal model control system based on intelligent variable bandwidth extended state observer, an n-order advanced internal model control system is obtained.

[0075] The second-order ADRC control system is obtained by adopting the design method of the ADRC control system based on the intelligent variable bandwidth extended state observer.

[0076] The second-order advanced internal model control system is obtained by adopting the design method of the advanced internal model control system based on the intelligent variable bandwidth extended state observer.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] 1. The present invention proposes an ADRC control system and design method based on an intelligent variable bandwidth extended state observer (Linear Extended State Observer with Scalable Bandwidth, LESO-SBW). The control system dynamically adjusts the observer bandwidth according to the change of the total disturbance estimation deviation. Compared with the observer based on the system output estimation error variable bandwidth, since the estimated error of the system output is caused by the total disturbance estimation error, the phase of the estimated error of the system output lags behind the phase of the total disturbance estimation error. The present invention can obtain a more timely and more advanced total disturbance estimation, realize rapid response changes, and can timely adjust the observer bandwidth under the premise of satisfying the observer gain, effectively suppressing the noise in the steady state.

[0079] 2. The present invention overcomes the problems of observation phase lag and system sensitivity to noise in existing observers, and the design process is simple, which is convenient for promotion and application in engineering.

[0080] 3. Compared with other methods based on interference estimation and compensation, the present invention has good estimation accuracy for time-varying disturbances such as ramp and sine in addition to constant disturbances; it has strong ability to resist sudden load disturbances; this method is suitable for designing self-disturbance rejection controllers of various orders and has good versatility; and the adjustable control parameters have clear physical meanings and are easy to set.

[0081] 4. The advanced internal model control system based on intelligent variable bandwidth expanded state observer (LESO-SBWbased Advanced Internal Model Control, LESO-SBW-AIMC) and design method proposed in the present invention, compared with other internal model control systems that require the establishment of accurate internal models, the internal model of the present invention is composed of the standard closed-loop ADRC system dynamics G cl (s) instead, there is no need to establish an accurate mathematical model of the controlled object, and the model accuracy is guaranteed, which improves the overall performance of the internal model control. At the same time, the intelligent variable bandwidth expansion state observer is used to make the actual closed-loop ADRC system dynamics Compared with the standard closed-loop ADRC system dynamics G cl The deviation between (s) is getting smaller and smaller, which further makes the internal model required by IMC more accurate. The present invention provides a new and practical solution for the internal model control design of complex nonlinear systems; it simplifies the modeling process of the control system and can be extended to other controls that require the establishment of accurate models.

[0082] Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention will be more clearly understood, and they constitute a part of the specification. Together with the following specific embodiments, they are used to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. Among them:

[0084] Figure 1 It is a second-order ADRC control system based on LESO-SBW;

[0085] Figure 2 It is the existing internal model control structure;

[0086] Figure 3 It is an internal model control system based on LESO-SBW-AIMC;

[0087] Figure 4 For different observer bandwidth ω o Next 1SBW With x 1 and z 1SBW Frequency domain response curve of and u;

[0088] Figure 4 Where (a) is z 1SBW With x 1 The frequency domain response of z 1SBW Frequency domain response curve of and u;

[0089] Figure 5 for Figure 3 The equivalent structure of LESO-SBW-AIMC;

[0090] Figure 6 is the time domain response curve of the system;

[0091] Figure 7 is the system frequency domain response curve;

[0092] Figure 8 It is an n-order ADRC control system based on LESO-SBW;

[0093] Fig. 9 Based on Figure 8 LESO-SBW's advanced internal model control system;

[0094] Fig.10 Trajectory tracking comparison diagram of LADRC, PD control of scaled bandwidth LESO based on system output estimation error, and PD control based on LESO-SBW;

[0095] Fig.11 The control signal comparison diagram of LADRC, SESO-based PD control and LESO-SBW-based PD control;

[0096] Fig.12 Comparison of total disturbance estimates of ESO, SESO and LESO-SBW;

[0097] Fig.13 This is the simulation result diagram output by LESO-SBW;

[0098] Fig.14 ω o =36 and ω o =12 when the trajectory tracking comparison diagram of PD control based on LESO-SBW;

[0099] Fig.15 Trajectory tracking comparison diagram of IMC, LADRC, IMC based on LADRC and LESO-SBW-AIMC;

[0100] Fig.16 Comparison diagram of control errors of IMC, LADRC, IMC based on LADRC and LESO-SBW-AIMC;

[0101] Fig.17 Comparison chart of control signals of IMC, LADRC, IMC based on LADRC and LESO-SBW-AIMC. DETAILED DESCRIPTION

[0102] Embodiment 1:

[0103] This example provides an ADRC control system based on an intelligent variable bandwidth extended state observer. The design method includes the following steps:

[0104] S1: Based on the mathematical model of the n-th order controlled object, the internal uncertainty and external disturbance of the controlled object are regarded as the total disturbance f and used as the state variables of the system. The mathematical model of the controlled object is expressed as an extended state equation, a linear extended state observer with fixed bandwidth is constructed, and the observer bandwidth ω is set according to the bandwidth parameterization method. o and the gain of the extended state observer L = [β 1 ,β 2 ,…β n ,β n+1 ] T ;

