High-precision model identification method of servo system

Abstract

The invention belongs to the technical field of servo system modeling, and discloses a high-precision model identification method for a servo system, which comprises the following steps: acquiring linear operation data of the servo system under a low-speed working condition; constructing a second-order controlled autoregression model; solving to-be-identified parameters of the second-order controlled autoregression model by using a variable recursive interval multi-innovation least square algorithm, obtaining predicted output of the second-order controlled autoregression model based on the to-be-identified parameters, and determining a dead zone range according to the predicted output and actual output of the second-order controlled autoregression model; designing a Hammerstein model with dead zone nonlinearity of the servo system according to the dead zone range; and performing off-line estimation on to-be-identified parameters of the Hammerstein model by adopting a linear auxiliary constraint particle swarm algorithm, and finally obtaining the dead-zone nonlinear Hammerstein model of the servo system. According to the method, the model identification precision is improved, the control performance of the alternating current servo system is improved, and a system model with higher precision is obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of modeling of servo systems, and specifically relates to a high-precision model identification method for a servo system, especially realizing model identification of a servo system under low-speed conditions, reducing the tracking error of the model under low-speed conditions, so as to more accurately describe the dynamic behavior of the servo system under high-speed and low-speed conditions, and provide a solid foundation for subsequent servo system design and optimization. Background Art

[0002] Modern industry is gradually developing towards large-scale and complex development. In order to ensure the stability of servo systems and the accuracy of control, traditional control theories and strategies based on quantitative mathematical models can no longer meet actual needs. Modern control strategies are receiving more and more attention due to their convenience of online calculation and their ability to adapt to process and environmental uncertainties.

[0003] Servo system modeling plays an important role in modern control strategies. However, nonlinear components are widely present in many complex control systems, and nonlinear phenomena in actual systems (such as friction creep, dead zone effect, backlash, etc.) have a significant impact on the accuracy of controllers designed based on linear models, especially under low-speed motion conditions.

[0004] To address this problem, the Hammerstein model provides an efficient solution. This method does not require the installation of additional test sensors, and can achieve decoupling and identification of the linear and nonlinear parts of the system through a single input and output data. The advantage of the Hammerstein model is that the Hammerstein model is widely applicable to complex systems containing nonlinear phenomena, especially in scenarios with significant nonlinearity such as friction creep, dead zone effect, and reverse clearance, which can effectively improve the accuracy of modeling. It also has strong decoupling capabilities. By decomposing the system into linear and nonlinear parts, the Hammerstein model can clearly describe the impact of nonlinear characteristics on the overall system performance and provide a basis for the optimization of different subsystems.

[0005] In the prior art, the Hammerstein model is often used to describe the nonlinear characteristics of the servo system and assist in control design. However, in practical applications, there are still problems such as insufficient low-speed performance, difficulty in balancing identification efficiency and accuracy, and insufficient controller adaptability. Summary of the invention

[0006] The purpose of the present invention is to provide a high-precision model identification method for a servo system, thereby improving the accuracy of model identification when the servo system is running at a low speed, improving the control performance of the AC servo system, and obtaining a higher-precision system model.

[0007] To achieve the above object, the technical solution adopted by the present invention is:

[0008] A high-precision model identification method for a servo system, the high-precision model identification method for a servo system comprising:

[0009] Obtain the linear operation data of the servo system under low-speed conditions;

[0010] A second-order controlled autoregressive model was constructed based on the linear running data;

[0011] The variable recursive interval multi-innovation least squares algorithm is used to solve the parameters to be identified of the second-order controlled autoregressive model, and based on the parameters to be identified, the predicted output of the second-order controlled autoregressive model is obtained, and the dead zone range is determined according to the predicted output and actual output of the second-order controlled autoregressive model;

[0012] Design the Hammerstein model of the servo system with dead zone nonlinearity according to the dead zone range;

[0013] The objective function is to minimize the cumulative error between the predicted output and the actual output of the Hammerstein model. According to the objective function, a linear auxiliary constrained particle swarm algorithm is used to offline estimate the parameters to be identified of the Hammerstein model, and finally a Hammerstein model with dead zone nonlinearity of the servo system is obtained.

[0014] Several optional methods are also provided below, but they are not intended to be additional limitations on the above-mentioned overall solution, but are merely further supplements or preferences. Under the premise that there are no technical or logical contradictions, each optional method can be combined with the above-mentioned overall solution separately, and multiple optional methods can also be combined.

