Non-matching disturbance rejection method and device based on extended compensation function observer

Abstract

The application relates to the field of automation advanced control theory and application technology, and provides a non-matching disturbance suppression method and equipment based on an extended compensation function observer.The method is used for a non-integral chain system with non-matching disturbance, the non-matching disturbance is subjected to an extended order processing, and an extended system with non-matching disturbance order derivative display is obtained; the extended compensation function observer is designed according to the extended system, error analysis is carried out on the extended compensation function observer, and the gain of the extended compensation function observer is selected according to the convergence principle of the extended error equation; and the model compensation control strategy is designed according to the extended compensation function observer and the state error feedback, so that the non-matching disturbance of the non-integral chain system is suppressed.The application can estimate the non-matching disturbance with the order derivative tending to zero, so that the restriction on the disturbance is greatly relaxed, and a more accurate and more applicable anti-disturbance control solution is provided.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of advanced control theory and application automation, and in particular to a non-matching disturbance suppression method and device based on an extended compensation function observer. BACKGROUND

[0002] Disturbances such as model mismatch, parameter drift, and external interference in control systems such as unmanned aerial vehicle flight control, robot motion control, motor drive, and electromagnetic suspension systems are key factors affecting control performance. Control strategies based on disturbance observers are an effective means to address this issue, as they estimate the lumped disturbance through an observer and provide feedforward compensation, significantly improving system robustness. To this end, researchers have developed various observers such as the Disturbance Observer (DOB), Extended State Observer (ESO), and Compensation Function Observer (CFO) to estimate system disturbances.

[0003] However, existing control techniques based on disturbance observers have two major limitations. First, the application scope is limited, and the excellent performance of traditional CFOs strictly depends on the assumption that the system satisfies the integral chain form and the disturbance is matching. For more general non-integral chain systems or scenarios with non-matching disturbances, traditional CFOs cannot be directly applied or their performance degrades to only estimating constant disturbances. Second, the disturbance assumption is too strong: existing solutions for non-matching disturbances such as control based on generalized ESO and sliding mode control based on nonlinear DOB mostly assume that the first derivative of the disturbance is bounded and tends to zero, which greatly limits their ability to estimate and suppress high-order time-varying disturbances. In actual systems such as unmanned aerial vehicle attitude systems and robot joint control systems, matching and non-matching disturbances often coexist. Therefore, there is an urgent need for a new type of observer and control strategy that can be applied to more general non-integral chain systems while relaxing the dynamic assumption of the disturbance, and can suppress high-order time-varying matching and non-matching disturbances. SUMMARY

[0004] The present application aims to at least solve one of the technical problems in the related art. To this end, the present application provides a non-matching disturbance suppression method and device based on an extended compensation function observer, which fundamentally improves the order of the traditional CFO, enabling it to be applied to non-integral chain systems and to estimate non-matching disturbances with a first derivative tending to zero, thereby significantly relaxing the disturbance restrictions and providing a more accurate and widely applicable anti-disturbance control solution.

[0005] The present application provides a non-matching disturbance suppression method based on an extended compensation function observer, comprising:

[0006] S1: Extend the order of the non-integral chain system with unmatched perturbation to obtain the extended system;

[0007] S2: Based on the design of the extended compensation function observer, perform error analysis on the extended compensation function observer to obtain the extended error equation;

[0008] S3: Select the gain of the observer based on the extended compensation function according to the extended error equation;

[0009] S4: Based on the gain of the extended compensation function observer, the extended compensation function observer, and the state error feedback, design a model compensation control strategy based on the extended compensation function observer. Suppress the mismatch disturbance of the non-integral chain system through the model compensation control strategy based on the extended compensation function observer.

[0010] Furthermore, in step S1, the unmatched disturbance includes model uncertainty, measurement uncertainty, external disturbance, and complex nonlinear terms that are difficult to handle. The non-integral chain system with unmatched disturbance includes UAV flight control system, robot motion control system, motor drive system, and electromagnetic levitation system.

