A switching modeling method for electromechanical servo system based on flatness parameter identification

Abstract

The application provides a switching modeling method for an electromechanical servo system based on flatness parameter identification, in order to overcome parameter uncertainty caused by manufacturing difference of a sensor, environmental change or other reasons, and establishes a switching model for the electromechanical servo system. In order to solve the chattering problem of the switching model, the model parameter which may change is set as an unknown parameter, the flatness theory is introduced in parameter identification, and the parameters of each sub-model are identified at the same time, so that each sub-model can guarantee model precision and meet the flatness condition. The application can effectively overcome the limitation of the switching model theory in application of the electromechanical servo system.

Description

Technical Field

[0001] This invention relates to a switching modeling method for electromechanical servo systems based on flatness parameter identification, belonging to the field of servo system modeling parameter identification. Background Technology

[0002] Electromechanical servo systems are widely used in radar, radio telescopes, initial stabilization platforms, and other electromechanical mobile systems. The accuracy of motor-driven servo systems is a crucial evaluation criterion in various applications. Therefore, accurate electrical and mechanical parameters are essential for model-based servo controller design. However, due to nonlinearity and external disturbances, electromechanical servo systems suffer from parameter uncertainties, especially under varying loads or speeds. These uncertainties significantly impact the accuracy of system modeling.

[0003] Regarding the parameter uncertainty problem in electromechanical servo systems, patent publication number CN106438593B, for electro-hydraulic servos with parameter uncertainty and load disturbances, firstly established an asymmetric electro-hydraulic servo actuator model, then used an adaptive parameter estimation law to estimate the unknown and uncertain hydraulic parameters in the model, and designed a backstepping control law, effectively improving the dynamic performance of the system. Patent publication number CN106066604B, in the nonlinear modeling of a DC rotary position servo system, considered the system's parameter uncertainty and external disturbances, and designed an adaptive parameter algorithm in the controller to estimate unknown parameters to address parameter uncertainty. Both of these inventions can effectively solve the parameter uncertainty problem, but the methods employed rely on the controller design, which limits the controller's performance design. Introducing switching model theory into electromechanical servo systems demonstrates the potential for describing and handling parameter uncertainty from a modeling perspective.

[0004] However, in some cases, during the switching process between sub-models, dynamic errors can occur between the current output value and the output value of the previous sub-model, leading to unsatisfactory instantaneous switching performance. Patent publication number CN112327627A addresses the poor practicality of nonlinear switching systems by designing an adaptive sliding mode switching controller based on a dynamic inverse technology framework and a composite learning strategy. It utilizes prediction errors to construct a time-varying gain function for sliding mode switching, reducing the amplitude of chattering and improving the performance of sliding mode control. Patent publication number CN112083735B discloses a switching control method for a modular variable-variable UAV system. It utilizes the approximation characteristics of an RBF neural network to adjust the gain parameters in real time. Simultaneously, it employs multiple self-learning methods in the RBF neural network learning algorithm to prevent the learning process from getting stuck in local optimization, thus effectively eliminating system chattering and ensuring the system's speed and robustness. While these two inventions can effectively solve the chattering problem in switching systems, they still rely heavily on the controller design. The model is crucial to the controller design, but such methods cannot guarantee the accuracy of the established switching model during switching. Therefore, how to solve the problem of accurate modeling of servo systems with parameter uncertainties and the switching error problem of servo models that introduce switching theory are key areas of focus. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and provide a switching modeling method for electromechanical servo systems based on flatness parameter identification. For electromechanical servo systems with parameter uncertainties, the switching model established by this invention has higher accuracy and smaller errors compared to traditional single models. It can effectively reduce the error phenomenon that occurs during switching between servo system sub-models and overcome the limitations of applying switching model theory to electromechanical servo systems. This modeling method is also applicable to system modeling under uncertain parameters or various complex operating conditions. This flatness-based parameter identification method is also applicable to parameter identification of switching models, effectively eliminating errors in the switching process.

