Design method of strong anti-interference frequency point adaptive switching extended state observer

Abstract

The invention provides a method for designing a strong anti-interference frequency point self-adaptive switching extended state observer, which comprises the following steps of: extracting a state variable needing to be subjected to disturbance observation in a controlled object system, and generating a system state equation aiming at the state variable; establishing a basic form of a frequency point adaptive switching extended state observer; a basic frequency point in the frequency point adaptive switching extended state observer is omega, a frequency conversion factor is xi, and the frequency conversion factor xi can be switched between xi 1 and xi 2 by designing frequency point adaptive switching logic conditions, so that adaptive switching of the extended state observer between the two frequency points xi 1 omega and xi 2 omega is realized; the method closely surrounds actual engineering requirements, can solve the problems of noise amplification caused by large bandwidth and high gain and difficulty in parameter setting of other complex expansion state observers, and achieves the purpose of giving consideration to both disturbance estimation rapidity and noise robustness.

Description

Technical Field

[0001] The invention belongs to the technical field of extended state observers and relates to a design method of a strongly anti-interference frequency point adaptive switching extended state observer. Background Art

[0002] In industrial automation, aerospace, robotic control and other related fields, actual control systems are always subject to different types of internal and external disturbances. These disturbances are caused by the coupling of multiple causes such as environmental mutations, component failures, structural changes, and measurement errors. They usually show strong uncertainty and nonlinear characteristics, and are often difficult to accurately predict and model, which brings great challenges to the stability and control performance of the control system. The extended state observer can not only observe the internal state of the controlled object by constructing a virtual extended state variable, but also estimate and compensate for unknown disturbances and uncertainties in the closed-loop system in real time, so that the controller can better cope with disturbances. Compared with the traditional state observer, the extended state observer has the advantages of high accuracy and low model dependence. It can significantly improve the robustness and adaptability of the closed-loop system and is an effective way to solve the problem of stable control under large disturbances and strong uncertainty conditions.

[0003] Although scholars at home and abroad have conducted some research on the extended state observer, there is always a problem that the rapidity of disturbance estimation requires a high error gain, which in turn leads to the problem of measurement noise amplification. 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 observer bandwidth will significantly amplify the impact of the noise, causing the estimated value of the disturbance to oscillate violently, resulting in a decrease in accuracy or even estimation failure, thus affecting the performance of the closed-loop system.

[0004] Among various uncertainties and disturbances, fast-changing / sudden disturbances are the most difficult to deal with in engineering. Further considering the influence of signal measurement noise, the traditional method of changing the bandwidth of the linear extended state observer by configuring the poles is difficult to select the appropriate frequency in practical application. Although increasing the observer bandwidth by configuring the observer system poles makes the convergence faster, it also amplifies the influence of noise.

[0005] For the extended state observer, how to balance the contradiction between rapid convergence and high error gain noise suppression is the primary difficulty faced by its further engineering application. Therefore, it is very necessary to carry out research on the design method of the extended state observer with strong anti-interference frequency adaptive switching, dynamically adjust the gain according to the error convergence situation, and lay the foundation for further improving the anti-interference ability of the control system and promoting the wider engineering application of the extended state observer. Summary of the invention

[0006] The present invention aims to solve at least one of the problems existing in the prior art.

[0007] To this end, the present invention provides a design method for an extended state observer with strong anti-interference frequency adaptive switching, and specifically provides a design method for an extended state observer that performs frequency adaptive switching according to a phase plane boundary of an observed error modulus and an error modulus change rate. The method closely focuses on actual engineering needs, can solve the problems of noise amplification caused by large bandwidth and high gain, and other difficult parameter setting problems of extended state observers in complex forms, and achieves the purpose of balancing rapidity of disturbance estimation and robustness to noise.

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

[0009] A design method for a frequency adaptive switching extended state observer with strong anti-interference, the specific steps are as follows:

[0010] Step 1, extracting the state variables that need to be disturbed and observed in the controlled object system, and generating the system state equation for the state variables;

[0011] Step 2, based on the system state equation of step 1, establish the basic form of the frequency adaptive switching extended state observer; the basic frequency point in the frequency adaptive switching extended state observer is ω, and the frequency conversion factor is ξ. By designing the frequency adaptive switching logic conditions, the frequency conversion factor ξ can be switched 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: According to the error modulus change rate The frequency adaptive switching logic condition described in step 2 is designed with respect to the error modulus |e| in the phase plane;

[0013] Step 4: Adjust the adjustable parameters of the frequency adaptive extended state observer according to the feasible domain constraints, wherein the adjustable parameters include ξ1 and ξ2; calculate the value range of ξ1 and ξ2 from the perspective of observer stability to achieve the adjustment of the adjustable parameters.