[0011] Furthermore, step S1 includes:

[0012] S11: Obtain a second-order non-integral chain system with unmatched perturbations;

[0013] S12: Extend the order of the second-order non-integral chain system with the unmatched perturbation as an extended state to obtain a third-order non-integral chain system.

[0014] S13: Continue extending the order of the third-order non-integral chain system until the unmatched perturbation... The order derivative is displayed, and the extended system is obtained.

[0015] Furthermore, in step S2, designing the extended compensation function observer based on the extended system includes:

[0016] S21: Design a second-order observer with a perturbation compensation term;

[0017] S22: By performing multinomial expansion on the second-order observer using perturbation compensation terms and auxiliary variables, an extended compensation function observer is obtained.

[0018] Furthermore, in step S21, the disturbance compensation term includes a first disturbance compensation term and a second disturbance compensation term. The calculation expression for the first disturbance compensation term is:

[0019]

[0020] in, This is the first disturbance compensation item. The observer gain coefficient, For the Laplace operator, For disturbance estimation, This is a non-matching perturbation. This is the second disturbance compensation item. for The estimated value, for The derivative of For integration operations;

[0021] The second disturbance compensation term satisfies:

[0022]

[0023] in, For the differentiation operation, For the first Level perturbation, For the first The parameters to be determined are of order. For the first Auxiliary variables of order, This is the first system state.

[0024] Furthermore, in step S22, the auxiliary variable is:

[0025]

[0026] in, for The derivative of As the first coefficient, As the second coefficient, This is the second system state. For the first Level perturbation, for The derivative of For the first Auxiliary variables of order, For the first The parameters to be determined.

[0027] Furthermore, the extended error equation is obtained by subtracting the extended compensation function observer from the extended system.

[0028] Furthermore, in step S3, according to the extended error equation, when the mismatched disturbance satisfies When the gain of the extended compensation function observer is selected by pole placement, and the error matrix is ​​a Hurwitz matrix, the extended compensation function observer achieves error-free estimation of mismatched perturbations. For disturbance First derivative, For time.

[0029] Furthermore, the model compensation control strategy based on the extended compensation function observer is as follows:

[0030]

[0031] in, To control the input, To control the allocation coefficient, To output the error vector, For error feedback, For the model feedforward term, Let be the state vector of the system. For disturbance compensation, For disturbance estimation, for The estimated value, for The derivative of This is a non-matching perturbation.

[0032] The present invention also provides an unmatched disturbance suppression device based on an extended compensation function observer, for performing the above-described unmatched disturbance suppression method based on an extended compensation function observer, comprising:

[0033] The construction module extends the order of a non-integral chain system with unmatched perturbations to obtain the unmatched perturbations. The extended system is presented by displaying the order derivative;

[0034] The extension module designs an extended compensation function observer based on the extended system design, and performs error analysis on the extended compensation function observer to obtain the extended error equation;

[0035] The selection module selects the gain of the observer based on the extended error equation;

[0036] The control module designs a model compensation control strategy based on the extended compensation function observer, the extended compensation function observer, and the state error feedback, and suppresses the mismatch disturbance of the non-integral chain system through the model compensation control strategy based on the extended compensation function observer.

[0037] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0038] This invention extends the traditional CFO compensation mechanism to non-integral chain systems, proposing ECFO (Extended CFO) through an extended-order design. ECFO only requires the assumption of the perturbation. When the first derivative approaches zero, accurate estimation can be achieved. Compared with traditional methods, this relaxes the restrictions on the dynamics of the disturbance and can effectively estimate time-varying disturbances of higher order, greatly expanding the application boundaries of CFO theory.

[0039] The ECFO-based model compensation control (ECFOBMCC) strategy can simultaneously and proactively compensate for matched and unmatched disturbances. Its control performance is superior to traditional methods, with smaller system output overshoot, shorter recovery time, and stronger robustness.