[0006] Technical solution of the present invention:

[0007] In a first aspect, the present invention provides a switching modeling method for electromechanical servo systems based on flatness parameter identification, the implementation steps of which are as follows:

[0008] Step 1: Based on the speed frequency domain characteristics of the electromechanical servo system, establish a switching model framework consisting of multiple sub-models and switching rules;

[0009] Step 2: Treat the mechanism model of the electromechanical servo system as multiple sub-models in the switching model framework, and treat some parameters in the multiple sub-models as unknown parameters;

[0010] Step 3: Identify the unknown parameters of each sub-model based on the flatness parameter identification method to obtain the identified parameters. When identifying, while meeting the tracking accuracy of the electro-mechanical servo system, the condition of flatness output of the electro-mechanical servo system is also satisfied;

[0011] Step 4: Substitute the obtained identified parameters into each sub-model, and according to the switching rule, obtain the final switching model of the electro-mechanical servo system.

[0012] To further optimize the above technical solution, the technical measures taken by the present invention also include:

[0013] Further, in the said Step 1, the switching rule uses the speed value as the switching basis, and realizes as follows based on the speed value:

[0014] (1) Divide the speed region according to the change interval of the speed frequency domain characteristics of the electro-mechanical servo system. Consider the speed interval of 0 to 1 rad / s as the low-speed region, the speed interval of 1 to 5 rad / s as the medium-speed region, and the speed interval greater than 5 rad / s as the high-speed region.

[0015]

[0016] Where, represents the switching model, v represents the speed value of the electro-mechanical servo system, k is a certain specific time, y1(k) is the output of the low-speed region sub-model, y2(k) is the output of the medium-speed region sub-model, and y3(k) is the output of the high-speed region sub-model;

[0017] (2) Use the speed value as the switching basis. When the speed value v ≤ 1 rad / s, the output of the switching model is equal to the output of the low-speed region sub-model; when the speed value 1 < v ≤ 5 rad / s, the output of the switching model is equal to the output of the medium-speed region sub-model, and when the speed value v > 5 rad / s, the output of the switching model is equal to the output of the high-speed region sub-model.

[0018] Further, in the said Step 3, the implementation based on the flatness parameter identification method is as follows:

[0019] (1) Use the particle swarm algorithm to identify the unknown parameters and generate the unknown parameter values as the initial solution;

[0020] (2) Use the algebraic representation function of flatness as the fitness function 1, i.e., fitness1, and use the error function of the switching model based on the unknown parameter values as the fitness function 2, i.e., fitness2. If the identified parameters meet both fitness function 1 and fitness function 2, then output the identified parameters. If not, continue the iterative identification until the unknown parameters simultaneously meet the conditions of fitness1 and fitness2. fitness1 and fitness2 are as follows:

[0021] fitness1=min|Sσ( 1:r )|

[0022]

[0023] Where σ(1:r) represents the mode transitioning from 1 to r, S σ(1:r) The matrix represents the variable function of the switching model under mode σ(1:r), where k is a specific time, r is the smallest integer that satisfies the left invertibility of the switching model, also known as the left intrinsic delay, and y(k) is the actual output value of the switching model at time k. To establish the ideal output value of the switching model at time k.

[0024] In a second aspect, the present invention provides an electronic device (computer, server, smartphone, etc.) including a processor and a memory;

[0025] Memory, used to store computer programs;

[0026] The processor is used to execute the computer program stored in the memory, and when executing it, it implements the above-mentioned electromechanical servo system switching modeling method based on flatness parameter identification.

[0027] Thirdly, the present invention provides a computer-readable storage medium (such as ROM / RAM, disk, optical disk) storing a computer program thereon, wherein the computer program, when executed by a processor, implements the above-mentioned electromechanical servo system switching modeling method based on flatness parameter identification.

[0028] The advantages of this invention compared to the prior art are:

[0029] (1) Based on the speed and frequency domain characteristics of the system, this invention establishes a switching model framework consisting of multiple sub-models and switching rules. For electromechanical servo systems with parameter uncertainties, existing technologies usually treat parameter uncertainties as unknowns and rely on controller design to solve them, without eliminating the influence of parameter uncertainties during the modeling process. This limits the performance design of the electromechanical servo system controller. This invention introduces switching model theory into the field of electromechanical servo systems, solves the parameter uncertainty problem in the modeling process, and can more accurately describe the system characteristics, avoiding the limitation of subsequent controller performance design in solving uncertain terms.