[0105] S2: Output variable z based on the extended state observer 1 ,z 2 ,...z n , design state feedback control law u 0 =k 1 (rz 1 )-k 2 z 2 -…k n z n , and set the controller bandwidth ω according to the bandwidth parameterization method c ,ω c >0, and then design the controller gain k i (i=1,2,…n); r is the set value;

[0106] S3: Estimation of the total disturbance z by the integrated extended state observer n+1 and the state feedback control law u 0 , design control law u=(u 0 -z n+1 ) / b 0 ; b 0 is the adjustable controller gain;

[0107] S4: Let ω'o =ω o +η|z n+1 -f|, construct an intelligent variable bandwidth extended state observer, and estimate the deviation |z with the total disturbance n+1 -f| is used as the adjustment basis to dynamically adjust the bandwidth of the observer. The bandwidth of the intelligent variable bandwidth expansion state observer is expressed as follows:

[0108] ω' o =ω o +η|z n+1 -f|=ω o +η|z n+1 -(y (n) -b 0 u)|

[0109] Where f = y (n) -b 0 u,y (n) is the nth-order differential of the output of the controlled object, which can be extracted by the tracking differentiator; b 0 is the adjustable controller gain, u is the input of the controlled object; η is the telescopic factor, which is used to adjust the bandwidth range of the observer, η>0;

[0110] The adaptive variable gain of the bandwidth parameterization configuration is as follows:

[0111]

[0112] S5: The intelligent variable bandwidth linear expansion observer is designed as follows:

[0113]

[0114] S6: Based on the output of the intelligent variable bandwidth extended state observer, the control law is adjusted accordingly:

[0115]

[0116] Among them, z 1SBW ,z 2SBW ,…z iSBW ,…z (n+1)SBW is the output of the intelligent variable bandwidth extended state observer;

[0117] S7: Use the ADRC control system based on intelligent variable bandwidth extended state observer to complete the control of the n-order controlled object and adjust the controller parameter ω o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0118] Based on the above design steps S1-S7, an ADRC control system based on an intelligent variable bandwidth extended state observer is obtained.

[0119] Embodiment 2:

[0120] Based on the first embodiment, this embodiment provides an advanced internal model control system based on an intelligent variable bandwidth extended state observer, and the design method includes the following steps:

[0121] S8: Based on the ADRC control system based on the intelligent variable bandwidth extended state observer designed in the first embodiment, when the extended state observer is reasonably designed, that is, z n+1 ≈f, the controlled object can be simplified to an n-order integral system y (n) =u 0 -z n+1 +f≈u 0 ; The closed-loop transfer function of the n-th order ADRC without zeros can be obtained, that is, the standard closed-loop ADRC system dynamics G cl (s):

[0122]

[0123] Among them, k i (i=1,2,…n) is the controller gain; all controller poles are configured to -ω c , we can get s (n) +k n s (n-1) +…+k 2 s+k 1 =(s+ω c ) n The characteristic polynomial of c is the controller bandwidth;

[0124] S9: Based on the standard closed-loop ADRC system dynamics G cl (s), and design the internal model controller G by combining the following formula c (s), internal model G m (s) and filter f c (s):

[0125]

[0126] f c (s) = 1 / (1 + αs) n

[0127] Where n is the order of the controlled object, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics. Compared with the standard closed-loop ADRC system dynamics G cl (s), where

[0128] S10: The internal model controller based on the intelligent variable bandwidth extended state observer completes the control of the controlled object and adjusts the controller parameters α, ω o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0129] Based on the above design steps S1-S10, an advanced internal model control system based on an intelligent variable bandwidth extended state observer is obtained.

[0130] Embodiment three:

[0131] like Figure 1 As shown, the design method of the second-order ADRC control system based on the intelligent variable bandwidth extended state observer includes the following steps:

[0132] S1: Establish a mathematical model of the second-order controlled object and obtain the model parameters of the controlled object through model identification; for the second-order controlled object, the mathematical model is:

[0133]

[0134] Among them, u is the control input of the system; y is the output of the system; is the first-order differential of the system output y; is the uncertainty inside the system; ω is the external disturbance; b is the gain of the controlled object;

[0135] The internal uncertainty and external disturbance of the controlled object are regarded as the total disturbance and as the state variables of the system. The mathematical model of the controlled object is expressed as an extended state equation.

[0136]

[0137] Among them, x 1 =y(t), The total disturbance is expressed as b 0 is the adjustable controller gain;

[0138] S2: Based on the extended state equation, a fixed bandwidth extended state observer is constructed:

[0139]

[0140] And set the observer bandwidth ω according to the bandwidth parameterization method o ,ω o >0, and then design the observer gain L=[β 1 ,β 2 ,β 3 ];

[0141] Among them, z 1 is the estimate of the system output y; z 2 is the estimate of the differential of the system output y; z 3 is the estimate of the total disturbance;

[0142] S3: Output variable z based on the extended state observer 1 ,z 2 , design PD controller u 0 =k 1 (rz 1 )-k 2 z 2 , and set the PD controller bandwidth ω according to the bandwidth parameterization method c ,ω c >0, and then design the PD controller gain k 1 ,k 2 ;