[0040] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0042] Figure 1 This is a flowchart illustrating a non-matching perturbation suppression method based on an extended compensation function observer provided by the present invention.

[0043] Figure 2 This is the overall block diagram of the ECFOBMCC strategy provided by the present invention.

[0044] Figure 3 This is a schematic diagram comparing the disturbance estimation and estimation error of each observer for the system disturbance in the numerical system embodiment of the present invention.

[0045] Figure 4 This is a graph showing the system output response and control input curves under various control conditions in the numerical system embodiment of the present invention.

[0046] Figure 5 This is a comparison chart of different observers and controllers under slope disturbance in the numerical system embodiment of the present invention.

[0047] Figure 6 This is a comparison chart of different observers and controllers under acceleration perturbation in the numerical system embodiment of the present invention.

[0048] Figure 7 This is a comparison diagram of the control effects of different controllers in the embodiment of the present invention for a quadcopter drone.

[0049] Figure 8This is a schematic diagram of the structure of an unmatched disturbance suppression system based on an extended compensation function observer provided by the present invention.

[0050] Figure label:

[0051] 101. Building module; 102. Extending module; 103. Selection module; 104. Control module. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but cannot be used to limit the scope of this invention.

[0053] In the description of the embodiments of the present invention, it should be noted that the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0054] The following is combined Figures 1 to 8 This invention describes a method and apparatus for suppressing unmatched disturbances based on an extended compensation function observer.

[0055] For non-integral chain systems with mismatched disturbances, following the traditional CFO design approach, we analyze how the CFO can estimate the type of mismatched disturbance.

[0056] The second-order non-integral chain system with unmatched perturbation is as follows:

[0057] (1)

[0058] in, This is the first system state. This is the second system state. for The derivative of for The derivative of As the first coefficient, As the second coefficient, This is a non-matching perturbation. The third coefficient, It is the fourth coefficient. To control the gain coefficient, To control the input, This is the output.

[0059] Mismatched perturbations include model uncertainties, measurement uncertainties, external disturbances, and complex nonlinear terms that are difficult to handle. It is usually unknown, and an observer needs to be designed to estimate it in advance, thereby suppressing its impact on the system.

[0060] The traditional CFO is initially designed as follows:

[0061] (2)

[0062] in, This is the state of the first observer. for The derivative of This is the state of the second observer. for The derivative of For the error vector, , This is the first error vector. This is the second error vector. This is the transpose of the matrix. For observer gain, , For the first observer gain, For the second observer gain, for The disturbance compensation, or compensator.

[0063] Equation (2) maintains the structure of Equation (1), and the corresponding perturbation estimate , ,Will Designed as The first-order low-pass filter, i.e. ;

[0064] The conclusion is The dynamic equation is:

[0065] (3)

[0066] in, The observer gain coefficient, for The derivative of For the Laplace operator.

[0067] Will Viewed as the third state, the traditional third-order CFO is derived as follows:

[0068] (4)

[0069] in, This is the state of the third observer. for The derivative;

[0070] make Equation (4) can be reformulated as:

[0071] (5)

[0072] in, For the first state estimator, for The derivative of For the second state estimator, for The derivative of For extended state, For the third state estimator, for The derivative of for The derivative;

[0073] Let the third error vector , , This is the extended error vector of the traditional CFO. Subtracting equation (5) from equation (2) yields the traditional error equation:

[0074] (6)

[0075] in, for The derivative of The vector of gain coefficients for the perturbation derivative. , This is the system error matrix of a traditional CFO. .

[0076] The traditional error equation shows that when the observer gain is selected to satisfy... The matrix is ​​a Hurwitz matrix, and the unmatched perturbation satisfies hour, For time, the disturbance estimation of a traditional CFO It can converge asymptotically to In other words, traditional CFOs can only estimate constant disturbances without error, which greatly limits the application scenarios of CFOs.

