A strong disturbance rejection frequency point adaptive switching extended state observer design method

Abstract

The application provides a strong anti-interference frequency point adaptive switching extended state observer design method, which comprises the following steps: extracting state variables needing disturbance observation in a controlled object system, and generating a system state equation for the state variables; and establishing a basic form of a frequency point adaptive switching extended state observer; the basic frequency point in the frequency point adaptive switching extended state observer is ω, and the frequency conversion factor is ξ; the frequency conversion factor ξ can be switched between ξ1 and ξ2 through the design of a frequency point adaptive switching logic condition, so as to realize adaptive switching of the extended state observer between the two frequency points of ξ1ω and ξ2ω; the method closely surrounds the actual engineering demand, can solve the problems of amplification of noise by a large bandwidth and high gain and parameter setting difficulty of other complex forms of extended state observers, and achieves the purpose of giving consideration to rapidity of disturbance estimation and robustness to noise.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of extended state observer, and relates to a strong anti-interference frequency point adaptive switching extended state observer design method. BACKGROUND

[0002] In industrial automation, aerospace, robot control and other related fields, actual control systems are always subject to different types of internal and external disturbances, which are caused by multi-dimensional reasons coupling of environmental mutations, element failures, structural changes, measurement errors, etc., and usually show strong uncertainty and nonlinearity characteristics, which are often difficult to accurately predict and model, bringing great challenges to the stability and control performance of the control system. The extended state observer can not only realize the observation of the internal state of the controlled object, but also estimate and compensate the unknown disturbance and uncertainty in the closed-loop system in real time by constructing virtual extended state variables, so that the controller can better cope with the disturbance. Compared with the traditional state observer, the extended state observer has the advantages of high precision and low model dependence, and can significantly improve the robustness and adaptability of the closed-loop system, and is an effective way to solve the stable control problem under strong disturbance and strong uncertainty conditions.

[0003] Although relevant scholars at home and abroad have carried out certain research on the extended state observer, there is always a high error gain requirement for the rapidity of disturbance estimation, which further brings the problem of amplification of measurement noise. The larger the bandwidth of the ESO (extended state observer), the higher the estimation accuracy and the better the rapidity; but when there is measurement noise, increasing the bandwidth of the observer will significantly amplify the influence of the noise, causing the estimated value of the disturbance to oscillate sharply, resulting in a decrease in accuracy and even estimation failure, thereby affecting the performance of the closed-loop system.

[0004] Among various uncertainties and disturbances, fast-changing / mutational disturbances are the most difficult to cope with in engineering, and further considering the influence of signal measurement noise, the traditional method of changing the bandwidth by configuring the poles of the linear extended state observer is difficult to select a suitable frequency point in actual application. Although increasing the bandwidth of the observer by configuring the poles of the observer system makes the convergence rapidity higher, it also amplifies the influence of the noise.

[0005] For the extended state observer, how to balance the contradiction between convergence rapidity and high error gain noise suppression is the primary problem faced by its further engineering application. Therefore, it is necessary to carry out research on the strong anti-interference frequency point adaptive switching extended state observer design method, and dynamically adjust the gain according to the error convergence, so as to further improve the anti-interference ability of the control system and lay a foundation for wider engineering application of the extended state observer. SUMMARY

[0006] The purpose of the present application is to solve at least one of the problems existing in the prior art.

[0007] To address this, the present invention provides a design method for a frequency-adaptive switching extended state observer with strong anti-interference capabilities. Specifically, it provides a design method for an extended state observer that adaptively switches frequencies based on the magnitude of the observation error and the phase plane boundary of the rate of change of the error magnitude. This method closely addresses practical engineering needs and can solve the problems of noise amplification due to large bandwidth and high gain, as well as the difficulty in tuning parameters of other complex extended state observers, achieving the goal of balancing the speed of disturbance estimation with robustness to noise.