[0014] Furthermore, in step 1, the state variable x that needs to be disturbed and observed in the controlled object system is taken out, and 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, N is the measurement noise, is the measured value of the state variable.

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

[0018]

[0019] Where 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 basic frequency of the frequency adaptive switching extended state observer, ξ is the frequency conversion factor, and ξ1>0,ξ2>0. By designing the switching logic conditions, namely conditon1 and conditon2, 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 conditon1 and conditon2 are:

[0021]

[0022] Among them, μ is the error switching factor, μ>0, and the boundary of the phase plane is changed by selecting the frequency conversion factors ξ1, ξ2 and the error switching factor μ to achieve adaptive switching of the frequency points; the frequency conversion factors ξ1, ξ2 determine the scaling of the real frequency point on the basic frequency point ω, and the error switching factor μ makes frequency switching decisions based on the two-dimensional information of the error size and error direction. Its size determines the influence of the error modulus and the error modulus change rate 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 two frequency points according to the relative position relationship in the phase plane composed of the error modulus and the error modulus change rate.

[0025] Furthermore, the process of calculating the value range of ξ1,ξ2 in step 4 is as follows:

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

[0027]

[0028] The equation (4) can be written in state space form as:

[0029]

[0030] in,

[0031]

[0032] As shown in formula (5), the stability of the observer system is determined by the A matrix. Considering the switching changes of the A matrix parameters, in order to analyze the stability of the observer system, it is necessary to find a positive definite real symmetric matrix P that satisfies:

[0033]

[0034] And A1 and A2 are:

[0035]

[0036] and

[0037] The stability of the frequency adaptive switching extended state observer is transformed into the judgment that formula (10) has no negative real eigenvalues. That is, if formula (10) does not have any negative real eigenvalues, it means that 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 , we only need to satisfy equation (12), which can ensure that equation (10) does not have any negative real eigenvalues, and further ensure 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 of χ, that is, equation (11), we can obtain When the relationship between ξ1 and ξ2 satisfies When the condition is , expression (10) does not have any negative real eigenvalues, which means that the frequency adaptive switching extended state observer is stable;

[0043] Therefore, under the premise of ensuring the stability of the frequency adaptive switching extended state observer, the value range of ξ1,ξ2 is:

[0044] Furthermore, in step 4, the adjustable parameters also include a basic frequency ω;

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

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

[0047] The error switching factor μ is set as follows: due to the existence of disturbance and noise, there is an order of magnitude difference between the error modulus value change rate and the error modulus value, and μ is set to be greater than 5.

[0048] Furthermore, for a multi-input and multi-output controlled object system, by designing a corresponding extended state observer for each state variable x, it is possible to estimate the external disturbance and uncertainty 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 method for designing an extended state observer with strong anti-interference frequency adaptive switching. The frequency switching logic of the extended state observer is designed based on the boundary between the error modulus and the error modulus change rate in the phase plane. This method can accelerate the convergence of the observer when the observation error is large and suppress noise during stable control. The method 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 value range of ξ1 and ξ2, the present invention converts the stability of the frequency adaptive switching extended state observer into the stability of the frequency adaptive switching extended state observer. There is no way to obtain any negative real eigenvalues, so the range of ξ1 and ξ2 that can ensure the stability of the observer can be given in analytical form, which is convenient 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 working process, it is equivalent to two linear extended state observers with different frequencies, which continuously switch 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, so the method proposed in the present invention has a strong engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

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

[0055] Figure 2 The feasible range diagram of the parameter values ​​of ξ1,ξ2 of the frequency adaptive switching extended state observer is given;

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

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

[0058] Figure 5 The x2 disturbance estimation curve of closed-loop control based on frequency adaptive switching extended state observer is given. DETAILED DESCRIPTION

[0059] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0061] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0062] Embodiment 1:

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

[0064] Step 1: Extract the system state equation of the controlled object according to the actual physical constraints:

[0065] Take out the state variable x that needs to be disturbed and observed 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 formula (1):

[0066]

[0067] In the formula, x is the state variable of the controlled system, u is the control input, f is the unknown nonlinear function, d is the unknown external disturbance, N is the measurement noise, is the measured value of the state variable.