[0015] Preferably, the step of constructing a second-order controlled autoregressive model based on linear operation data comprises:

[0016] According to the Mason formula, the transfer function from the output end to the input end of the servo system is obtained:

[0017]

[0018] In the formula, G(s) represents the transfer function of the servo system, U(s) is the frequency domain input of the servo system, and V(s) is the frequency domain output of the servo system. is the speed loop gain, K a is the current loop gain, K L is the elastic modulus, J M is the moment of inertia of the motor in the servo system, J L is the load moment of inertia, D L is the viscous friction coefficient, s represents the complex variable in the Laplace transform domain;

[0019] The transfer function of the simplified servo system is:

[0020]

[0021] Where Y(s) represents the frequency domain output of the simplified servo system, and K is a combination of proportional constants, including the speed loop gain Current loop gain K a and elastic modulus K L , T is the time constant;

[0022] The second-order controlled autoregressive model is constructed as follows:

[0023] A(q -1 )y(k)=B(q -1 )u(k)

[0024] A(q -1 )=1+a1q -1 +a2q -2

[0025] B(q -1 )=b1q -1 +b2q -2

[0026] In the formula, A(q -1 ) and B(q -1 ) represent the discrete polynomial of the input characteristic and the discrete polynomial of the output characteristic of the servo system, u(k) and y(k) are the actual input and actual output of the servo system at time k, a1, a2, b1 and b2 are the four parameters to be identified of the second-order controlled autoregressive model, and q represents the shift operator.

[0027] Preferably, the method of obtaining a predicted output of a second-order controlled autoregressive model based on the parameters to be identified, and determining a dead zone range according to the predicted output and actual output of the second-order controlled autoregressive model, comprises:

[0028] Calculate the residuals of the second-order controlled autoregressive model as follows:

[0029] e(k)=y(k)-y linear (k)

[0030] Where e(k) represents the residual of the second-order controlled autoregressive model at time k, y(k) is the actual output of the servo system at time k, and y linear (k) is the predicted output of the second-order controlled autoregressive model at time k;

[0031] In the motor commutation area under the low-speed condition of the servo system, the critical point with the largest residual e(k) is found and marked as the dead zone critical point, so as to extract the dead zone range of the target dead zone parameter as follows: and d1 min is the minimum value of the first dead zone range, is the maximum value of the first dead zone range, is the minimum value of the second dead zone range, It is the maximum value of the second dead zone range.

[0032] Preferably, the designing of a Hammerstein model of a servo system with dead zone nonlinearity according to the dead zone range comprises:

[0033] Construct the input-output model of the servo system with dead zone nonlinearity as follows:

[0034]

[0035] In the formula, u(k) and y(k) are the actual input and output of the servo system at time k, respectively. F(·) represents the dynamic model with dead zone nonlinearity. u m (k) is an intermediate variable, representing the predicted output of the kinetic model F(·), G(q -1 ) represents the linear part transfer function in the Hammerstein model, that is, the second-order controlled autoregressive model, y m (k) is an intermediate variable, indicating that the model G(q -1 ), q is the shift operator, v(k) is the measurement noise with a mean of zero and a variance of Gaussian white signal, A(q -1 ) and B(q -1 ) represent the discrete polynomial of the input characteristic and the discrete polynomial of the output characteristic of the servo system respectively;

[0036] The processing process of the dynamic model F(·) with dead zone nonlinearity for the input u(k) is as follows:

[0037]

[0038] The second-order controlled autoregressive model G(q -1 ) for the intermediate variable u m The processing of (k) is as follows:

[0039]

[0040] Then we get the Hammerstein model with dead zone nonlinearity, as follows:

[0041]

[0042] Where l1 and l2 are the slopes of the linear segments of the dynamic model with dead zone nonlinearity. The parameter to be identified of the Hammerstein model is θ = [a1, a2, b1l1d1, l1b1, b1l2d2, b1l2, b2l1d1, l1b2, b2l2d2, b2l2] T , where a1, a2, b1, and b2 are the parameters to be identified in the second-order controlled autoregressive model, which are known quantities in the Hammerstein model, and d1 ≥ 0 and d2 ≤ 0 are the unknown dead zone parameters within the dead zone range.