[0008] The technical solution of the present invention is as follows:

[0009] A design method for a frequency-adaptive switching extended state observer with strong anti-interference capabilities is presented, with the following specific steps:

[0010] Step 1: Extract the state variables in the controlled object system that need to be observed for disturbances, and generate the system state equation for the state variables;

[0011] Step 2: Based on the system state equation in Step 1, establish the basic form of the frequency-adaptive switching extended state observer; the base frequency in this frequency-adaptive switching extended state observer is ω, and the frequency conversion factor is ξ. By designing the frequency-adaptive switching logic condition, the frequency conversion factor ξ can switch between ξ1 and ξ2, thereby realizing the adaptive switching of the extended state observer between the two frequency points ξ1ω and ξ2ω.

[0012] Step 3, based on the rate of change of the error modulus The frequency adaptive switching logic condition described in step 2 is designed relative to the error modulus |e| in the phase plane.

[0013] Step 4: Tune the adjustable parameters of the frequency-adaptive extended state observer according to the feasible region constraint. The adjustable parameters include ξ1 and ξ2. Calculate the range of values ​​for ξ1 and ξ2 from the perspective of observer stability to achieve the tuning of the adjustable parameters.

[0014] Furthermore, in step 1, the state variable x that needs to be observed for disturbance in the controlled object system is extracted. Then, the system state equation of the single-input single-output nonlinear controlled object with external disturbance and measurement noise is:

[0015]

[0016] In the formula, x is the state variable of the controlled system, u is the control input, f is the nonlinear function, d is the external disturbance, and N is the measurement noise. These are the measured values ​​of the state variables.

[0017] Furthermore, in step 2, the basic form of the frequency-adaptive switching extended state observer is as follows:

[0018]

[0019] In the formula, z1 is the observed value of the state variable x, z2 is the observed value of the external disturbance d and the nonlinear function f, β1=-2ω, β2=-ω 2 ω is the base frequency of the frequency-adaptive switching extended state observer, ξ is the frequency conversion factor, and ξ1>0, ξ2>0. By designing switching logic conditions, namely condition1 and condition2, the frequency conversion factor ξ is switched between ξ1 and ξ2, thereby realizing the adaptive switching of the extended state observer between the two frequency points ξ1ω and ξ2ω.

[0020] Furthermore, in step 3, the designed frequency adaptive switching logic conditions condition1 and condition2 are:

[0021]

[0022] Where μ is the error switching factor, μ > 0. By selecting the frequency conversion factors ξ1, ξ2 and the error switching factor μ, the boundary of the phase plane is changed to achieve adaptive switching of frequency points. The frequency conversion factors ξ1, ξ2 determine the scaling of the real frequency point on the base frequency point ω. The error switching factor μ makes frequency switching decisions based on two-dimensional information of error magnitude and error direction. Its magnitude determines the degree of influence of the error magnitude and the rate of change of the error magnitude on the switching logic of the observer switching system.

[0023] Furthermore, when ξ1=ξ2, the switching system of the frequency-adaptive switching extended state observer will degenerate into a linear extended state observer, operating at a fixed frequency.

[0024] When ξ1≠ξ2, the frequency-adaptive extended state observer dynamically adjusts the error gain between the two frequency points based on the relative positional relationship in the phase plane composed of the error magnitude and the rate of change of the error magnitude.

[0025] Furthermore, the process of calculating the range of values ​​for ξ1 and ξ2 in step 4 is as follows:

[0026] Let the actual observation error be e1 = z1 - x, e2 = z2 - df, and e1 = eN. Combining equations (1) and (2), we can obtain the state equation of the actual error as follows:

[0027]

[0028] Equation (4) can be written in state-space form as follows:

[0029]

[0030] in,

[0031]

[0032] The stability of the observer system shown in equation (5) is determined by matrix A. Further considering the switching changes of the parameters of matrix A, to analyze the stability of the observer system, a positive definite real symmetric matrix P needs to be found that satisfies:

[0033]

[0034] And A1 and A2 are respectively:

[0035]

[0036] and

[0037] The stability of the frequency-adaptive switching extended state observer is determined by the fact that equation (10) has no negative real eigenvalues. That is, if equation (10) has no negative real eigenvalues, the frequency-adaptive switching extended state observer is stable.