[0030] (2) This invention addresses the error phenomena that occur during the switching process of a switching model and the unknown parameters of each sub-model by designing a parameter identification method based on flatness. Existing technologies typically involve designing techniques in the controller to predict or limit the switching frequency and increasing the number of integrated models to reduce errors during switching. However, this also relies heavily on the controller design; the model is crucial to the controller design, and such methods cannot guarantee that the established switching model will not have errors during switching. Furthermore, flatness is a concept introduced from control theory, but it is often limited to theoretical numerical analysis and has limited practical applications. This invention uses a parameter identification method based on flatness to identify the unknown parameters of each sub-model, ensuring that the switching model meets the flatness condition. This effectively reduces errors between sub-model switching without affecting controller performance design. This invention establishes an accurate switching model with higher precision than traditional single models, enabling a more accurate description of electromechanical servo systems with parameter uncertainties. During the modeling process, parameter uncertainties are addressed, facilitating the design of other controller performance aspects. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0032] Figure 2 This is the nonlinear Bode plot surface of the present invention;

[0033] Figure 3 These are nine Bode plot curves with different rotational speeds selected in the Bode plot surface of this invention;

[0034] Figure 4 This is a schematic diagram of the dynamic error of the non-flatness switching model of the present invention;

[0035] Figure 5 This is a flowchart of the flatness calculation of the present invention;

[0036] Figure 6 The diagram shows a comparison of the flatness test results of the present invention. (a) shows the comparison between the switching model obtained without flatness parameter identification and the ideal output of the electromechanical servo system. The dashed line represents the output of the switching model obtained without flatness parameter identification, and the solid line represents the ideal output of the electromechanical servo system. (b) shows the comparison between the switching model obtained based on flatness parameter identification and the ideal output of the electromechanical servo system. The dashed line represents the output of the switching model obtained based on flatness parameter identification, and the solid line represents the ideal output of the electromechanical servo system. Detailed Implementation

[0037] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0038] This invention proposes a switching modeling method for electromechanical servo systems based on flatness parameter identification.

[0039] Based on the variation range of the speed frequency domain characteristics of the electromechanical servo system, a switching model framework was established. This framework consists of three sub-models—low-speed, medium-speed, and high-speed regions—and switching rules based on speed values. The mechanistic model of the electromechanical servo system is used as multiple sub-models within the switching model framework, with some parameters in these sub-models treated as unknown parameters. Because the switching model introduces errors during the switching process, a flatness-based parameter identification method is used to simultaneously identify the unknown parameters of each sub-model, obtaining identified parameters. During identification, the conditions of tracking accuracy and flatness output of the electromechanical servo system must be simultaneously met. The obtained identified parameters are then substituted into each sub-model, and according to the switching rules, the final switching model of the electromechanical servo system is obtained.

[0040] like Figure 1 As shown, the linear switching modeling method based on flatness parameter identification of the present invention specifically includes the following steps:

[0041] 1. Based on the frequency domain characteristics of electromechanical servo systems, a switching model framework consisting of multiple sub-models and switching rules is established.

[0042] 1.1) The speed frequency domain characteristics of the electromechanical servo system are characterized using a nonlinear Bode plot, such as... Figure 2 As shown in the Bode plot, sinusoidal sweep signals u = γsin(ω) with different amplitudes are used as input signals. The nonlinear Bode plot of the servo system at different speeds is calculated according to L(ω) = 20lg(A(ω)), where u is the input sinusoidal signal, γ is the amplitude of the sinusoidal signal, ω is the frequency of the sinusoidal signal, k(ω) represents the ratio of the output amplitude of the sinusoidal signal to the input amplitude, and L(ω) represents 20 times the natural logarithm of the ratio of the output amplitude of the sinusoidal signal to the input amplitude, i.e., the amplification in decibels. Figure 2 The horizontal axis represents frequency, the vertical axis represents velocity, and the vertical axis represents L(ω). The horizontal and vertical axes together form a Bode plot curve at a certain velocity.