[0077] like Figure 1 As shown, a compensation control method for mismatched disturbances based on ECFO includes:

[0078] S1: Extend the order of the non-integral chain system with unmatched perturbation to obtain the extended system;

[0079] S11: Obtain a second-order non-integral chain system with unmatched perturbations;

[0080] S12: Extend the order of the second-order non-integral chain system with the unmatched perturbation as an extended state to obtain a third-order non-integral chain system. The calculation expression is as follows:

[0081] (7)

[0082] in, for The derivative of for The derivative of , , , It must simultaneously satisfy that equation (1) is controllable and equation (7) is observable.

[0083] S13: Continue extending the order of the third-order non-integral chain system until the unmatched perturbation... The order derivative is displayed, and the extended system is obtained.

[0084] The third-order non-integral chain system is further extended until the perturbation... The order derivative is displayed, and the calculation expression for the extended system is:

[0085] (8)

[0086] in, This is the fourth system state. For the first A system state, for The derivative of For disturbance The first derivative.

[0087] S2: Based on the design of the extended compensation function observer, perform error analysis on the extended compensation function observer to obtain the extended error equation;

[0088] S21: Design a second-order observer with a perturbation compensation term;

[0089] Based on the design concept of traditional compensation function observers, a preliminary design of a second-order observer with a novel perturbation compensation term is presented for non-integral chain systems with unmatched perturbations.

[0090] The disturbance compensation term includes a first disturbance compensation term and a second disturbance compensation term. The calculation expression for the first disturbance compensation term is as follows:

[0091] (9)

[0092] in, This is the first disturbance compensation item. The observer gain coefficient, For the Laplace operator, For disturbance estimation, This is a non-matching perturbation. This is the first disturbance compensation item. for The estimated value, For integration operations;

[0093] The second disturbance compensation term satisfies:

[0094] (10)

[0095] in, To find the derivative, For the first Level perturbation, For the first The parameters to be determined are of order. For the first Auxiliary variables of order.

[0096] For equation (1), a preliminary second-order observer is obtained through perturbation compensation, and the calculation expression is:

[0097] (11)

[0098] S22: By performing multinomial expansion of the second-order observer with perturbation compensation terms and auxiliary variables, an extended compensation function observer is obtained.

[0099] The auxiliary variable is:

[0100] (12)

[0101] in, for The derivative of As the first coefficient, As the second coefficient, This is the first system state. This is the second system state. For the first Level perturbation, for The derivative of For the first Auxiliary variables of order, For the first The parameters to be determined.

[0102] make: This is the state of the fourth observer. For the first Observer state,

[0103]

[0104]

[0105] Get the expanded The ECFO order is:

[0106] (13)

[0107] in, This is the state of the first observer. for The derivative of This is the state of the first observer. for The derivative of This is the state of the third observer. for The derivative of This is the state of the fourth observer. for The derivative of This is the state of the fifth observer. for The derivative of This is the state of the sixth observer. for The derivative of For the first Observer state, for The derivative of For the first Observer state, As the first coefficient, As the second coefficient, For observer gain, For the error vector, The third coefficient, It is the fourth coefficient. To control the gain coefficient, To control the input, The observer gain coefficient, For the third-order parameters to be determined, For the fourth-order parameters to be determined, For the first The parameters to be determined are of order. For the first The parameters to be determined are of order. As auxiliary parameters, , This is the first system state. This is the second system state. The ECFO design is now complete.

[0108] The extended error equation is obtained by subtracting the extended compensated observer from the extended system.

[0109] make ECFO can be expressed as:

[0110] (14)

[0111] in, For the fourth state estimator, for The derivative of For the fifth state estimator, for The derivative of For the first State estimator For the first State estimator for The derivative of

[0112] Subtracting equation (14) from equation (8) yields the extended error equation:

[0113] (15)

[0114] in, for The derivative of For ECFO's Order error vector, , For the first Error vector; For the first The gain coefficient vector of the order perturbation derivative. , Here is the error matrix of ECFO.

[0115] (16)

[0116] in, This is the second error submatrix. , This is the third error submatrix. , This is the fourth error submatrix. .