[0038]

[0039] And χ=β2(ξ1) 2 +ξ2 2 )+β1 2 ξ1ξ2(11)

[0040] When β1=-2ω, β2=-ω 2 When equation (12) is satisfied, it can be guaranteed that equation (10) has no negative real eigenvalues, further ensuring the stability of the frequency-adaptive switching extended state observer:

[0041] (ξ1 2 +ξ2 2 ) / ξ1ξ2<6 (12)

[0042] Substituting equation (12) into the expression for χ, i.e., equation (11), we obtain... When the relationship between ξ1 and ξ2 satisfies Under certain conditions, expression (10) has no negative real eigenvalues, which means that the frequency-adaptive switching extended state observer is stable;

[0043] Therefore, assuming the frequency-adaptive switching extended state observer remains stable, the ranges of ξ1 and ξ2 are:

[0044] Furthermore, in step 4, the adjustable parameter also includes the fundamental frequency ω;

[0045] The tuning of the fundamental frequency ω is as follows: the fundamental frequency ω determines the gain and speed of the observer. The larger ω is, the greater the error gain, the more accurate the estimation of external disturbance d under noise-free conditions, and the faster the convergence speed. The value of the fundamental frequency ω is selected based on experience.

[0046] Furthermore, in step 4, the adjustable parameter also includes an error switching factor μ;

[0047] The error switching factor μ is tuned as follows: due to the presence of disturbances and noise, there is an order of magnitude difference between the rate of change of the error magnitude and the error magnitude, so μ is set to a value greater than 5.

[0048] Furthermore, for a controlled object system with multiple inputs and multiple outputs, by designing a corresponding extended state observer for each state variable x, it is possible to estimate the external disturbances and uncertainties of all states of the controlled object system separately.

[0049] By applying the above technical solution, the present invention has the following beneficial effects:

[0050] (1) The present invention provides a design method for an extended state observer with strong anti-disturbance frequency adaptive switching. The method designs an extended state observer frequency switching logic based on the boundary between the error magnitude and the rate of change of the error magnitude in the phase plane. This enables the observer to accelerate convergence when the observation error is large and suppress noise during stable control. It can be used to guide the design of disturbance observers under strong disturbance and strong uncertainty conditions.

[0051] (2) In the process of calculating the range of values ​​of ξ1 and ξ2, this invention transforms the determination of the stability of the frequency adaptive switching extended state observer into the determination of... The method, which has no negative real eigenvalues, can provide the range of values ​​for ξ1 and ξ2 in analytical form to ensure the stability of the observer, making it easier for designers to quickly complete the observer parameter tuning.

[0052] (3) The strong anti-interference frequency adaptive switching extended state observer of the present invention still conforms to the basic characteristics and design ideas of the traditional linear extended state observer. In its actual operation, it is equivalent to two linear extended state observers with different frequencies continuously switching frequencies according to the switching logic to achieve the purpose of accelerating convergence and suppressing noise. The traditional linear extended state observer has been widely used in control systems in various fields. Therefore, the method proposed in this invention has extremely strong engineering application value. Attached Figure Description

[0053] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0054] Figure 1 The switching logic diagram of the frequency-adaptive switching extended state observer is given;

[0055] Figure 2 The feasible region range of parameter values ​​ξ1 and ξ2 for the frequency adaptive switching extended state observer is given.

[0056] Figure 3 The closed-loop control structure diagram based on the frequency-adaptive switching extended state observer is given;

[0057] Figure 4 The closed-loop control x1 step response curve based on the frequency-adaptive switching extended state observer is given;

[0058] Figure 5 The curves for estimating the x2 disturbance by the closed-loop control based on the frequency-adaptive switching extended state observer are presented. Detailed Implementation

[0059] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0061] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0062] Example 1:

[0063] This embodiment provides a design method for a strong anti-interference frequency-point adaptive switching extended state observer, the specific steps of which are as follows:

[0064] Step 1: Extract the system state equations of the controlled object based on the actual physical constraints.

[0065] If we extract the state variable x that needs to be observed for disturbance in the controlled object system, then the system state equation of the single-input single-output nonlinear controlled object with external disturbance and measurement noise can be expressed as equation (1):

[0066]

[0067] In the formula, x is the state variable of the controlled system, u is the control input, f is an unknown nonlinear function, d is an unknown external disturbance, and N is the measurement noise. These are the measured values ​​of the state variables.