[0043] Preferably, the linear auxiliary constrained particle swarm algorithm outputs the optimal solution of the parameters to be identified of the Hammerstein model, and the dead zone parameters d1 and d2 are calculated according to the optimal solution, respectively. and θ3 represents the third item in the parameter θ to be identified of the Hammerstein model, θ4 represents the fourth item in the parameter θ to be identified of the Hammerstein model, θ5 represents the fifth item in the parameter θ to be identified of the Hammerstein model, and θ6 represents the sixth item in the parameter θ to be identified of the Hammerstein model.

[0044] Preferably, the linear auxiliary constraint range of the linear auxiliary constraint particle swarm algorithm is a dead zone range.

[0045] Preferably, the method of offline estimating the parameters to be identified of the Hammerstein model using a linear auxiliary constrained particle swarm algorithm according to the objective function comprises:

[0046] Initialize particle positions, particle velocities and fitness functions, set population size, maximum number of iterations and learning factor;

[0047] During the particle convergence process, the particle position and particle velocity are updated, and it is determined whether the updated particle position exceeds the set linear auxiliary constraint range. If it exceeds, it is forced to be projected to the boundary of the dead zone range; otherwise, forced projection is not performed;

[0048] The fitness function is calculated repeatedly and the particle position and particle velocity are updated until the objective function converges or the maximum number of iterations is reached, and the optimal solution of the parameters to be identified of the Hammerstein model is obtained.

[0049] Preferably, it is determined whether the updated particle position exceeds the set linear auxiliary constraint range, and if so, forced projection is performed to the boundary of the dead zone range; otherwise, forced projection is not performed, and the following is performed:

[0050] The dead zone parameter is calculated according to the updated particle position, and it is determined whether the dead zone parameter is within the dead zone range. If the dead zone parameter is less than the dead zone range, the dead zone parameter is projected as the minimum value of the dead zone range. If the dead zone parameter is greater than the dead zone range, the dead zone parameter is projected as the maximum value of the dead zone range. Then, the updated particle position after projection is obtained by reversely solving the projected dead zone parameter. If the dead zone parameter is within the dead zone range, no forced projection is performed, and the updated particle position is directly accepted.

[0051] In the prior art, when the low-speed high-precision servo system is running, the nonlinear factors such as dead zone and friction caused by the system commutation affect the overall control performance. Therefore, the present invention introduces a linear auxiliary model and combines the linear auxiliary constrained particle swarm algorithm to significantly improve the modeling accuracy of the Hammerstein model in the low-speed area, improve the low-speed tracking and dynamic response performance of the servo system, accelerate the parameter identification process, and improve the identification accuracy, which is especially effective when the dead zone parameters are significant or the model is complex.

[0052] The present invention provides a high-precision model identification method for a servo system. In the linear operation stage of the servo system, a second-order controlled autoregressive (CAR) linear parameter model of the servo system is established, and the interval-varying multi-innovation least squares algorithm (V-MILS) algorithm is used to identify the servo system in the low-speed linear stage, thereby removing the influence of the system's identification accuracy reduction caused by bad data, and preliminarily obtaining the range of the dead zone parameter; in the nonlinear operation stage of the low-speed area, a Hammerstein model containing nonlinear characteristics is established, and a linear auxiliary constrained particle swarm algorithm is proposed to identify the servo system model. By introducing the range of the dead zone parameter to define the search space of the particle swarm algorithm, the accuracy of the local search is enhanced, the convergence of the algorithm in the complex search space is accelerated, and the accuracy of the final identification result is improved. Thereby, the accuracy of model identification is improved, the control performance of the AC servo system is improved, and a higher-precision system model is obtained, which is suitable for modern industrial servo systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A flow chart of a high-precision model identification method for a servo system according to the present invention;

[0054] Figure 2 A control block diagram of a second-order controlled autoregressive model constructed for the present invention;

[0055] Figure 3 It is a control block diagram of a simplified second-order controlled autoregressive model of the present invention;

[0056] Figure 4This is a schematic diagram of selecting a variable period sequence in the V-MLS algorithm;

[0057] Figure 5 Schematic diagram of the input-output Hammerstein model with dead-zone input nonlinearity;

[0058] Figure 6 It is a schematic diagram of the actual speed and the estimated speed based on the linear auxiliary constraint particle swarm algorithm in the present invention under the condition of low speed superposition of a small amplitude sine curve;

[0059] Figure 7 for Figure 6 A local enlarged schematic diagram between 0 seconds and 3.5 seconds. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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. Based on the embodiments of 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.