[0143] S4: Estimation of the total disturbance z by the integrated extended state observer 3 and the PD controller output u 0 , generate control output u according to the control law;

[0144]

[0145] in, r is the set value;

[0146] S5: Let ω' o =ω o +η|z 3 -f|, construct an intelligent variable bandwidth extended state observer, and estimate the deviation |z with the total disturbance 3 -f| is used as the adjustment basis to dynamically adjust the bandwidth of the observer. The bandwidth of the intelligent variable bandwidth expansion state observer is expressed as follows:

[0147]

[0148] in, is the second-order differential of the output of the controlled object, which can be extracted by the tracking differentiator; b 0 is the adjustable controller gain, u is the input of the controlled object; η is the telescopic factor, which is used to adjust the bandwidth range of the observer, η>0;

[0149] The adaptive variable gain of the bandwidth parameterization configuration is as follows:

[0150]

[0151] S6: Design an intelligent variable bandwidth extended state observer and adjust the control law accordingly;

[0152]

[0153] Among them, z 1SBW ,z 2SBW ,z 3SBW is the output of the intelligent variable bandwidth extended state observer; η>0 is the scaling factor, which is used to adjust the variation range of the observer bandwidth.

[0154] Accordingly, the control law is adjusted as follows:

[0155]

[0156] S7, ADRC control system based on intelligent variable bandwidth extended state observer completes the control of the second-order controlled object and adjusts the controller parameter ω o ,ω c , b 0 and η, so that the system can work normally until the desired control effect is achieved.

[0157] Based on the above design steps S1-S7, an ADRC control system based on an intelligent variable bandwidth extended state observer is obtained.

[0158] Embodiment 4:

[0159] Based on the third embodiment, this embodiment further designs an advanced internal model control system (LESO-SBW-AIMC) based on an intelligent variable bandwidth extended state observer. The existing internal model control structure is as follows: Figure 2 As shown, the advanced internal model control system of the present application is as follows Figure 3 As shown, the design steps for the second-order system are as follows:

[0160] S8: Ignoring the estimation error of the extended state observer for the total disturbance, the second-order controlled object can be equivalent to an integral series type, that is, the standard closed-loop ADRC system dynamics G cl (s):

[0161]

[0162] S9: Based on the standard closed-loop ADRC system dynamics G cl (s), and design the internal model controller G by combining the following formula c (s), internal model G m (s) and filter f c (s):

[0163]

[0164] f c(s) = 1 / (1 + αs) 2

[0165] Where n is the order of the controlled object, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics G p (s) and the standard closed-loop ADRC system dynamics G cl The deviation between (s),

[0166] S10: The internal model controller based on the intelligent variable bandwidth extended state observer completes the control of the controlled object and adjusts the controller parameters α, ω o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0167] Based on the above design steps S1-S10, an advanced internal model control system based on an intelligent variable bandwidth extended state observer is obtained.

[0168] Analysis of the design principle of the advanced internal model control system in this example:

[0169] like Figure 2 , Figure 3 It can be seen that the present invention uses ADRC to control the controlled object, and the closed-loop dynamics based on ADRC can be obtained. That is, the red dotted box indicates that To represent the entire closed-loop system, the actual model in the internal model control is That is

[0170] When the present invention designs the inner mold structure, G cl (s) as the internal model G m (s), combined with the filter f c (s) = 1 / (1 + αs) 2 The internal model controller G c (s), i.e.

[0171] for and G cl (s) In simple terms, The actual closed-loop ADRC dynamics is obtained by controlling the controlled object through ADRC. However, due to the uncertainty and disturbance in the system, the ESO has estimation deviation and cannot fully meet the standard closed-loop ADRC system dynamics. Actual closed-loop ADRC system dynamics Compared with the standard closed-loop ADRC system dynamics G cl There will be a deviation Δ between (s), that is,

[0172] Internal model control relies on an accurate model of the controlled object. c (s) and G m (s) are based on G cl (s), and the actual model of the controlled object is The closer to G cl (s), the more accurate the actual model of the controlled object is.

[0173] The intelligent variable bandwidth ESO designed by the present invention can reduce the deviation Δ. As Δ decreases, Closer to G cl (s), i.e. The higher the model accuracy of internal model control.

[0174] This application uses G when designing the inner mold structure. cl (s) as the internal model G m (s), ensuring the accuracy of the model without the need to establish an accurate mathematical model of the controlled object, thereby improving the overall performance of the internal model control. It can be seen that the present application can make the internal model required for IMC more accurate, without the need to establish an accurate mathematical model of the controlled object, and provides a new and practical solution for the internal model control design of complex nonlinear systems.

[0175] Embodiment five:

[0176] This example is based on the advanced internal model control system based on the intelligent variable bandwidth extended state observer designed in the fourth embodiment. For the second-order system, the controller parameters include α, ω o ,ω c , b 0 and η.

[0177] Parameters that need to be adjusted in LESO-SBW-AIMC, observer bandwidth ω of LESO-SBW o , scaling factor η, filter parameter α of IMC, controller bandwidth ω c and the controller gain b 0 .