[0068] Step 2, design the basic form of the frequency-adaptive switching extended state observer, as shown in equation (2):

[0069]

[0070] In the formula, z1 is the observed value of the state variable x of the controlled system shown in equation (1), z2 is the observed value of the external disturbance d and the nonlinear function f of the controlled system shown in equation (1), and β1 = -2ω, β2 = -ω 2ω is the base frequency of the frequency-adaptive switching extended state observer, and ξ is the frequency conversion factor. By designing switching logic conditions (i.e., condition 1 and condition 2), the frequency conversion factor ξ is switched between ξ1 and ξ2 (ξ1 > 0, ξ2 > 0), thereby realizing the adaptive switching of the extended state observer between the two frequency points ξ1ω and ξ2ω. At this time, the observer system is essentially a switching system composed of two subsystems with poles of -ξ1ω, -ξ1ω and -ξ2ω, -ξ2ω.

[0071] Step 3, design based on the rate of change of error modulus The frequency-adaptive switching logic is relative to the error modulus |e| in the phase plane, i.e., the switching logic conditions condition 1 and condition 2 are designed; the frequency-adaptive switching logic proposed in this embodiment is shown in equation (3):

[0072]

[0073] Where μ is the error switching factor, μ > 0. By selecting the frequency conversion factors ξ1, ξ2 and the error switching factor μ, the boundary of the phase plane is changed to achieve adaptive switching of frequency points. The frequency conversion factors ξ1, ξ2 determine the scaling of the real frequency point on the base frequency point ω. The error switching factor μ makes frequency switching decisions based on two-dimensional information of error magnitude and error direction. Its magnitude determines the degree of influence of the error magnitude and the rate of change of the error magnitude on the switching logic of the observer switching system.

[0074] When ξ1 = ξ2, the switching system of the frequency-adaptive switching extended state observer degenerates into a linear extended state observer, operating at a fixed frequency. When ξ1 ≠ ξ2, the frequency-adaptive extended state observer possesses the characteristic of dynamically adjusting the error gain between two frequency points based on the relative positional relationship in the phase plane composed of the error magnitude and the rate of change of the error magnitude. Its switching logic is as follows: Figure 1 As shown.

[0075] If -μ < the rate of change of the error modulus divided by the error modulus < the error switching factor μ, then ξ = ξ2. The observer is in a state where the observation error is large and the error changes slowly, and it will not converge in a short time. At this time, the observer's working bandwidth switches to the larger of ξ1 and ξ2, i.e., ξ2, thereby accelerating the convergence speed of the observer and enabling effective estimation when abrupt changes occur. If the rate of change of the error modulus divided by the error modulus is ≥ the error switching factor μ or ≤ -μ, then ξ = ξ1. The observer is in a state where the observation error is small and the error changes rapidly. From the perspective of suppressing high-frequency noise, the observer's working bandwidth switches to the smaller of ξ1 and ξ2, i.e., ξ1, to suppress the influence of measurement noise when the observation error is small.

[0076] Step 4: Tune the adjustable parameters of the frequency-adaptive extended state observer according to the feasible region constraints:

[0077] The adjustable parameters of the frequency-adaptive switching extended state observer include: ξ1, ξ2, ω, and μ;

[0078] (1) Tuning of the fundamental frequency ω: Since the fundamental frequency ω determines the gain and speed of the observer, its impact on the frequency-adaptive switching extended state observer is similar to its impact on the linear extended state observer. The larger ω is, the greater the error gain, the more accurate the estimation of the external disturbance d under noise-free conditions, and the faster the convergence speed. Therefore, for rapidly changing or high-intensity disturbances, a larger fundamental frequency ω should be selected; for slowly changing or low-intensity disturbances, a smaller fundamental frequency ω should be selected. The value of the fundamental frequency ω can be selected based on experience.

[0079] (2) Tuning of μ: Due to the presence of disturbances and noise, the rate of change of the error modulus differs from the error modulus by orders of magnitude. μ is generally taken to be above 5.