[0061] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0062] In order to comprehensively improve the control performance of AC servo systems, improve the system modeling accuracy, and especially enhance the system's ability to resist nonlinear interference in low-speed and motion commutation scenarios, this paper proposes a high-precision model identification method for servo systems. This method aims to improve the modeling performance in the low-speed area and effectively improves the control accuracy and dynamic response performance of the servo system by optimizing the model identification process.

[0063] like Figure 1 As shown, this embodiment provides a high-precision model identification method for a servo system, comprising the following steps:

[0064] Step 1: Obtain the linear operation data of the servo system under low speed conditions.

[0065] All operating data used for parameter identification are values ​​obtained in real time on the platform at intervals of sampling period units. This embodiment takes the towing motor servo system as an example to illustrate the servo system. In the towing motor servo system, the control is performed through the host computer platform, and the speed and torque of the motor are obtained.

[0066] In order to obtain a linear low-speed auxiliary model, a suitable excitation signal needs to be designed. The input selected here is The upper computer platform controls and obtains the speed (in rpm) input and position output data. Wherein, u(k) is the actual input of the servo system at time k, M represents the number of sine waves superimposed on the input signal, and in this embodiment, the value M=5, a i represents the amplitude of the i-th sine wave. In this embodiment, the values ​​are {a1, ..., a5} = {8, 8, 32, 4, 4}, and f i represents the frequency of the i-th sine wave. In this embodiment, the value is {f1, ..., f5} = {0.125, 0.25, 0.5, 0.8, 1}, and T represents time.

[0067] Step 2: Construct a second-order controlled autoregressive (CAR) model based on the linear operation data.

[0068] Step 21. When the servo drive is configured to work in speed mode, the overall structure diagram of the single-axis servo system is as follows: Figure 2 As shown, the motor and mechanical parts are controlled by speed loop and current loop.

[0069] Step 22: According to the Mason formula, the transfer function from the output end to the input end of the servo system can be obtained:

[0070]

[0071] Where G(s) represents the transfer function of the second-order controlled autoregressive model, U(s) is the frequency domain input of the servo system, and V(s) is the frequency domain output of the servo system. is the speed loop gain, K a is the current loop gain, K L is the elastic modulus, J M is the moment of inertia of the permanent magnet synchronous servo motor (motor), J L is the load moment of inertia, D L is the viscous friction coefficient, and s represents a complex variable in the Laplace transform domain.

[0072] Step 23: After analyzing the motion characteristics of the industrial mechatronic servo system, simplify the entire system structure framework as follows: Figure 3 As shown, its transfer function is:

[0073]

[0074] When the time constant T is small, the above formula can be approximated as:

[0075]

[0076] Where Y(s) represents the frequency domain output of the simplified servo system, and K is a series of proportional constants, including is the speed loop gain, K a is the current loop gain, K L is the elastic coefficient.

[0077] Step 24: Introduce the second-order controlled autoregressive model as shown below:

[0078] A(q -1 )y(k)=B(q -1 )u(k)

[0079] A(q -1 )=1+a1q -1 +a2q -2

[0080] B(q -1 )=b1q -1 +b2q -2

[0081] In the formula, A(q -1 ), B(q -1 ) represent the discrete polynomial of the input characteristic and the discrete polynomial of the output characteristic of the servo system respectively; u(k) and y(k) are the input discrete time series and the corresponding output discrete time series at time k respectively, that is, the actual input and actual output of the servo system at time k, a1, a2, b1, b2 are the four parameters to be identified, q represents the shift operator, also called the time lag operator.

[0082] Step 3: Use the variable recursive interval multi-innovation least squares algorithm to solve the unidentified parameters a1, a2, b1 and b2 of the second-order controlled autoregressive model, and based on the unidentified parameters, obtain the predicted output of the second-order controlled autoregressive model, and determine the dead zone range according to the predicted output and the actual output, which will be used for the subsequent linear auxiliary constrained particle swarm algorithm model identification.

[0083] Step 31: For the data consisting of the stimulus and the output response, take p groups of data from time k-p+1 to time k, and obtain:

[0084]

[0085] Where Y(p,k) represents the output sequence consisting of the actual output y(k-p+1) at time k-p+1 to the actual output y(k) at the previous k time; V(p,k) represents the input sequence consisting of the actual input v(k-p+1) at time k-p+1 to the actual input v(k) at the previous k time; Φ(p,k) represents the parameters to be identified of the second-order controlled autoregressive model at time k-p+1 The parameters to be identified of the second-order controlled autoregressive model at the previous k time points A sequence of parameters consisting of represents a p-dimensional array, Represents an n×p two-dimensional matrix.