[0178] For the second-order ADRC control system based on intelligent variable bandwidth extended state observer, when adjusting the controller parameters, the observer bandwidth ω o and the scaling factor η are tuned online according to the following formulas:

[0179] (1) LESO-SBW observer bandwidth and scaling factor η: From the expression of LESO-SBW, we can deduce z 1SBW The transfer function is:

[0180]

[0181] From the above formula, we can get z 1SBW With x 1 and z 1SBW The transfer function between and u is:

[0182]

[0183] in: Essentially, the actual observer bandwidth ω' o is the initial value of the observer bandwidth ω o and Composition. Different observer bandwidth ω o Next 1SBW With x 1 and z 1SBW The frequency domain response of u is as follows Figure 4 shown.

[0184] Figure 4 Where (a) is z 1SBW With x 1 (b) is the frequency domain response curve of z 1SBW The frequency domain response curve of and u. Figure 4 As can be seen from (a), with ω o As increases, the frequency domain characteristic curve shifts to the right, indicating that the phase lag of the LESO-SBW output observation curve decreases, the estimation error converges faster, and is beneficial to improving the dynamic performance of the system. Figure 4 As can be seen from (b), the disturbance gain increases with ω o The increase of , indicates that the anti-interference performance of the system has been improved. LESO-SBW has a higher ability to suppress the interference of control input u, and the input signal x 1 The introduced noise is the main factor affecting the performance of LESO-SBW. In addition, choosing too large ω o It will cause high-frequency noise pollution, which will cause system oscillation or even instability. Therefore, the actual selection should be adjusted from small to large until the noise impact can no longer meet the requirements of the system.

[0185] For the expansion factor η: It can be seen that η is used to adjust the range of variation of the observer bandwidth and can be selected by considering the rate of change of the observed system behavior and the accuracy requirements.

[0186] (2) Controller bandwidth ω c And the filter parameter α:

[0187] Figure 5 is the equivalent structure of LESO-SBW-AIMC, in which the feedback controller is:

[0188] C(s)=G c(s)[1-G c (s)G m (s)] -1

[0189] The open loop transfer function is:

[0190]

[0191] Therefore, the given adjustment time is: t s =3.5α.

[0192] The overshoot is: In this case, it can be seen from the above open-loop transfer function that the damping ratio and natural angular frequency are: 1 / ω c and ω c / α.

[0193] Figure 6 is the time domain response curve, Figure 7 is the frequency domain response curve; Figure 6 (a) and Figure 7 As can be seen from (a), when ω c When fixed, adjust the time t s As α decreases, it decreases. Similarly, from Figure 6 (b) and Figure 7 As can be seen from (b), when α is fixed, the overshoot σ% increases with ω. c In other words, reducing α and ω c The closed-loop performance of the control system can be improved. Figure 6 (c) and Figure 7 As can be seen in (c), reducing α and ω simultaneously c More noise will also be introduced in the high frequency band. Therefore, the PD controller bandwidth ω c The initial value of and the initial value of the filter parameter α can be adjusted according to the required adjustment time t s and overshoot σ%, and then further select appropriate α and ω according to actual needs c .

[0194] (3) Adjustable controller gain b 0

[0195] b 0 is the estimated value of the system gain b, that is, b 0 ≈b, which affects the system's anti-interference performance and response speed. In order to design the controller, it is necessary to calculate b 0 If b 0 If the information of is unknown, the estimated value of b can be used, and then the term (bb 0)u is included in the total disturbance f. Usually, the system identification value b is selected to ensure basic dynamic performance and stability, and finally further adjusted according to actual needs.

[0196] Among the parameters to be tuned, b 0 The system identification value b can be used as the initial value; the controller bandwidth ω c The filter parameter α can be calculated based on the preset adjustment time and overshoot indicators. Therefore, during the controller parameter adjustment process, only the observer bandwidth ω needs to be focused on. o and online tuning of the scaling factor η.

[0197] Embodiment six:

[0198] like Figure 8 As shown, this example provides a design method for an ADRC control system based on an intelligent variable bandwidth extended state observer. The design process is as follows:

[0199] S1: Consider a nonlinear time-varying system with a single input and a single output:

[0200] y (n) (t) = F(y (n-1) (t),…,y(t))+bu+d (1)

[0201] Among them, u is the control input of the system; y is the output of the system; F(y (n-1) (t),…,y(t)) are the internal dynamics of the system; let b 0 is the estimate of the control gain b, denoted by f(y (n-1) (t),…,y(t),d,u)=F(y (n-1) (t),…,y(t))+d+(bb 0 )u is the total disturbance of the system, and is defined as , write equation (1) into the state equation of the controlled object in the form of equation (2):

[0202]

[0203] Where X = [x 1 …x n+1 ] T is the system state variable,

[0204] S2: Based on the extended state equation of the controlled object, the fixed bandwidth linear extended state observer is designed as:

[0205]

[0206] Where L = [β 1 ,β2 ,…β n ,β n+1 ] T is the observer gain, and the observer gain is selected so that s (n+1) +β 1 s (n-1) +…β i s (i-1) +…+β n Satisfy the Hurwitz stability condition; configure all observer poles to -ω o At , we get the characteristic polynomial of equation (3); at the observer bandwidth ω o When the value is reasonable, z 1 →x 1 ,z 2 →x 2 ,…,z i →x i ,…,z n-1 →x n-1 ,z n →x n ,z n+1 →f(y (n-1) (t),…,y(t),d,u);