[0117] S3: Select the gain of the observer based on the extended compensation function according to the extended error equation, and obtain the error matrix;

[0118] According to the extended error equation, when the mismatched disturbance satisfies Conditions (where, For disturbance First derivative, (For time), by selecting the gain of the observer through pole placement and ensuring that the error matrix is ​​a Hurwitz matrix, we can obtain:

[0119] (17)

[0120] Therefore, ECFO can not only guarantee the estimation of disturbances Undifferentiated asymptotic convergence to system perturbation Its derivatives can also be estimated asymptotically. The estimable perturbation of ECFO satisfies This means that disturbances are allowed to appear in higher-order forms, which greatly increases the types of disturbances that can be estimated, unlike the traditional CFO which can only estimate constant disturbances.

[0121] S4: Based on the gain of the extended compensation function observer, the extended compensation function observer, and the state error feedback, design a model compensation control strategy based on the extended compensation function observer, and suppress the mismatch disturbance of the non-integral chain system through the model compensation control strategy based on the extended compensation function observer;

[0122] For a second-order non-integral chain system with unmatched perturbations, the desired output is defined as follows: The set control objective is to control the input. Under the influence of the system, the output Able to asymptotically track the desired output For the output equation Find the derivative twice If displayed, we can obtain:

[0123] (18)

[0124] in, for The second derivative of .

[0125] ECFO-based model compensation control strategies, such as Figure 2 As shown, the calculation expression is:

[0126] (19)

[0127] in, To control the input, To control the allocation coefficient, , To output the error vector, , To output the error scalar, of The derivative of for The derivative of for The derivative of and It can be obtained through a higher-order differentiator (HOD). For error feedback, , To control the gain vector, , The first control gain, For the second control gain, For the model feedforward term, , Let be the state vector of the system. For disturbance compensation, , For disturbance estimation, for The estimated value.

[0128] Pole placement, sliding mode, and linear quadratic optimization methods can be used to obtain the poles. In some specific embodiments of this invention, pole placement of the output error is used. yes The estimated value, yes The estimated value, and It can be obtained through ECFO.

[0129] Select the observer gain so that The Hurwitz matrix is ​​selected, and at the same time... Using the proposed ECFOBMCC as the control input, the output channel of the controlled system can avoid the influence of unmatched lumped disturbances, meaning that the system output can asymptotically converge to any desired output.

[0130] Example:

[0131] Consider the following nonlinear second-order nonintegral chain system containing unmatched uncertainties:

[0132] (20)

[0133] in, For system disturbances, the mismatched disturbance is represented as Then equation (20) will take the form of equation (1), and be expressed as:

[0134] (twenty one)

[0135] Extending equation (21), we get:

[0136] (twenty two)

[0137] in, for The second derivative of .

[0138] The designed ECFO is as follows:

[0139] (twenty three)

[0140] Choosing the observer poles as the characteristic equation The root is approximately equal to ,in The value is the imaginary unit. Based on this pole, the observer gain of ECFO can be derived as: .

[0141] For equation (21), the control objective is to require the system output to be... Able to stably track the desired signal And avoid the influence of system disturbances. Taking the derivative of the output of equation (21) twice, we can get:

[0142] (twenty four)

[0143] Then ECFOBMCC can be designed as follows:

[0144] (25)

[0145] in, , Based on ECFO estimation, the controller gain is set to... .

[0146] To further highlight the superior performance of the present invention, based on the model of this embodiment, a GESO-based control (GESOBC) and a traditional CFO-based control (CFOBC) that can handle system mismatch disturbances were also designed as a control group for comparison.

[0147] like Figure 3 Figure (a) shows the system disturbance estimates for CFO and ECFO1. It converges to the actual system perturbation after approximately 1.3 s and 0.7 s, respectively. GESO, on the other hand, takes approximately 3 seconds. Figure 3 As shown in Figure (b), the disturbance estimation errors of CFO and ECFO1 are also much smaller than those of GESO.