[0043] from Figure 2 It can be clearly seen that as the speed of the electromechanical servo system increases, the Bode plot at 10... -2 Hz to 10 4 The frequency domain characteristics of electromechanical servo systems also change within the Hz frequency range. When the system frequency is low, i.e., in the 10 Hz range... -2 Within the range of 1 Hz, the amplification decibels for 0–1 rad / s differ from those for 1–10 rad / s, indicating a difference. When the frequency is at 10... 2 ~10 4At Hz, the amplification decibels of the electromechanical servo system change with the speed value. Between 1 and 5 rad / s, the amplification decibels are relatively close. After 5 rad / s, the amplification decibels of the electromechanical servo system change less. This indicates that the frequency domain characteristics are similar between 1 and 5 rad / s, and even closer after 5 rad / s.

[0044] Figure 3 Nine Bode plot curves with different rotational speeds were selected from the Bode plot surface. The three Bode plot curves in the first row have speeds of 0.377 rad / s, 0.503 rad / s, and 0.754 rad / s, all belonging to the low-speed region. The three Bode plot curves in the second row have speeds of 1.257 rad / s, 1.885 rad / s, and 2.513 rad / s, belonging to the medium-speed region. The three Bode plot curves in the last row belong to the high-speed region, with speeds of 4.398 rad / s, 6.283 rad / s, and 8.168 rad / s. Selecting three curves in each speed region allows for a clearer observation of the changes in the system's frequency domain characteristics. A Bode plot curve has a maximum value, called the resonant peak. The frequency value corresponding to the point where the change begins after the peak is called the corner frequency. This can be observed from... Figure 3 It can be seen that the resonance peak value of the curve in the low-speed region is higher than that in the medium- and high-speed regions. Furthermore, the cutoff frequency of the low-speed region curve is approximately 40 Hz, which is lower than the 70 Hz cutoff frequency of the medium- and high-speed regions. Meanwhile, the resonance peak value in the high-speed region is approximately 4 dB, which is lower than the resonance peak values ​​in the low-speed and medium-speed regions. Therefore, it is reasonable to consider the speed range of 0–1 rad / s as the low-speed region, the speed range of 1–5 rad / s as the medium-speed region, and the speed range greater than 5 rad / s as the high-speed region.

[0045] Based on the speed frequency domain characteristic analysis of the electromechanical servo system, it can be clearly seen that the frequency domain characteristics of the electromechanical servo system are different when the rotation speed is different. This means that parameter uncertainty does exist. At the same time, it is also an inspiration and verification for the application of the switching model in the electromechanical servo system.

[0046] 1.2) Therefore, by analyzing the speed frequency domain characteristics of the electromechanical servo system, the speed region is divided into three regions: the speed range of 0–1 rad / s is considered the low-speed region, the speed range of 1–5 rad / s is considered the medium-speed region, and the speed range greater than 5 rad / s is considered the high-speed region. This yields a switching model based on speed as the switching rule. The framework is as follows:

[0047]

[0048] in, y1(k) represents the switching model, v represents the speed value of the electromechanical servo system, k is a specific time, y1(k) is the output of the low-speed region sub-model, y2(k) is the output of the medium-speed region sub-model, and y3(k) is the output of the high-speed region sub-model.

[0049] 2. The mechanism model of the electromechanical servo system is used as multiple sub-models in the switching model framework, and some parameters in the multiple sub-models are treated as unknown parameters.

[0050] 2.1) Analyze nine selected Bode plot curves at different rotational speeds on the Bode plot surface, and solve for the inflection slopes of the Bode plot curves, such as... Figure 3 As shown.

[0051] To determine the order of the established mechanistic model, it is necessary to further analyze the speed frequency domain characteristics of the electromechanical servo system, select Bode plot curves with different rotational speeds from the Bode plot surface, and calculate their inflection slopes.

[0052] Select two points [ω1, L] after the corner frequency. a [ω1)] and [ω2,L] a [ω2], where ω1 and ω2 are the frequency values ​​of two selected points, L a (ω1) and L a (ω2) is the logarithmic value corresponding to the frequency value. Its transition slope l is calculated as shown in the following formula. Figure 3 In the diagram, two points are selected for each curve, and the dashed lines represent the x-coordinate and y-coordinate of the points.