[0086] Step 32: For the model to be identified: Y(p,k)=Φ T (p,k)θ′+V(p,k), where θ′ represents the information vector of the model to be identified, and an integer sequence is defined to satisfy where t s represents the time series corresponding to the valid data starting from time s, and represents the time series corresponding to the valid data obtained after removing the obviously oversized or missing data in the collected operating data, t s-1 Represents the time series corresponding to the valid data starting from time s-1, Represents the time series t s length, using t s Substituting k in the model to be identified, the identification model of the variable recursive interval multi-innovation least squares algorithm can be obtained as follows:

[0087] Y(p,t s )=Φ T (p,t s )θ+V(p,t s )

[0088] In the formula, Y(p,t s ) represents the output sequence after replacement, V(p,t s ) represents the replaced input sequence, Φ(p,t s ) represents the replaced parameter sequence, Φ T (p,t s ) represents Φ(p,t s ) is the transpose of .

[0089] like Figure 4 The data shown, y(3) and y(14) are missing or unavailable, two missing output data, and y(9) is a bad or unbelievable data because it obviously deviates greatly from the data range around it. In order to handle these missing data and unbelievable data situations, define a valid data sequence that satisfies 0≤t0<t1<t2<t3<...<t s-1 <t s <..., yes So for any s (s=0,1,2,...), {y(t s )} are all available. For example Figure 4The valid data used in is: y(0), y(1), y(2), y(4), y(5), y(6), y(7), y(8), y(10), y(11), y(12), y(13), y(15), y(16), y(17), y(18). Then we get

[0090] Step 33: Use the variable recursive interval multi-innovation least squares algorithm to identify and find the parameters to be identified of the second-order controlled autoregressive model, including the parameter vectors of a1, a2, b1, and b2. The formula is as follows:

[0091]

[0092] L(t s )=P(t s )Φ(p,t s )=P(t s-1 )Φ(p,t s )[I p +Φ T (p,t s )P(t s-1 )Φ(p,t s )] -1

[0093] P(t s )=P(t s-1 )-L(t s )Φ T (p,t s )P(t s-1 )

[0094] Y(p,t s )=[y(t s ),y(t s -1),…,y(t s -p+1)] T

[0095]

[0096] In the formula, Indicates the time series t corresponding to the valid data s The estimated value of the parameter to be identified of the second-order controlled autoregressive model is the result of updating the current observation data and historical data. Represents the use of time series t s-1 The estimated values ​​of the parameters to be identified of the second-order controlled autoregressive model are used as the initial values ​​for the update. represents the estimated value of the parameters to be identified in the second-order autoregressive model at time t, L(t s ) indicates the use of time series ts The obtained gain matrix is ​​used to adjust the contribution of the current observation data to the model parameter update, P(t s ) indicates the use of time series t s The obtained covariance matrix, P(t s-1 ) indicates the use of time series t s-1 The resulting covariance matrix, I p represents the identity matrix, y(t s ) represents the time series t s The actual output of the servo system is obtained below. The same applies to other systems. Indicates that in the time series t s The parameters to be identified of the second-order controlled autoregressive model are obtained below, and the other parameters are understood in the same way.

[0097] Step 34: Calculate the residual according to the predicted output and the actual output of the second-order controlled autoregressive model, and preliminarily determine the dead zone range according to the residual.

[0098] Step 341: Calculate the residual of the second-order controlled autoregressive model. The residual is defined as the difference between the predicted value and the actual output of the second-order controlled autoregressive model, as follows:

[0099] e(k)=y(k)-y linear (k)

[0100] Where e(k) represents the residual of the second-order controlled autoregressive model at time k, y(k) is the actual output of the servo system at time k, and y linear (k) is the predicted output of the second-order controlled autoregressive model at time k. If e(k) shows significant deviations, especially in the area where the input is close to zero, it may be caused by a dead zone.

[0101] Step 342, analyze the relationship between the actual input u(k) and e(k) of the servo system at time k: in the dead zone, the dead zone causes the output y(k) to deviate from the predicted value. At this time, the residual e(k) shows an obvious nonlinear trend. By statistically analyzing the distribution of e(k) in different intervals of u(k), the critical point with the largest residual e(k) is found in the motor commutation area and marked as the dead zone critical point, thereby extracting the target dead zone parameter range: and d1 min is the minimum value of the first dead zone range, is the maximum value of the first dead zone range, is the minimum value of the second dead zone range, It is the maximum value of the second dead zone range.