[0148] like Figure 4 As shown, controllers GESOBC, CFOBC, and ECFOBMCC can all enable the system output to asymptotically converge to a given output under constant system disturbances. The control performance of both CFOBC and the ECFOBMCC proposed in this invention is superior to GESOBC. Specifically, CFOBC has the shortest settling time, while the settling times of ECFOBMCC and GESOBC are basically the same; ECFOBMCC has the smallest overshoot, followed by CFOBC, and GESOBC has the largest overshoot and the largest oscillation amplitude. Figure 4 Figure (a) shows the system output under the action of the three controllers. Figure 4 Figure (b) shows the control inputs for the three controllers.

[0149] To further illustrate that the observer and controller proposed in this invention can eliminate the influence of higher-order disturbances on the system, the system disturbances are respectively set as ramp signals ( ) and acceleration signal ( ).

[0150] Figure 5 The study compares the observer disturbance estimation and controller control performance of three control strategies when the system disturbance is a ramp disturbance. Figure 5 Figure (a) shows the system disturbances estimated by GESO, CFO, and ECFO1. All are consistent with actual slope disturbances The trend is consistent, except that GESO has a significant error. Figure 5 At the viewpoint scale of Figure (a), the remaining curves almost coincide with the actual disturbance curve, and their estimation error comparison curves are from Figure 5 Figure (b) is given in the middle. Figure 5As can be seen from Figure (b), under the influence of slope disturbance, the disturbance estimation error of ECFO1 eventually converges to 0; while GESO and CFO both have constant steady-state errors in estimating system disturbances, but the error of CFO (approximately 0.006) is much smaller than that of GESO (approximately 0.2). Figure 5 Figure (c) shows the changes in system output under ramp disturbance under three control strategies. Similar to the observer's estimation results, ECFOBMCC can achieve error-free tracking of the given signal, while GESOBC and CFOBC eventually have constant steady-state tracking errors. Figure 6 This paper compares the observer disturbance estimation and controller control performance for three types of control strategies when the system disturbance is an acceleration disturbance. Figure 6 As shown, from Figure 6 Figure (a) shows the system disturbances estimated by GESO, CFO, and ECFO1. Both are consistent with the actual acceleration disturbance trend. Consistent, with Figure 5 The results were consistent, except that GESO exhibited significant errors. Figure 6 At the viewpoint scale of Figure (a), the remaining curves almost coincide with the actual disturbance curve, and their estimation error comparison curves are from Figure 6 Figure (b) is given in the middle. Figure 6 As can be seen in Figure (b), under the influence of acceleration disturbances, ECFO1 exhibits a constant steady-state error (0.0077), while the estimation errors of GESO and CFO both gradually increase with a fixed slope; from Figure 6 As shown in Figure (c), the corresponding controller exhibits a similar trend. The reason for the steady-state error in ECFO1's estimation of acceleration disturbances is that the acceleration disturbances satisfy... ECFO1 corresponds to A value of 2 indicates that only one function can be processed. To achieve error-free estimation of acceleration disturbances, ECFO needs to be further extended.

[0151] To further illustrate the practicality of this invention in real-world scenarios, a quadcopter drone's attitude system is used as another embodiment. The nonlinear attitude mechanism model of the quadcopter drone can be expressed as:

[0152] (26)

[0153] in, Euler angles, For the body's angular velocity, for The derivative of To describe Euler angular rate With body angular velocity The rotation relation matrix, , for The set of real matrices, The moment of inertia of the quadcopter. , For gyro torque, For aerodynamic drag torque, This represents the torque generated by the propeller on the fuselage shaft. Taking the roll channel of a quadcopter UAV as an example, the resulting controlled object model is as follows:

[0154] (27)

[0155] in, For roll angle, for The derivative of For the roll rate, for The derivative of This is the known part of the roll channel mechanism model for quadcopter UAVs. The moment of inertia of the rolling channel. The rolling torque is generated by the four rotors. For the non-matched perturbation of the nonlinear attitude of the quadcopter UAV, This is a matching perturbation for the nonlinear attitude of a quadcopter drone. The control objective of this embodiment is the roll angle of the quadcopter drone. Able to stably track a given signal under the influence of system disturbances .