[0207] s (n+1) +β 1 s (n) +…+β n s+β n+1 =(s+ω o ) n+1 (3)

[0208] S3: Estimate z by compensating for the total disturbance n+1 , the control law is designed as follows:

[0209]

[0210] S4: Substitute equation (4) into equation (2), when the total disturbance estimate z n+1 Better estimate of total disturbance Sometimes, there is

[0211] y (n) =u 0 -z n+1 +f≈u 0 (5)

[0212] S5: The extended state observer actively compensates and the control law compensates the total disturbance in real time. The system (2) can be dynamically linearized into an integrator series form, and the state feedback control law u 0 The design is as follows:

[0213] u 0 =k1 (rz 1 )-k 2 z 2 -…k n z n (6)

[0214] Among them, k i (i=1,2,…n) is the controller gain, and all controller poles are configured to -ω c , we can get s (n) +k n s (n-1) +…+k 2 s+k 1 =(s+ω c ) n Characteristic polynomial of ; r is the set value;

[0215] S6: If we ignore the total disturbance estimate z n+1 The total disturbance The estimated deviation can simplify the controlled object into an n-order integral system y (n) =u 0 -z n+1 +f≈u 0 ; The closed-loop transfer function of the n-th order ADRC without zeros can be obtained, that is, the standard closed-loop ADRC system dynamics G cl (s):

[0216]

[0217] S7: To further reduce the total disturbance estimation deviation, the total disturbance estimation deviation |z n+1 -f| is used as the basis for adjusting the bandwidth of the extended state observer to dynamically adjust the bandwidth of the extended state observer, that is, ω' o =ω o +η|z n+1 -f|=ω o +η|z n+1 -(y (n) -b 0 u)|, the bandwidth parameterization is configured as follows:

[0218]

[0219] The intelligent variable bandwidth linear expansion observer is designed as follows:

[0220]

[0221] Among them, z 1SBW ,z 2SBW ,…z iSBW ,…z (n+1)SBWis the output of the intelligent variable bandwidth expansion state observer; η>0 is the scaling factor, which is used to adjust the variation range of the observer bandwidth;

[0222] S7: Accordingly, the control law is adjusted as follows:

[0223]

[0224] S8: Based on the internal model controller of the intelligent variable bandwidth extended state observer, the controlled object is controlled and the controller parameters α, ω are adjusted. o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0225] Based on the above design steps S1-S8, an ADRC control system based on an intelligent variable bandwidth extended state observer is obtained.

[0226] Based on the ADRC control system of the intelligent variable bandwidth extended state observer, the advanced internal model control system of LESO-SBW is further obtained by using the design method of the present invention, such as Fig. 9 shown.

[0227] Embodiment seven:

[0228] This example is a specific embodiment. Taking the control system of the Van der Pol oscillator as an example, an advanced internal model control system based on an intelligent variable bandwidth extended state observer is designed. The specific steps are as follows:

[0229] S1: Establish a mathematical model of the second-order controlled object and obtain the model parameters of the controlled object through model identification.

[0230] The control problem of the Van der Pol oscillator can be described by the following differential equation:

[0231]

[0232] in, are position, velocity and acceleration respectively; u is the control input signal.

[0233] The controlled object model is given by parameters, [η 1 ,η 2 ,η 3 ]=[1.5,1.5,1.0] T , initial state

[0234] S2: Consider the internal uncertainty and external disturbance in the van der Pol oscillator control system as a total disturbance and rewrite its differential equation into a form that includes the total disturbance. The total disturbance of the system is defined as: Among them, b 0is the adjustable controller gain. Let x 1 =y(t), The expanded state equation of the van der Pol oscillator is expressed as follows:

[0235]

[0236] S3: Based on the extended state equation, the extended state observer ESO is constructed, and the observer bandwidth ω is set according to the bandwidth parameterization method o , we can get:

[0237]

[0238] Among them, z 1 is the estimate of the system output y; z 2 is the estimate of the differential of the system output y; z 3 is the estimate of the total disturbance;

[0239] S4: ESO-based output variable z 1 ,z 2 and set value r, the PD controller is designed as: 0 =k 1 (rz 1 )-k 2 z 2 According to the bandwidth parameterization idea, we can get:

[0240] S5: Estimation of the total disturbance z by integrated ESO 3 and the PD controller output u 0 , according to the control law, the control output u is generated as follows:

[0241]

[0242] S6: Ignoring the estimation error of the total disturbance f by the extended state observer, the van der Pol oscillator control system can be equivalent to an integral series type, and the closed-loop transfer function of the n-order ADRC without zeros can be obtained:

[0243]

[0244] S7: To further reduce the total disturbance estimation deviation, the total disturbance estimation deviation |z 3 -f| is used as the basis for adjusting the bandwidth of the observer to dynamically adjust the bandwidth of the observer, that is, The bandwidth parameterization configuration of the intelligent variable bandwidth extended state observer is as follows:

[0245]

[0246] S8: The constructed intelligent variable bandwidth expansion observer is as follows:

[0247]

[0248] Among them, z 1SBW ,z 2SBW ,z 3SBW is the output of the intelligent variable bandwidth extended state observer; η>0 is the scaling factor, which is used to adjust the variation range of the observer bandwidth.