[0102] Step 4: Design a Hammerstein model of the servo system with dead zone nonlinearity according to the dead zone range.

[0103] Step 41: Assume that the servo system is in low-speed working condition and the dynamic model with dead zone nonlinearity in discrete time is as follows, where V(k) is the input speed, i.e., the actual input u(k) of the servo system at time k, V l (k) is the speed command, which is understood as the value of the target speed.

[0104]

[0105] Among them, d1≥0,d2≤0 is the unknown dead zone parameter, and d1 is the first dead zone parameter, and the dead zone range is d2 is the second dead zone parameter, and the dead zone range is

[0106] Step 42: According to Figure 5 The input-output model schematic diagram with dead-zone input nonlinearity is shown in the figure. The target speed u(k) and position y(k) are the actual input command and the measured actual output respectively. Therefore, the input-output model of the self-designed towing motor servo system with dead-zone input nonlinearity can be expressed as:

[0107]

[0108] Where F(·) represents the dynamic model with dead zone nonlinearity, u m (k) is an intermediate variable, representing the predicted output of model F(·), G(·) represents the second-order controlled autoregressive model, y m (k) is an intermediate variable, representing the predicted output of the model G(·), q is a shift operator, and the unknown measurement noise v(k) is assumed to have a mean of zero and a variance of Gaussian white signal. Continue to use the existing linear part modeling, the coprime polynomial A(q -1 ) and B(q -1 ) is defined as follows:

[0109] A(q -1 )y(k)=B(q -1 )u(k)

[0110] A(q -1 )=1+a1q -1 +a2q -2

[0111] B(q -1 )=b1q -1 +b2q -2

[0112] Coprime polynomials A(z -1 ) and B(z -1) is a coprime polynomial that represents the input and output characteristics of the system. In the tow servo platform, according to the transfer function characteristics of the linear segment of the current loop, there are n a =n b =2, then:

[0113]

[0114] Step 43: According to the nonlinear dead zone model in step 42, the output u of the nonlinear module is input m (k) is defined as follows:

[0115]

[0116] Where l1 and l2 are the slopes of the linear segments of the nonlinear input function. So u m (k) can also be expressed as follows:

[0117] u m (k)=(l1u(k)-l1d1)h(u(k))+(l2u(k)-l2d2)h(-u(k))

[0118] -l1(u(k)-d1)h(u(k))h(d1-u(k))

[0119] -l2(u(k)-d2)h(-u(k))h(u(k)-d2)

[0120] Here h(x) is the following function, and x is the input of the function:

[0121]

[0122] Step 44: Rewrite u using matrix polynomial multiplication m (k) obtain:

[0123]

[0124] The intermediate variable and θ s The values ​​of are as follows:

[0125]

[0126] θ s =[l1d1 l1 l2d2 l2] T

[0127] ζ1(k)=h(u(k))h(d1-u(k))-h(u(k))

[0128] ζ2(k)=u(k)h(u(k))-u(k)h(u(k))h(d1-u(k))

[0129] ζ3(k)=h(-u(k))h(u(k)-d2)-h(-u(k))

[0130] ζ4(k)=u(k)h(-u(k))-u(k)h(-u(k))h(u(k)-d2)

[0131] Among them, ζ1(k), ζ2(k), ζ3(k) and ζ4(k) are intermediate variables, so the Hammerstein model of the tow motor servo system with dead zone nonlinearity is:

[0132]

[0133] Step 45: According to the formulas in step 42 and step 44, we obtain:

[0134]

[0135] Step 46, then the parameter vector θ and information vector of the dead zone model of the Hammerstein model It can be defined as follows:

[0136]

[0137] where n m Represents the total number of dimensions, and n m =n a +n b =4, then in the tow motor servo system, the parameter vector θ to be identified by the Hammerstein model is:

[0138] θ=[a1,a2,b1l1d1,l1b1,b1l2d2,b1l2,b2l1d1,l1b2,b2l2d2,b2l2] T

[0139] The actual output y(k) is as follows:

[0140]

[0141] Step 47: No noise term is added here, so v(k) = 0, and the prediction output error can be calculated by the following formula:

[0142]

[0143] Step 5: Take the objective function as the minimum cumulative error between the predicted output and the actual output of the Hammerstein model, and use the linear auxiliary constrained particle swarm algorithm to offline estimate the parameters to be identified of the Hammerstein model according to the objective function, and finally obtain the Hammerstein model with dead zone nonlinearity of the servo system.