[0053]

[0054] Table 1. Slope of the Bode plot curves at different speeds

[0055]

[0056]

[0057] Table 1 shows the inflection slope *l* corresponding to the nine Bode plot curves at different speeds. Because the speed changes in the low-speed region are subtle, the computer cannot detect accurate output values, resulting in errors. This leads to larger inflection slopes for the three curves in the low-speed region. To determine the accuracy of the mechanistic model order, slope values ​​of approximately -100 dB / dec were chosen for the medium-speed and high-speed regions. Each -20 dB / dec interval corresponds to approximately one integral element. Since the system contains n integral elements, the system order is n. Therefore, a reasonable order for the sub-model of the switching model is determined to be 5.

[0058] 2.2) Based on the reasonable order of the sub-model being 5, establish the 5th order discrete state-space equation of the electromechanical servo system;

[0059]

[0060]

[0061] This mechanistic model is obtained after normalization, and all state variables are dimensionless. K a K is the amplification factor of the drive device. b and K t It is the back electromotive force and the torque constant, R m and L m J represents the armature resistance and inductance. m and J L These are the moments of inertia of the motor and the load, respectively, B m and B L B is the damping constant of the motor and the load. s K represents the equivalent damping of the transmission device. s This indicates the wind-induced stiffness of the transmission lead screw.

[0062] Table 2 System Parameters

[0063]

[0064]

[0065] The servo system has parameter uncertainties, which may cause changes in parameters such as load inertia and motor coefficients, thus affecting B. m B L B s J L J m K s Set the parameters as unknown and perform parameter identification.

[0066] 3. Based on the flatness parameter identification method, the unknown parameters of each sub-model are identified simultaneously to obtain the identified parameters, which meet the requirements of both tracking accuracy and flatness output of the electromechanical servo system.

[0067] like Figure 4 The figure shows a schematic diagram of the dynamic error of the switching model obtained by identifying the flatness parameter. The solid black line represents the ideal output, and the dashed line represents the output of the switching model without flatness. The switching model includes three modes: σ(k1), σ(k2), and σ(k3). Figure 4 The horizontal axis represents time, at t k At any given moment, the ideal output is No flatness output As can be seen from the graph, there is a significant error between the two outputs. Similarly, at t nk At any given moment, the ideal output is No flatness output Errors also exist between the two. These dynamic errors between the sub-model outputs during the switching process can significantly affect the system's performance and stability. Therefore, it is crucial to determine a solution that minimizes the impact of these errors on the system, which implies the importance of introducing flatness into parameter identification.

[0068] 3.1) Determine the value of r

[0069] If the system is flat, then the following condition must be met regarding the output y. (k) The property of left invertibility. If its rank satisfies:

[0070]

[0071] I m×r =[1 m 0 m×(m·r) ]

[0072] The system is about y (k) Left-invertible. Starting from r=0, if... Not equal to rankM σ(k:k+r) The test is repeated after incrementing r by 1. The value of r is limited by the model dimension n, so the iteration process stops after a finite number of tests. Indicates that M σ(k:k+r) and I m×r The rank of the matrix formed, rank M σ(k:k+r) Indicates M σ(k:k+r) The rank of a matrix, M σ(k:k+r) It is the input coefficient matrix when the system outputs an iteration forward by r steps, where σ(k:k+r) is the pattern sequence from k to k+r, and I m×r For identity matrix, 1 m It is an m-dimensional identity matrix, 0 m×(m·r) A zero matrix with m rows and m·r columns.

[0073] 3.2) Based on the flatness theory, calculations are performed, such as... Figure 5 As shown.

[0074] Assume the model switching is as follows:

[0075] x(k+1)=A σ(k) x(k)+B σ(k) u(k)

[0076] y(k)=C σ(k) x(k)+D σ(k) u(k)

[0077] Where x(k+1) is the state vector at time k+1, y(k) is the output at time k, x(k) is the state vector at time k, u(k) is the input at time k, and Aσ(k) B represents the state matrix under mode σ(k) at time k. σ(k) Let C represent the input matrix under mode σ(k) at time k. σ(k) D represents the output matrix under mode σ(k) at time k. σ(k) Let D represent the direct transition matrix under mode σ(k) at time k. The output depends only on the state variable x(k), so D σ(k) =0.

[0078] According to the definition of flatness, the system model must be a left-reversible switching model with left intrinsic delay, when the system is composed of an input sequence. and pattern sequence σ (k:k+r) Drive, then Assuming the switching model described above is left-invertible and has a left-inherent delay r, the input sequence of the system can be recovered from the output sequence in a sequential manner.