[0156] For the controlled object model of equation (27), the ECFO proposed in this invention can be designed as follows:

[0157] (28)

[0158] in, for The derivative of The gain parameter of the first observer. This is the gain coefficient of the second observer. For the third observer gain parameter, For the fourth observer gain parameter, For the fifth observer gain parameter, For the sixth observer gain parameter, This refers to the gain parameter of the seventh observer. , , , .

[0159] The ECFO-based model compensation controller can be designed as follows:

[0160] (29)

[0161] in, For controller parameters, , For the first controller parameters, For the second controller parameters, To control the error vector, , for The derivative of for Second derivative, for The estimated value, for The derivative of for The estimated value, and All can be derived from ECFO, and are expressed as follows:

[0162]

[0163] .

[0164] In this embodiment, cascade PID control, model compensation control (MCC), and GESO-based control are introduced as control groups for comparison with the controller of this invention. The comparison results are obtained by... Figure 7 Display. Set a given roll angle, such as... Figure 7 The black line in figure (a) is shown, and it is introduced between 57 and 67 seconds. A matching perturbation is introduced between 75 and 85 seconds. .according to Figure 7 In Figure (a), under the condition of no disturbance, the cascade PID control has a slightly better speed than other controllers, but it has overshoot; the settling times of MCC, GESOBC, and ECFOBMCC are basically the same, and their tracking curves are also basically the same. From Figure 7 As shown in Figure (b), ECFOBMCC exhibits the best suppression effect after introducing the unmatched perturbation, with its maximum error amplitude not exceeding 0.01. This is followed by GESOBC, then cascaded PID, and finally MCC. Figure 7 As can be seen from Figure (c), under the influence of matching perturbation, ECFOBMCC and MCC have consistent overall performance, with MCC slightly outperforming ECFOBMCC, followed by cascaded PID, and finally GESOBC.

[0165] like Figure 8As shown, an unmatched disturbance suppression device based on an extended compensation function observer is used to perform an unmatched disturbance suppression method based on an extended compensation function observer, comprising:

[0166] Module 101 extends the order of the non-integral chain system with unmatched perturbations to obtain the unmatched perturbations. The extended system is presented by displaying the order derivative;

[0167] Extension module 102 designs an extended compensation function observer based on the extended system, and performs error analysis on the extended compensation function observer to obtain the extended error equation;

[0168] Module 103 selects the gain of the observer based on the extended error equation;

[0169] The control module 104 designs a model compensation control strategy based on the extended compensation function observer based on the gain of the extended compensation function observer, the extended compensation function observer, and the state error feedback. The model compensation control strategy based on the extended compensation function observer suppresses the mismatch disturbance of the non-integral chain system.

[0170] Through the coordinated operation of the above modules, this invention extends the traditional CFO compensation mechanism to non-integral chain systems, and proposes ECFO through extended-order design. ECFO only requires the assumption of perturbation. When the first derivative approaches zero, accurate estimation can be achieved. Compared with traditional methods, this relaxes the restrictions on disturbance dynamics and can effectively estimate time-varying disturbances of higher order, greatly expanding the application boundaries of CFO theory. It can be effectively applied to complex control systems with high requirements for robustness and control accuracy, such as UAV flight control, robot motion control, motor drive, and electromagnetic levitation systems.