[0144] Step 51: Introduce the linear auxiliary constrained particle swarm algorithm to estimate the model parameters of the system offline, and consider the optimal fit as the minimum cumulative error between the model estimation output and the actual measured position output. The objective function J(θ) is given as follows:

[0145] J(θ)=minF=minΣe h 2 (k)

[0146]

[0147] Where y(k) is the actual measured output signal time series data, It is the output signal time series data of the Hammerstein model under the same input excitation signal. minΣe h 2 (k) is understood as the cumulative minimum of all errors, which is used here as a general error calculation formula.

[0148] Using the dead zone range of the dead zone parameter initially extracted in step 342 and Constrain the search space.

[0149] Step 52: Initialize the particle position, velocity, and fitness function. Set the population size to 40, the maximum number of iterations to 1000, the learning factor c1=c2=1.49445, and the particle position P d ∈[-10,10], particle velocity V d ∈[-20,20],σ max =0.9 corresponds to the maximum value of the inertia weight, σ min =0.4 corresponds to the minimum value of inertia weight.

[0150] Step 53, during the particle swarm convergence process, the speed and position update formula of the linear auxiliary constraint particle swarm algorithm is:

[0151] v(t+1)=σv(t)+c1r1(p best -p(t))+c2r2(g best -p(t))

[0152] p(t+1)=p(t)+v(t+1)

[0153] Where v(t+1) is the updated particle velocity, v(t) is the particle velocity before the update, p(t) is the particle position before the update, p(t+1) is the particle position after the update, σ is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers, and p best is the particle’s own historical optimal position, g best is the global optimal position.

[0154] Determine whether the updated particle position exceeds the set linear auxiliary constraint range. If it exceeds, force projection to the boundary of the dead zone range; otherwise, no forced projection is performed. The specific implementation is as follows:

[0155] The dead zone parameter is calculated according to the updated particle position, and it is determined whether the dead zone parameter is within the dead zone range. If the dead zone parameter is less than the dead zone range, the dead zone parameter is projected as the minimum value of the dead zone range. If the dead zone parameter is greater than the dead zone range, the dead zone parameter is projected as the maximum value of the dead zone range. Then, the updated particle position after projection is obtained by reversely solving the projected dead zone parameter. If the dead zone parameter is within the dead zone range, no forced projection is performed, and the updated particle position is directly accepted.

[0156] Since the dead zone parameters include d1 and d2, when judging whether it exceeds the dead zone range, a judgment is made for each dead zone parameter. After projection, the corrected values ​​of d1 and d2 are obtained, and then multiplied with the corresponding parameters (including b1l1, b1l2, b2l1 and b2l2) to obtain the parameters to be identified of the Hammerstein model after projection update.

[0157] Step 54, repeat the fitness calculation and particle update. If the particle has the best fitness in all dimensions, the particle is updated to the historical optimal solution. If not, repeat the above process until the objective function converges or the maximum number of iterations is reached. The global optimal point is obtained, and the optimal solution of the parameters to be identified of the Hammerstein model is obtained.

[0158] Taking the tow motor servo system as an example, the parameters of the Hammerstein model obtained according to the optimal solution are θ=[a1,a2,b1l1d1,l1b1,b1l2d2,b1l2,b2l1d1,l1b2,b2l2d2,b2l2] T , then the dead zone parameter is obtained as and Thus, the Hammerstein model of the servo system is obtained. a =n b =2, so here represents the third term of vector θ divided by the fourth term; It means dividing the fifth term of the vector θ by the sixth term.

[0159] The recognition effect of the recognition method designed by this embodiment can be seen in Figure 6 and Figure 7 In the figure, the vertical axis ω is the speed in rpm, the horizontal axis Time is the time in s, and Actual in the icon represents the actual value, and Estimated represents the estimated value. The Hammerstein model identified by the method of the present invention is tested on the towing motor servo system platform to obtain the actual speed value of the towing motor servo system and the estimated speed value output by the Hammerstein model. From the test result image, it can be seen that the towing motor servo system has a high-precision following effect under low-speed conditions.