[0079]

[0080]

[0081]

[0082]

[0083] I m×r =[1 m 0 m×(m·r) ]

[0084] in, and Let be the input and initial conditions of the left-invertible system at time k+r, respectively. Let k be the state variable at time k+r+1. M is the extended observability matrix when the system output is shifted forward by r steps. σ(k:k+r) It is the input coefficient matrix when the system outputs the input coefficient matrix and moves forward r steps. It is M σ(k:k+r) The Mulpenrose generalized inverse matrix, P σ(k:k+r) It is an invertible transition matrix, I m×r For identity matrix, 1 m It is an m-dimensional identity matrix, 0 m×(m·r) A zero matrix with m rows and m·r columns, y (k:k+r) This indicates the output sequence of the system from time k to k+r.

[0085] 3.3) Different P σ(k:k+r) Matrix using Q σ'(k) Matrix representation;

[0086] Different sequences σk:k+r It may lead to the same P σ(k:k+r) To reduce computation, different P matrices are used. σ(k:k+r) The matrix is ​​composed of Q σ'(k) It means that Q σ'(k) The switching model is S.

[0087] 3.4) Calculate all P σ(k:k+r) Matrix, assigned S σ(1:r) The matrix is ​​initialized, and the calculation is performed iteratively according to the following formula, with a maximum number of iterations of nJ. r Determine S σ(1:r) Check if the result is 0. If the result is 0, output the iteration count and stop iterating; if the result is not 0, continue iterating until the maximum number of iterations is reached and output S. σ(1:r) As a result, a re-identification was performed.

[0088] S σ(1:r) =∑ j∈J P jσ(1:r) S jσ(1:(r-1)) P jσ(1:r) ;

[0089] Where σ(1:r) represents the mode transitioning from 1 to r, S σ(1:r) The matrix represents the variable function of the switching model in mode σ(1:r), where r is the smallest integer that satisfies the left invertibility of the switching model, also known as the left intrinsic delay.

[0090] y (k) =C σ(k) x (k) It is the output of a left-invertible system with a left intrinsic delay r, if there exists a non-negative integer K for all J r+1 For all pattern sequences in the set, when k≥0, for a switching model with flat output, we can obtain:

[0091] S σ(1:r) =0

[0092] 3.5) Therefore, S σ(1:r) =0 is set as fitness function 1, and the tracking error function is set as fitness function 2. The particle swarm algorithm is used for parameter identification. If the conditions are met, the parameter identification meets the requirements. Substitute them into the model, and the modeling is completed.

[0093] fitness1 = min|S σ(1:r) |

[0094]

[0095] Let k be a specific time, and y(k) be the actual output value of the switching model at time k. To establish the ideal output value of the switching model at time k.

[0096] 4. Substitute the identified parameters into the sub-model to obtain the final switching model.

[0097] Figure 6 The image shows a comparison of the performance of the switching model obtained without flatness parameter identification and the switching model obtained based on flatness parameter identification. Figure 6 In the figure, (a) shows the comparison between the switching model obtained without flatness parameter identification and the ideal output of the electromechanical servo system. The dashed line represents the output of the switching model obtained without flatness parameter identification, and the solid line represents the ideal output of the electromechanical servo system. Figure 6 In Figure (b), the comparison between the switching model obtained based on flatness parameter identification and the ideal output of the electromechanical servo system is shown. The dashed line represents the output of the switching model obtained based on flatness parameter identification, and the solid line represents the ideal output of the electromechanical servo system. Figure 6 (a) and Figure 6 Comparing with (b) in the previous section, it can be found that the switching model obtained without flatness parameter identification will have a relatively large error during the switching process, while the switching model obtained based on flatness parameter identification has no significant error. This indicates that the flatness parameter identification method in this invention can effectively reduce the error phenomenon in the switching process of the switching model.

[0098] The identified low-speed and medium-speed sub-models, along with the traditional single transfer function model, were compared with the switching model established based on this invention. The errors of each model are shown in Table 3. The average error of the traditional transfer function model is 0.0204%, while the average errors of the low-speed and medium-speed models are 0.00149% and 0.0229%, respectively. The switching model has the smallest average error at 0.011%. The root mean square error (RMS) of the traditional transfer function model is 0.6658%, while those of the low-speed and medium-speed models are 0.9541% and 0.7027%, respectively. Due to fluctuations in the zero-crossing point of the switching model, its RMS error of 0.6658% is not the minimum. However, based on the maximum error index, the maximum error of the switching model is 4.31%, lower than the other models. According to this error analysis, the established electromechanical servo system switching model has smaller and more accurate errors.