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

[0069]

[0070] Where 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), β1 = -2ω, β2 = -ω 2, ω is the basic frequency of the frequency adaptive switching extended state observer, ξ is the frequency conversion factor, and by designing the switching logic conditions (i.e., conditon1 and conditon2), 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 respectively -ξ1ω, -ξ1ω and -ξ2ω, -ξ2ω.

[0071] Step 3: Design the error modulus change rate The frequency adaptive switching logic relative to the error modulus |e| in the phase plane, that is, the switching logic conditions conditon1 and conditon2 are designed; the frequency adaptive switching logic proposed in this embodiment is shown in formula (3):

[0072]

[0073] Among them, μ is the error switching factor, μ>0, and the boundary of the phase plane is changed by selecting the frequency conversion factors ξ1, ξ2 and the error switching factor μ to achieve adaptive switching of the frequency points; the frequency conversion factors ξ1, ξ2 determine the scaling of the real frequency point on the basic frequency point ω, and the error switching factor μ makes frequency switching decisions based on the two-dimensional information of the error size and error direction. Its size determines the influence of the error modulus and the error modulus change rate on the switching logic of the observer switching system.

[0074] When ξ1=ξ2, the switching system of the frequency adaptive switching extended state observer will degenerate into a linear extended state observer, working at a fixed frequency. When ξ1≠ξ2, the frequency adaptive extended state observer has the characteristic of dynamically adjusting the error gain between two frequencies according to the relative position relationship in the phase plane composed of the error modulus and the error modulus change rate. Its switching logic is as follows: Figure 1 shown.

[0075] If -μ<error modulus change rate divided by error modulus<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 working bandwidth of the observer is switched to the larger of ξ1 and ξ2, that is, ξ2, thereby accelerating the convergence speed of the observer and making effective estimation when a mutation occurs; if the error modulus change rate divided by the error modulus is ≥ 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 quickly. From the perspective of suppressing high-frequency noise, the working bandwidth of the observer is switched to the smaller of ξ1 and ξ2, that is, ξ1, to suppress the influence of measurement noise when the observation error is small.

[0076] Step 4: Adjust the adjustable parameters of the frequency adaptive extended state observer according to the feasible domain constraints:

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

[0078] (1) Setting of the basic frequency ω: Since the basic frequency ω determines the size and rapidity of the observer gain, its influence on the frequency adaptive switching extended state observer is similar to that on the linear extended state observer. The larger the ω, the larger 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 fast-changing or high-intensity disturbances, a larger basic frequency ω should be selected; for slow-changing or low-intensity disturbances, a smaller basic frequency ω should be selected. The value of the basic frequency ω can be selected based on experience.

[0079] (2) Setting of μ: Due to the presence of disturbance and noise, the error modulus change rate and the error modulus value are orders of magnitude different. μ is generally set to a value greater than 5.

[0080] (3) Setting of ξ1, ξ2: Calculate the value range of ξ1, ξ2 from the perspective of observer stability;

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

[0082]

[0083] Written in state space form as shown in formula (5):

[0084]

[0085] in,

[0086]

[0087] As shown in formula (5), the stability of the observer system is determined by the A matrix. Considering the switching changes of the A matrix parameters, in order to analyze the stability of the observer system, it is necessary to find a positive definite real symmetric matrix P that satisfies:

[0088]

[0089] And A1 and A2 are:

[0090]