[0249] Accordingly, the control law is:

[0250]

[0251] The above active disturbance rejection controller ADRC (PD+LESO-SBW) based on intelligent variable bandwidth extended state observer is designed from S1-S8.

[0252] S9: Based on the standard closed-loop ADRC system dynamics G cl (s) to design the internal model G of IMC m (s), based on the internal model and selecting the appropriate filter f c (s) Design the internal model controller G c (s), we can get:

[0253]

[0254] f c (s) = 1 / (1 + αs) 2

[0255] Among them, G m (s) is the internal model, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics Compared with the standard closed-loop ADRC system dynamics G cl The deviation between (s),

[0256] S10: The advanced internal model controller based on intelligent LESO-SBW completes the control of the van der Pol oscillator and adjusts the controller parameters α, ω o ,ω c , b 0 and η make the system work normally until the desired control effect is achieved.

[0257] The result is an advanced internal model control system based on intelligent variable bandwidth extended state observer (LESO-SBW-AIMC).

[0258] Test example:

[0259] The following two cases are used to evaluate the performance of PD+LESO-SBW and LESO-SBW-AIMC designed in Example 7.

[0260] Case 1 is used to study trajectory tracking control in the presence of time-varying disturbances to evaluate the performance of the PD+LESO-SBW designed in this application. The comparison controllers include: the existing LADRC controller (PD control based on LESO, referred to as LADRC (PD+LESO)); PD control based on SESO (Invention Patent No. 2019112412522 provides a variable bandwidth self-disturbance rejection control method, which uses the estimated error of the system output to dynamically adjust the observer bandwidth, referred to as PD+SESO). For fair comparison, the above three control methods are the same except for the different observers.

[0261] Case 2 is used to evaluate the performance of the advanced internal model controller based on LESO-SBW-AIMC of the present invention. The comparison controllers include: existing IMC, existing LADRC controller (same as case 1), and IMC based on LADRC (IMC+LADRC).

[0262] For the design of the existing IMC, in this example, the internal model G is first designed based on the differential equation of the controlled object Van der Pol oscillator of the seventh embodiment. m (s), then based on the internal model G m (s), combined with the filter f c (s) Design the internal model controller G c (s), for the internal model G in IMC m (s) and the internal model controller G c (s), which is designed based on an accurate model of the controlled object.

[0263] For LADRC-based IMC, the existing LADRC controller (PD+LESO) in Case 1 is adopted, and the IMC design uses the standard closed-loop ADRC system dynamics G cl (s) to replace the internal model G m (s), combined with G cl (s) and filter f c (s), design the internal model controller G c (s) design. The IMC in this part is different from the IMC introduced above. The internal model here is based on the standard closed-loop ADRC system dynamics G cl (s) provided.

[0264] The controller parameters selected for the test are shown in Table 1:

[0265] Table 1 Controller parameters

[0266]

[0267] Case 1: Performance test of PD+LESO-SBW

[0268] Let the setting value be 1, that is, r(t) = 1(t), and add a time-varying disturbance from 3s to 5s: d(t) = 10sin(6t) + 10cos(6t). The trajectory tracking, control signal, total disturbance estimation and LESO-SBW output are respectively as follows: Figure 10-13 As shown. Among them, from Fig.10 It can be seen that under time-varying disturbances, all three control methods achieve the specified tracking performance. However, compared with the existing linear active disturbance rejection controller LADRC and the existing SESO-based PD controller, the PD+LESO-SBW controller of the present invention has a shorter recovery time and significantly less fluctuation. The control signal is as follows Fig.11 As shown in Figure 2, the PD+LESO-SBW controller of the present invention responds faster to time-varying disturbances than other methods. The total disturbance estimation is as follows: Fig.12 As shown in FIG. 1 , the total disturbance estimation of the LESO-SBW of the present invention always outperforms the existing LADRC controller and the existing SESO-based PD controller. Fig.13 (a) and Fig.13 In (b), it can be seen that the PD+LESO-SBW controller of the present invention has 1SBW and z 2SBW It can well estimate the system output y and .also, Fig.13 (c) confirms that the PD+LESO-SBW controller 3SBW The time-varying total disturbance f can be estimated accurately and timely. Therefore, the PD+LESO-SBW controller of the present invention achieves better tracking response.

[0269] In addition, noise sensitivity is another key issue. In the low frequency range, ESO can perform well, but in the high frequency band, ESO is sensitive to noise. Set the controller parameters to: 0 =1,ω o =12,ω c =5,η=10. Fig.14 It can be seen that even if ω o It is reduced to one third of the original value and still has better performance. In other words, a relatively low initial observer bandwidth can be set to make the system less susceptible to noise. The LESO-SBW-based PD controller of the present invention can better balance noise sensitivity and total disturbance estimation.

[0270] Case 2: Performance test of the advanced internal model controller based on LESO-SBW-AIMC of the present invention.