[0080] (3) Tuning of ξ1 and ξ2: Calculate the range of values ​​of ξ1 and ξ2 from the perspective of observer stability;

[0081] Let the actual observation error be e1=z1-x, e2=z2-df, and e1=eN. Combining equations (1) and (2), the state equation of the actual error can be obtained as shown in equation (4):

[0082]

[0083] The state-space form is shown in equation (5):

[0084]

[0085] in,

[0086]

[0087] The stability of the observer system shown in equation (5) is determined by matrix A. Further considering the switching changes of the parameters of matrix A, to analyze the stability of the observer system, a positive definite real symmetric matrix P needs to be found that satisfies:

[0088]

[0089] And A1 and A2 are respectively:

[0090]

[0091] and

[0092] Using the existence criterion for the common quadratic Lyapunov function of a second-order system in switching system theory, it can be known that if the switching system has a common quadratic Lyapunov function, then the switching system is stable. Therefore, the stability of the frequency-adaptive switching extended state observer can be further transformed into judging whether equation (10) has no negative real eigenvalues. That is, if equation (10) has no negative real eigenvalues, it means that the frequency-adaptive switching extended state observer is stable.

[0093]

[0094] And χ=β2(ξ1) 2 +ξ2 2 )+β1 2 ξ1ξ2(11)

[0095] When β1=-2ω, β2=-ω 2 When equation (12) is satisfied, it can be guaranteed that equation (10) has no negative real eigenvalues, further ensuring the stability of the frequency-adaptive switching extended state observer:

[0096] (ξ1 2 +ξ2 2 ) / ξ1ξ2<6 (12)

[0097] Substituting equation (12) into the expression for χ, i.e., equation (11), we obtain... When the relationship between ξ1 and ξ2 satisfies Under certain conditions, expression (10) has no negative real eigenvalues, thus indicating that the frequency-adaptive switching extended state observer is stable; the feasible region composed of ξ1 and ξ2 is as follows: Figure 2 As shown, the feasible domain of ξ1 and ξ2 for adaptive frequency switching is relatively wide. In particular, when 0 < ξ1 < 1, the two frequency points ξ1ω and ξ2ω of the extended state observer are in the form of one large and one small (i.e. ξ2ω is greater than ω, and ξ1ω is less than ω), which plays a role in suppressing the influence of measurement noise in steady state and enabling the observer to converge quickly when the disturbance is large.

[0098] Example 2:

[0099] This embodiment, based on Embodiment 1, focuses on the design and verification process of a frequency-adaptive observer for a common second-order system in industry, specifically as the controlled object:

[0100] The first step is to write out the corresponding system state equation for a certain second-order system, as shown in equation (13).

[0101]

[0102] In the formula, x1 and x2 are the state variables of the second-order system, u is the control input, d is the unknown external disturbance, f is the unknown nonlinear function, and y is the output of the second-order system.

[0103] The second step involves designing the frequency-adaptive extended state observer and related parameters:

[0104] For a controlled object system with multiple inputs and multiple outputs, it is necessary to design a corresponding extended state observer for each state variable x, so as to similarly estimate the external disturbances and uncertainties of all states of the controlled object system. Generally, the second-order controlled object system based on the real physical process generally has the characteristic that the control input u only affects the second-order state variable x2. Considering that u is needed to compensate for the observed disturbances in the future, in this embodiment, it is only necessary to design a corresponding extended state observer for x2.

[0105] Therefore, a disturbance observer is designed for the state variable x2 of the controlled object system, and then the disturbance is compensated by u. The frequency-adaptive extended state observer designed according to equation (2) in Example 1 can be written as shown in equation (15):

[0106]

[0107] In the formula, Let z1 be the measured value of the state variable x2, z2 be the observed value of the state variable x2 of the second-order system, and z3 be the observed value of the external disturbance d and the nonlinear function f of the second-order system, where β1 = -2ω and β2 = -ω. 2 u d For the compensation control input to the disturbance, N is the measurement noise, ξ1 and ξ2 are selected according to the constraints of equation (12), and μ is selected as a suitable positive real number. The parameters of the frequency point adaptive extended state observer designed for equation (13) are shown in Table 1:

[0108] Table 1. Parameters of the Frequency-Adaptive Extended State Observer

[0109]

[0110] The third step is to design a closed-loop control law and compensate for the estimated disturbances:

[0111] To illustrate the impact of the frequency-adaptive switching extended state observer proposed in this embodiment on closed-loop control, proportional-derivative control, commonly used in engineering, is selected as the basic control outer loop for state variable x1, and a control input u for the disturbance of x2 is introduced. d As compensation, this is to verify the effectiveness of the frequency-adaptive switching extended state observer designed in this embodiment.