[0091] and

[0092] With the help of the existence criterion of the public quadratic Lyapunov function of the second-order system in the switching system theory, it can be known that if the switching system has a public quadratic Lyapunov function, the switching system is stable. Therefore, the stability of the frequency adaptive switching extended state observer can be further transformed into the judgment that formula (10) has no negative real eigenvalues. That is, if formula (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 , we only need to satisfy equation (12), which can ensure that equation (10) does not have any negative real eigenvalues, and further ensure 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 of χ, that is, equation (11), we can obtain When the relationship between ξ1 and ξ2 satisfies When the condition is met, expression (10) does not have any negative real eigenvalues, which means that the frequency adaptive switching extended state observer is stable; the feasible domain composed of ξ1 and ξ2 is as follows: Figure 2 As shown in the figure, the feasible domain range of ξ1,ξ2 of frequency adaptive switching is relatively wide. In particular, when 0<ξ1<1, the two frequency points ξ1ω and ξ2ω of the extended state observer appear in the form of one large and one small (i.e., ξ2ω is greater than ω, and ξ1ω is less than ω), thereby suppressing the influence of measurement noise in the steady state and making the observer converge quickly when the disturbance is large.

[0098] Embodiment 2:

[0099] Based on Example 1, this example designs and verifies a frequency adaptive observer for a second-order system commonly used in the industry as a controlled object, specifically:

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

[0101]

[0102] In the formula, x1, 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; y is the output of the second-order system.

[0103] The second step is to design the frequency adaptive extended state observer and related parameters:

[0104] For a multi-input and multi-output controlled object system, it is necessary to design a corresponding extended state observer for each state variable x, so as to achieve the estimation of external disturbances and uncertainties of all states of the controlled object system in a similar manner; generally, a second-order controlled object system established based on a real physical process generally has the characteristic that the control input u only acts on the second-order state quantity x2. Considering that u needs to be used to compensate for the observed disturbance 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 compensation is realized through u. The frequency adaptive extended state observer designed according to formula (2) in embodiment 1 can be written as shown in formula (15):

[0106]

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

[0108] Table 1 Frequency adaptive extended state observer parameters

[0109]

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

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

[0112] The closed-loop control law is shown in formula (16):

[0113]

[0114] in, is the tracking control error for x1, x 1c is the command input, k p is the proportional control parameter, k d is the differential control parameter;

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

[0116] Table 2 Proportional-derivative control parameters and command input

[0117]

[0118] The fourth step is to verify the effectiveness of the design method by simulation:

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

[0122] Depend on Figure 4 It is known that when only proportional differential control is used, the adjustment time of the x1 step response is about 2s, and the steady-state error of about 0 to 0.25 will appear due to disturbances and noise, affecting the closed-loop control performance; after adding the frequency adaptive extended state observer to estimate and compensate for the disturbance, the influence of the disturbance on the x1 step response in the steady state is significantly reduced, and the steady-state error is maintained between ±0.06 while retaining good rapidity.

[0123] Depend on Figure 5 It is known that the curve of the actual disturbance and the frequency adaptive switching ECO basically coincide, and the frequency adaptive extended state observer still maintains a good tracking estimation of the disturbance under the noise condition, and no oscillation and divergence occur. This shows that the frequency switching logic designed in this embodiment has achieved the expected purpose, while taking into account the rapidity of disturbance estimation and suppressing noise during stable control.

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

[0125] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. If not otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0126] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A design method for a frequency adaptive switching extended state observer with strong anti-interference, characterized in that: The specific steps are as follows: Step 1, extracting the state variables that need to be disturbed and observed in the controlled object system, and generating the system state equation for the state variables; Step 2, based on the system state equation in step 1, establish the basic form of the frequency adaptive switching extended state observer; The basic frequency point in the frequency adaptive switching extended state observer is ω, and the frequency conversion factor is ξ. By designing the frequency adaptive switching logic conditions, the frequency conversion factor ξ can be switched between ξ1 and ξ2, thereby realizing the adaptive switching of the extended state observer between the two frequency points ξ1ω and ξ2ω. Step 3: According to the error modulus change rate The frequency adaptive switching logic condition described in step 2 is designed with respect to the error modulus |e| in the phase plane; Step 4: Adjust the adjustable parameters of the frequency adaptive extended state observer according to the feasible domain constraints, wherein the adjustable parameters include ξ1 and ξ2; calculate the value range of ξ1 and ξ2 from the perspective of observer stability to achieve the adjustment of the adjustable parameters.

2. The design method of a frequency adaptive switching extended state observer with strong anti-interference as claimed in claim 1 is characterized in that: In step 1, the state variable x that needs to be disturbed and observed in the controlled object system is taken out, and 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, N is the measurement noise, is the measured value of the state variable.