[0271] In this set of simulation tests, the same reference values ​​as in case (1) are selected. The same time-varying disturbance is added from 5s to 7s. The trajectory tracking, control error, and control signal are respectively Figure 15-17 As shown. Among them, from Fig.15 It can be seen that the undesirable factors severely degrade the tracking performance of the existing IMC controller. However, compared with the existing IMC controller, the existing LADRC controller and the existing LADRC-based IMC controller exhibit shorter rise and recovery times and significantly less fluctuations. With the help of the present invention based on LESO-SBW, the LESO-SBW-AIMC controller of the present invention further improves the closed-loop system performance. Fig.16 It also proves that the trajectory tracking error fluctuation of the LESO-SBW-AIMC controller of the present invention is minimal. Fig.17 As shown, the LESO-SBW-AIMC controller of the present invention responds faster to time-varying disturbances than other methods.

[0272] The present invention provides an advanced internal model control system based on an intelligent variable bandwidth extended state observer, which achieves satisfactory control effects in complex nonlinear systems with time-varying disturbances. Through ingenious design, the present invention successfully replaces the internal model in the IMC with the standard dynamics given by the ADRC, providing a new and practical solution for the IMC design of complex nonlinear systems; the total disturbance estimation deviation, an important performance indicator reflecting the real-time estimation effect of the observer, is used as the basis for the observer bandwidth adjustment, which is more timely and more phase-advanced than adjusting the bandwidth using the output estimation deviation. According to different states of the system (transition process or steady-state process), the observer bandwidth is dynamically adjusted to achieve the goal of both rapid response to changes and noise suppression in steady state, and a good compromise between tracking speed and noise sensitivity is obtained. In terms of tracking performance and disturbance suppression performance, the closed-loop system formed by the present invention achieves better tracking performance, has stronger anti-interference ability, and can more effectively suppress the influence of external disturbances on system performance, providing a new and practical solution for the IMC design of complex nonlinear systems.

[0273] The optional implementation modes of the embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but it should be noted that the present invention is not limited to the above specific details. Within the technical concept of the present invention, a variety of simple modifications can be made to the technical solution, and these modifications all belong to the protection scope of the present invention. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from its spirit and scope. Therefore, if these changes and modifications fall within the scope of the claims of the present invention and their equivalent technologies, they are also intended to be included in the protection of the present invention.

Claims

1. A design method for an ADRC control system based on an intelligent variable bandwidth extended state observer, characterized in that: The following steps are involved: S1: Based on the mathematical model of the n-th order controlled object, the internal uncertainty and external disturbance of the controlled object are regarded as the total disturbance f and used as the state variables of the system. The mathematical model of the controlled object is expressed as an extended state equation, a linear extended state observer with fixed bandwidth is constructed, and the observer bandwidth ω is set according to the bandwidth parameterization method. o and the gain of the extended state observer L = [β1,β2,…β n ,β n+1 ] T ; S2: Output variables z1,z2,...z based on the extended state observer n , design state feedback control law u0=k1(r-z1)-k2z2-…k n z n , and set the controller bandwidth ω according to the bandwidth parameterization method c ,ω c >0, and then design the controller gain k i (i=1,2,…n); r is the set value; S3: Estimation of the total disturbance z by the integrated extended state observer n+1 And the state feedback control law u0, the design control law u=(u0-z n+1 ) / b0; b0 is the adjustable controller gain; S4: Let ω' o =ω o +η|z n+1 -f|, construct an intelligent variable bandwidth extended state observer, and estimate the deviation |z with the total disturbance n+1 -f| is used as the adjustment basis to dynamically adjust the bandwidth of the observer. The bandwidth of the intelligent variable bandwidth expansion state observer is expressed as follows: oh o =ω o +η|z n+1 -f|=ω o +η|z n+1 -(y (n) -b0u)| Where f = y (n) -b0u,y (n) is the nth-order differential of the output of the controlled object, b0 is the adjustable controller gain, u is the input of the controlled object; η is the telescopic factor, which is used to adjust the bandwidth range of the observer, η>0; The adaptive variable gain of the bandwidth parameterization configuration is as follows: S5: The intelligent variable bandwidth linear expansion observer is designed as follows: S6: Based on the output of the intelligent variable bandwidth extended state observer, the control law is adjusted accordingly: Among them, z 1SBW ,z 2SBW ,…z iSBW ,…z (n+1)SBW is the output of the intelligent variable bandwidth extended state observer; S7: Use the ADRC control system based on intelligent variable bandwidth extended state observer to complete the control of the n-order controlled object and adjust the controller parameter ω o ,ω c , b0 and η make the system work normally until the desired control effect is achieved.

2. A design method for an advanced internal model control system based on an intelligent variable bandwidth extended state observer, characterized in that: The following steps are involved: S8: The ADRC control system based on the intelligent variable bandwidth extended state observer designed in claim 1 is adopted. When the extended state observer is reasonably designed, that is, z n+1 ≈f, the controlled object can be simplified to an n-order integral system y (n) =u0-z n+1 +f≈u0; the closed-loop transfer function of the nth-order ADRC without zeros can be obtained, that is, the standard closed-loop ADRC system dynamics G cl (s): Among them, k i (i=1,2,…n) is the controller gain; S9: Based on the standard closed-loop ADRC system dynamics G cl (s), and design the internal model controller G by combining the following formula c (s), internal model G m (s) and filter f c (s): f c (s)=1 / (1+αs) n Where n is the order of the controlled object, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics. Compared with the standard closed-loop ADRC system dynamics G cl (s), where S10: The internal model controller based on the intelligent variable bandwidth extended state observer completes the control of the controlled object and adjusts the controller parameters α, ω o ,ω c , b0 and η make the system work normally until the desired control effect is achieved.