[0112] The closed-loop control law is shown in equation (16).

[0113]

[0114] in, To address the tracking control error of x1, x 1c For instruction input, k p k is the proportional control parameter. d These are differential control parameters;

[0115] The final closed-loop control structure is as follows Figure 3 As shown in Table 2, the proportional-derivative control parameters and command inputs are as follows.

[0116] Table 2 Proportional-Derivative Control Parameters and Command Inputs

[0117]

[0118] The fourth step is to verify the effectiveness of the design method through simulation.

[0119] To illustrate the superiority of the frequency-adaptive switching extended state observer, a measurement noise N(t) and a complex disturbance of fast-slow coupling are introduced into the controlled system during closed-loop control simulation, as shown in Equation (17). Here, N(t) ~ N(0, 0.025) follows a standard Gaussian distribution with a variance of 0.025. The simulation results are as follows: Figure 4 , Figure 5 As shown.

[0120]

[0121] Where t is time, 1 / 6, 5, and 10 are the values ​​of angular velocity, d1(t), d2(t), and d3(t) represent disturbances of different frequencies, and d represents the total synthesized disturbance.

[0122] Depend on Figure 4 It is known that when using proportional-derivative control alone, the settling time of the x1 step response is about 2 seconds. A steady-state error of about 0 to 0.25 will appear due to disturbances and noise, which affects the closed-loop control performance. After adding a frequency-adaptive extended state observer to estimate and compensate for disturbances, the influence of disturbances on the steady-state x1 step response is significantly reduced, and the steady-state error is maintained within ±0.06 while retaining good speed.

[0123] Depend on Figure 5 It is known that the actual disturbance curve basically coincides with the frequency adaptive switching ECO curve. The frequency adaptive extended state observer still maintains good tracking and estimation of the disturbance under noisy conditions, and no oscillation or divergence occurs. This shows that the frequency switching logic designed in this embodiment has achieved the expected purpose, suppressing noise during smooth control while taking into account the speed of disturbance estimation.

[0124] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0125] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0126] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a frequency-adaptive switching extended state observer with strong anti-interference capabilities, characterized in that, The specific steps are as follows: Step 1: Extract the state variables in the controlled object system that need to be observed for disturbances, and generate the system state equation for the state variables; Step 2: Based on the system state equations in Step 1, establish the basic form of the frequency-adaptive switching extended state observer; The base frequency point in this frequency-adaptive switching extended state observer is w, and the frequency conversion factor is x. By designing the frequency-adaptive switching logic condition, the frequency conversion factor x can switch between x1 and x2, thereby realizing the adaptive switching of the extended state observer between the two frequency points x1w and x2w. Step 3, based on the rate of change of the error modulus The frequency adaptive switching logic condition described in step 2 is designed relative to the error modulus |e| in the phase plane. Step 4: Tune the adjustable parameters of the frequency-adaptive extended state observer according to the feasible region constraint. The adjustable parameters include x1 and x2. Calculate the value range of x1 and x2 from the perspective of observer stability to achieve the tuning of the adjustable parameters. In step 1, the state variable x that needs to be observed for disturbance in the controlled object system is extracted. Then, the system state equation of the single-input single-output nonlinear controlled object with external disturbance and measurement noise is: In the formula, x is the state variable of the controlled system, u is the control input, f is the nonlinear function, d is the external disturbance, and N is the measurement noise. These are the measured values ​​of the state variables; In step 2, the basic form of the frequency-adaptive switching extended state observer is as follows: In the formula, z1 is the observed value of the state variable x, z2 is the observed value of the external disturbance d and the nonlinear function f, b1 = -2w, b2 = -w 2 w is the base frequency of the frequency-adaptive switching extended state observer, x is the frequency conversion factor, and x1>0, x2>0. By designing switching logic conditions, namely condition1 and condition2, the frequency conversion factor x is switched between x1 and x2, thereby realizing the adaptive switching of the extended state observer between the two frequency points x1w and x2w.