3. A design method for a frequency adaptive switching extended state observer with strong anti-interference as claimed in claim 2, characterized in that: In step 2, the basic form of the frequency adaptive switching extended state observer is: Where 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 basic frequency of the frequency adaptive switching extended state observer, ξ is the frequency conversion factor, and ξ1>0,ξ2>0. By designing the switching logic conditions, namely conditon1 and conditon2, 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.

4. The design method of a frequency adaptive switching extended state observer with strong anti-interference as claimed in claim 3 is characterized in that: In step 3, the designed frequency adaptive switching logic conditions conditon1 and conditon2 are: Among them, μ is the error switching factor, μ>0, and the boundary of the phase plane is changed by selecting the frequency conversion factors ξ1, ξ2 and the error switching factor μ to achieve adaptive switching of the frequency points; the frequency conversion factors ξ1, ξ2 determine the scaling of the real frequency point on the basic frequency point ω, and the error switching factor μ makes frequency switching decisions based on the two-dimensional information of the error size and error direction. Its size determines the influence of the error modulus and the error modulus change rate on the switching logic of the observer switching system.

5. A design method for a strongly anti-interference frequency adaptive switching extended state observer as claimed in claim 3 or 4, characterized in that: When ξ1=ξ2, the switching system of the frequency adaptive switching extended state observer will degenerate into a linear extended state observer, working at a fixed frequency. When ξ1≠ξ2, the frequency adaptive extended state observer dynamically adjusts the error gain between two frequency points according to the relative position relationship in the phase plane composed of the error modulus and the error modulus change rate.

6. The design method of a frequency adaptive switching extended state observer with strong anti-interference as claimed in claim 4, characterized in that: The process of calculating the value range of ξ1 and ξ2 in step 4 is as follows: Let the true observation error be e1=z1-x, e2=z2-df, and e1=eN. Combining equations (1) and (2), the state equation of the true error can be obtained as follows: The equation (4) can be written in state space form as: in, As shown in formula (5), the stability of the observer system is determined by the A matrix. Considering the switching changes of the A matrix parameters, in order to analyze the stability of the observer system, it is necessary to find a positive definite real symmetric matrix P that satisfies: And A1 and A2 are: and The stability of the frequency adaptive switching extended state observer is transformed into the judgment that formula (10) has no negative real eigenvalues. That is, if formula (10) does not have any negative real eigenvalues, it means that the frequency adaptive switching extended state observer is stable: and When β1=-2ω,β2=-ω 2 When , we only need to satisfy equation (12), which can ensure that equation (10) does not have any negative real eigenvalues, and further ensure the stability of the frequency adaptive switching extended state observer: (ξ1 2 +ξ2 2 ) / ξ1ξ2<6 (12) Substituting equation (12) into the expression of χ, that is, equation (11), we can obtain When the relationship between ξ1 and ξ2 satisfies When the condition is , expression (10) does not have any negative real eigenvalues, which means that the frequency adaptive switching extended state observer is stable; Therefore, under the premise of ensuring the stability of the frequency adaptive switching extended state observer, the value range of ξ1,ξ2 is:

7. A design method for a strongly anti-interference frequency adaptive switching extended state observer according to any one of claims 1 to 4 or 6, characterized in that: In step 4, the adjustable parameters also include a basic frequency point ω; The basic frequency point ω is set as follows: the basic frequency point ω determines the size and rapidity of the observer gain. The larger the ω, the larger the error gain, the more accurate the estimation of the external disturbance d under noise-free conditions, and the faster the convergence speed. The value of the basic frequency point ω is selected based on experience.

8. A design method for a frequency adaptive switching extended state observer with strong anti-interference as claimed in any one of claims 1 to 4 or 6, characterized in that: In step 4, the adjustable parameters also include an error switching factor μ; The error switching factor μ is set as follows: due to the existence of disturbance and noise, there is an order of magnitude difference between the error modulus value change rate and the error modulus value, and μ is greater than 5.

9. A design method for a frequency adaptive switching extended state observer with strong anti-interference as claimed in any one of claims 1 to 4 or 6, characterized in that: For a multi-input and multi-output controlled object system, by designing a corresponding extended state observer for each state variable x, it is possible to estimate the external disturbance and uncertainty of all states of the controlled object system separately.

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