[0171] The ECFOBMC strategy can simultaneously and proactively compensate for matched and unmatched disturbances. Its control performance is superior to traditional methods, with smaller system output overshoot, shorter recovery time, and stronger robustness.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for suppressing unmatched perturbations based on an extended compensation function observer, characterized in that, include: S1: Extend the order of the non-integral chain system with unmatched perturbation to obtain the extended system; S2: Based on the design of the extended compensation function observer, perform error analysis on the extended compensation function observer to obtain the extended error equation; The extended compensation function observer, designed according to the extended system, includes: S21: Design a second-order observer with a perturbation compensation term; The disturbance compensation term includes a first disturbance compensation term and a second disturbance compensation term. The calculation expression for the first disturbance compensation term is as follows: in, This is the first disturbance compensation item. The observer gain coefficient, For the Laplace operator, For disturbance estimation, This is a non-matching perturbation. This is the second disturbance compensation item. for The estimated value, for The derivative of For integration operations; The second disturbance compensation term satisfies: in, For the differentiation operation, For the first Level perturbation, For the first The parameters to be determined are of order. For the first Auxiliary variables of order, This is the first system state; S22: By performing multinomial expansion of the second-order observer with perturbation compensation terms and auxiliary variables, an extended compensation function observer is obtained. The auxiliary variable is: in, for The derivative of As the first coefficient, As the second coefficient, This is the second system state. For the first Level perturbation, for The derivative of For the first Auxiliary variables of order, For the first The parameters to be determined; S3: Select the gain of the observer based on the extended compensation function according to the extended error equation; S4: Based on the gain of the extended compensation function observer, the extended compensation function observer, and the state error feedback, design a model compensation control strategy based on the extended compensation function observer. Suppress the mismatch disturbance of the non-integral chain system through the model compensation control strategy based on the extended compensation function observer.

2. The method for suppressing unmatched perturbations based on an extended compensation function observer according to claim 1, characterized in that, In step S1, the unmatched disturbance includes model uncertainty, measurement uncertainty, external disturbance, and complex nonlinear terms that are difficult to handle. The non-integral chain system with unmatched disturbance includes UAV flight control system, robot motion control system, motor drive system, and electromagnetic levitation system.

3. The method for suppressing unmatched perturbations based on an extended compensation function observer according to claim 1, characterized in that, Step S1 includes: S11: Obtain a second-order non-integral chain system with unmatched perturbations; S12: Extend the order of the second-order non-integral chain system with the unmatched perturbation as an extended state to obtain a third-order non-integral chain system. S13: Continue extending the order of the third-order non-integral chain system until the unmatched perturbation... The order derivative is displayed, and the extended system is obtained.

4. The method for suppressing unmatched perturbations based on an extended compensation function observer according to claim 1, characterized in that, The extended error equation is obtained by subtracting the extended compensation function observer from the extended system.

5. The method for suppressing unmatched perturbations based on an extended compensation function observer according to claim 1, characterized in that, In step S3, according to the extended error equation, when the unmatched disturbance satisfies When the gain of the extended compensation function observer is selected by pole placement, and the error matrix is ​​a Hurwitz matrix, the extended compensation function observer achieves error-free estimation of mismatched perturbations. For disturbance First derivative, For time.

6. The method for suppressing unmatched perturbations based on an extended compensation function observer according to claim 1, characterized in that, The model compensation control strategy based on the extended compensation function observer is as follows: in, To control the input, To control the allocation coefficient, To output the error vector, For error feedback, For the model feedforward term, Let be the state vector of the system. For disturbance compensation, For disturbance estimation, for The estimated value, for The derivative of This is a non-matching perturbation.

7. An unmatched disturbance suppression device based on an extended compensation function observer, for performing an unmatched disturbance suppression method based on an extended compensation function observer as described in any one of claims 1 to 6, comprising: The construction module extends the order of a non-integral chain system with unmatched perturbations to obtain the unmatched perturbations. The extended system is presented by displaying the order derivative; The extension module designs an extended compensation function observer based on the extended system design, and performs error analysis on the extended compensation function observer to obtain the extended error equation; The selection module selects the gain of the observer based on the extended error equation; The control module designs a model compensation control strategy based on the extended compensation function observer, the extended compensation function observer, and the state error feedback, and suppresses the mismatch disturbance of the non-integral chain system through the model compensation control strategy based on the extended compensation function observer.

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