[0099] Table 3 Error Analysis of the Model

[0100]

[0101]

[0102] In summary, the switching model established based on this invention has smaller errors and can more accurately describe the characteristics of electromechanical servo systems compared to traditional single models. The electromechanical servo system switching modeling method based on flatness parameter identification of this invention breaks through the limitations of switching model theory in electromechanical servo systems, and can eliminate parameter uncertainty problems in modeling, thus facilitating controller performance design.

[0103] Based on the same inventive concept, another embodiment of the present invention provides an electronic device (computer, server, smartphone, etc.) including a memory and a processor, wherein the memory stores a computer program configured to be executed by the processor, and the computer program includes instructions for performing the steps of the method of the present invention.

[0104] Based on the same inventive concept, another embodiment of the present invention provides a computer-readable storage medium (such as ROM / RAM, disk, optical disk), which stores a computer program that, when executed by a computer, implements the various steps of the method of the present invention.

[0105] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A switching modeling method for electromechanical servo systems based on flatness parameter identification, characterized in that, The implementation steps are as follows: Step 1: Based on the speed frequency domain characteristics of the electromechanical servo system, establish a switching model framework consisting of multiple sub-models and switching rules; Step 2: Treat the mechanism model of the electromechanical servo system as multiple sub-models in the switching model framework, and treat some parameters in the multiple sub-models as unknown parameters; Step 3: Identify the unknown parameters of each sub-model based on the flatness parameter identification method to obtain the identification parameters. During identification, the identification parameters satisfy both the tracking accuracy of the electromechanical servo system and the flatness output condition of the electromechanical servo system. Step 4: Substitute the obtained identification parameters into each sub-model, and obtain the final electromechanical servo system switching model according to the switching rules; In step 3, the flatness parameter identification method is implemented as follows: (1) Use the particle swarm optimization algorithm to identify the unknown parameters and generate the unknown parameter values ​​as the initial solution; (2) The algebraic representation function of flatness is used as the fitness function for identifying unknown parameters, i.e. The error function of the switching model based on unknown parameter values ​​is used as the fitness function 2. If the identified parameters simultaneously satisfy both fitness function 1 and fitness function 2, then the identified parameters are output. If they do not satisfy both, the identification process continues iteratively until the unknown parameters simultaneously satisfy the conditions. , as follows: in, This indicates a conversion from 1 to... The pattern The matrix is ​​used to switch models in mode. The variable function under, For a certain time, The smallest integer that satisfies left invertibility for switching models, also known as left intrinsic delay. To switch models in The actual output value at time 1. To establish a handover model in The ideal output value at any given time.

2. The electromechanical servo system switching modeling method based on flatness parameter identification according to claim 1, characterized in that: in step 1, the switching rule uses speed value as the switching basis, and the speed value is used as the basis to achieve the following: (1) Based on the speed frequency domain characteristics of the electromechanical servo system, the speed range is divided into regions. The speed range of 0~1 rad / s is regarded as the low speed region, the speed range of 1~5 rad / s is regarded as the medium speed region, and the speed range of greater than 5 rad / s is regarded as the high speed region. in, Indicates switching models, This indicates the speed value of the electromechanical servo system. For a certain time, This is the output of the low-speed region sub-model. This is the output of the sub-model for the medium-speed region. This is the output of the high-speed region sub-model; (2) Use the speed value as the switching basis. When the speed value When the speed is ≤1 rad / s, the output of the switching model is equal to the output of the low-speed region sub-model; When the speed value is 1 < When the velocity value is ≤5 rad / s, the output of the switching model is equal to the output of the sub-model in the medium-speed region. When the speed is >5 rad / s, the output of the switching model is equal to the output of the high-speed region sub-model.

3. An electronic device, characterized in that, Including processor and memory; Memory, used to store computer programs; A processor for executing a computer program stored in memory, which, when executed, implements the method described in any one of claims 1-2.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1-2.

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