2. The design method for a strong anti-interference frequency adaptive switching extended state observer as described in claim 1, characterized in that, In step 3, the designed frequency adaptive switching logic conditions condition1 and condition2 are: Where m is the error switching factor, m>0. By selecting the frequency conversion factors x1, x2 and the error switching factor μ, the boundary of the phase plane is changed to achieve adaptive switching of frequency points. The frequency conversion factors x1, x2 determine the scaling of the real frequency point on the base frequency point w. The error switching factor μ makes frequency switching decisions based on two-dimensional information of error magnitude and error direction. Its magnitude determines the degree of influence of the error magnitude and the rate of change of the error magnitude on the switching logic of the observer switching system.

3. The design method for a strong anti-interference frequency adaptive switching extended state observer as described in claim 1 or 2, characterized in that, When x1 = x2, the switching system of the frequency-adaptive switching extended state observer will degenerate into a linear extended state observer, operating at a fixed frequency. When x11x2, the frequency-adaptive extended state observer dynamically adjusts the error gain between two frequency points based on the relative positional relationship in the phase plane composed of the error magnitude and the rate of change of the error magnitude.

4. The design method for a strong anti-interference frequency adaptive switching extended state observer as described in claim 2, characterized in that, The process of calculating the range of values ​​for x1 and x2 in step 4 is as follows: Let the actual observation error be e1 = z1 - x, e2 = z2 - df, and e1 = eN. Combining equations (1) and (2), we can obtain the state equation of the actual error as follows: Equation (4) can be written in state-space form as follows: in, The stability of the observer system shown in equation (5) is determined by matrix A. Further considering the switching changes of the parameters of matrix A, to analyze the stability of the observer system, a positive definite real symmetric matrix P needs to be found that satisfies: And A1 and A2 are respectively: and The stability of the frequency-adaptive switching extended state observer is determined by the fact that equation (10) has no negative real eigenvalues. That is, if equation (10) has no negative real eigenvalues, the frequency-adaptive switching extended state observer is stable. and When b1 = -2w, b2 = -w 2 When equation (12) is satisfied, it can be guaranteed that equation (10) has no negative real eigenvalues, further ensuring the stability of the frequency-adaptive switching extended state observer: Substituting equation (12) into the expression for c, i.e., equation (11), we obtain the solution. When the relationship between x1 and x2 satisfies Under certain conditions, expression (10) has no negative real eigenvalues, which means that the frequency-adaptive switching extended state observer is stable; Therefore, assuming the frequency-adaptive switching extended state observer remains stable, the range of values ​​for x1 and x2 is:

5. A design method for a strong anti-interference frequency adaptive switching extended state observer as described in any one of claims 1, 2, or 4, characterized in that, In step 4, the adjustable parameters also include the fundamental frequency point w; The tuning of the fundamental frequency w is as follows: the fundamental frequency w determines the gain and speed of the observer. The larger w is, the greater the error gain, the more accurate the estimation of external disturbance d under noise-free conditions, and the faster the convergence speed. The value of the fundamental frequency w is selected based on experience.

6. A design method for a strong anti-interference frequency adaptive switching extended state observer as described in any one of claims 1, 2, or 4, characterized in that, In step 4, the adjustable parameter further includes an error switching factor m; The error switching factor μ is tuned as follows: due to the presence of disturbances and noise, there is an order of magnitude difference between the rate of change of the error modulus and the error modulus, and m is set to a value greater than 5.

7. A design method for a strong anti-interference frequency adaptive switching extended state observer as described in any one of claims 1, 2, or 4, characterized in that, For a controlled object system with multiple inputs and multiple outputs, by designing a corresponding extended state observer for each state variable x, it is possible to estimate the external disturbances and uncertainties of all states of the controlled object system separately.

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