3. A design method for an ADRC control system based on an intelligent variable bandwidth extended state observer, characterized in that: For a second-order ADRC controller, the design approach includes the following steps: S1: Establish a mathematical model of the second-order controlled object and obtain the model parameters of the controlled object through model identification; for the second-order controlled object, the mathematical model is: Among them, u is the control input of the system; y is the output of the system; is the first-order differential of the system output y; is the uncertainty inside the system; ω is the external disturbance; b is the gain of the controlled object; the internal uncertainty and external disturbance of the controlled object are regarded as the total disturbance and used as the state variables of the system, and the mathematical model of the controlled object is expressed as an extended state equation; Where x1=y(t), The total disturbance is expressed as b0 is the adjustable controller gain; S2: Based on the extended state equation, a fixed bandwidth extended state observer is constructed: And set the observer bandwidth ω according to the bandwidth parameterization method o ,ω o >0, and then design the observer gain L = [β1, β2, β3]; Among them, z1 is the estimate of the system output y; z2 is the estimate of the differential of the system output y; z3 is the estimate of the total disturbance; S3: Based on the output variables z1, z2 of the extended state observer, design the PD controller u0=k1(r-z1)-k2z2, and set the PD controller bandwidth ω according to the bandwidth parameterization method c ,ω c >0, and then design the PD controller gains k1, k2; S4: Combine the total disturbance estimate z3 of the extended state observer and the output u0 of the PD controller to generate the control output u according to the control law; in, r is the set value; S5: Let ω' o =ω o +η|z3-f|, construct an intelligent variable bandwidth extended state observer, and dynamically adjust the bandwidth of the observer based on the total disturbance estimation deviation |z3-f|. The bandwidth of the intelligent variable bandwidth extended state observer is expressed as follows: in, is the second-order differential of the output of the controlled object, b0 is the adjustable controller gain, u is the input of the controlled object; η is the telescopic factor, which is used to adjust the bandwidth range of the observer, η>0; The adaptive variable gain of the bandwidth parameterization configuration is as follows: S6: Design an intelligent variable bandwidth extended state observer and adjust the control law accordingly; Among them, z 1SBW ,z 2SBW ,z 3SBW is the output of the intelligent variable bandwidth extended state observer; η>0 is the scaling factor, which is used to adjust the variation range of the observer bandwidth. Accordingly, the control law is adjusted as follows: S7, ADRC control system based on intelligent variable bandwidth extended state observer completes the control of the second-order controlled object and adjusts the controller parameter ω o ,ω c , b0 and η, so that the system can work normally until the desired control effect is achieved.

4. A design method for an advanced internal model control system based on an intelligent variable bandwidth extended state observer, characterized in that: The following steps are involved: S8: The ADRC control system based on the intelligent variable bandwidth extended state observer designed in claim 3 is adopted, and the estimation deviation of the extended state observer to the total disturbance is ignored. The second-order controlled object can be equivalent to an integral series type, and the standard closed-loop ADRC system dynamics G is obtained. cl (s): S9: Based on the standard closed-loop ADRC system dynamics G cl (s), and design the internal model controller G by combining the following formula c (s), internal model G m (s) and filter f c (s): f c (s)=1 / (1+αs) 2 Where n is the order of the controlled object, α is the time constant, and Δ is the actual closed-loop ADRC system dynamics. Compared with the standard closed-loop ADRC system dynamics G cl The deviation between (s), S10: The internal model controller based on the intelligent variable bandwidth extended state observer completes the control of the controlled object and adjusts the controller parameters α, ω o ,ω c , b0 and η make the system work normally until the desired control effect is achieved.

5. The design method of the advanced internal model control system based on the intelligent variable bandwidth extended state observer according to claim 4 is characterized in that: In step S10, when adjusting the controller parameters, at a given adjustment time t s , when the error tolerance range is ±5%, the initial value of the filter parameter α can be determined by the following formula: t s ＝3.5α。 6. The design method of advanced internal model control system based on intelligent variable bandwidth extended state observer according to claim 4 is characterized in that: In step S10, when adjusting the controller parameters, under the given overshoot σ%, the PD controller bandwidth ω c The initial value of can be determined by the following formula:

7. An n-order ADRC control system obtained based on the design method of the ADRC control system based on the intelligent variable bandwidth extended state observer as claimed in claim 1.

8. An n-order advanced internal model control system is obtained based on the design method of the advanced internal model control system based on the intelligent variable bandwidth extended state observer as described in claim 2.

9. A second-order ADRC control system obtained based on the design method of the ADRC control system based on the intelligent variable bandwidth extended state observer as claimed in claim 3.

10. A second-order advanced internal model control system obtained based on the design method of the advanced internal model control system based on intelligent variable bandwidth extended state observer as claimed in claim 4.

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