[0160] The method of the present invention uses the V-MLS method to identify the servo system in the low-speed linear stage, removes the influence of bad data on the system, and preliminarily obtains the range of dead zone parameters; the system uses the linear auxiliary constrained particle swarm algorithm for identification in the nonlinear stage, and introduces the range of dead zone parameters to define the search space, thereby enhancing the accuracy of local search, accelerating the convergence of the algorithm in the complex search space, and improving the accuracy of the final identification result. The model identified in this way has higher accuracy and better characterizes the actual characteristics of the controlled system. It is not only suitable for this towing servo platform, but also has a wide range of applications in modern industrial equipment.

[0161] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0162] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A high-precision model identification method for a servo system, characterized in that: The high-precision model identification method of the servo system comprises: Obtain the linear operation data of the servo system under low-speed conditions; A second-order controlled autoregressive model was constructed based on the linear running data; The variable recursive interval multi-innovation least squares algorithm is used to solve the parameters to be identified of the second-order controlled autoregressive model, and based on the parameters to be identified, the predicted output of the second-order controlled autoregressive model is obtained, and the dead zone range is determined according to the predicted output and actual output of the second-order controlled autoregressive model; Design the Hammerstein model of the servo system with dead zone nonlinearity according to the dead zone range; The objective function is to minimize the cumulative error between the predicted output and the actual output of the Hammerstein model. According to the objective function, a linear auxiliary constrained particle swarm algorithm is used to offline estimate the parameters to be identified of the Hammerstein model, and finally a Hammerstein model with dead zone nonlinearity of the servo system is obtained.

2. The high-precision model identification method of a servo system according to claim 1, characterized in that: The second-order controlled autoregressive model is constructed according to the linear operation data, comprising: According to the Mason formula, the transfer function from the output end to the input end of the servo system is obtained: In the formula, G(s) represents the transfer function of the servo system, U(s) is the frequency domain input of the servo system, and V(s) is the frequency domain output of the servo system. is the speed loop gain, K a is the current loop gain, K L is the elastic modulus, J M is the moment of inertia of the motor in the servo system, J L is the load moment of inertia, D L is the viscous friction coefficient, s represents the complex variable in the Laplace transform domain; The transfer function of the simplified servo system is: Where Y(s) represents the frequency domain output of the simplified servo system, and K is a combination of proportional constants, including the speed loop gain Current loop gain K a and elastic modulus K L , T is the time constant; The second-order controlled autoregressive model is constructed as follows: A(q -1 )y(k)=B(q -1 )u(k) A(q -1 )=1+a1q -1 +a2q -2 B(q -1 )=b1q -1 +b2q -2 In the formula, A(q -1 ) and B(q -1 ) represent the discrete polynomial of the input characteristic and the discrete polynomial of the output characteristic of the servo system, u(k) and y(k) are the actual input and actual output of the servo system at time k, a1, a2, b1 and b2 are the four parameters to be identified of the second-order controlled autoregressive model, and q represents the shift operator.

3. The high-precision model identification method of a servo system according to claim 1, characterized in that: The method of obtaining a predicted output of a second-order controlled autoregressive model based on the parameters to be identified and determining a dead zone range according to the predicted output and actual output of the second-order controlled autoregressive model includes: Calculate the residuals of the second-order controlled autoregressive model as follows: e(k)=y(k)-y linear (k) Where e(k) represents the residual of the second-order controlled autoregressive model at time k, y(k) is the actual output of the servo system at time k, and y linear (k) is the predicted output of the second-order controlled autoregressive model at time k; In the motor commutation area under the low-speed condition of the servo system, the critical point with the largest residual e(k) is found and marked as the dead zone critical point, so as to extract the dead zone range of the target dead zone parameter as follows: and d1 min is the minimum value of the first dead zone range, is the maximum value of the first dead zone range, is the minimum value of the second dead zone range, It is the maximum value of the second dead zone range.

4. The high-precision model identification method of a servo system according to claim 1, characterized in that: The method of designing a Hammerstein model of a servo system with dead zone nonlinearity according to the dead zone range includes: Construct the input-output model of the servo system with dead zone nonlinearity as follows: In the formula, u(k) and y(k) are the actual input and output of the servo system at time k, respectively. F(·) represents the dynamic model with dead zone nonlinearity. u m (k) is an intermediate variable, representing the predicted output of the kinetic model F(·), G(q -1 ) represents the linear part transfer function in the Hammerstein model, that is, the second-order controlled autoregressive model, y m (k) is an intermediate variable, indicating that the model G(q -1 ), q is the shift operator, v(k) is the measurement noise with a mean of zero and a variance of Gaussian white signal, A(q -1 ) and B(q -1 ) represent the discrete polynomial of the input characteristic and the discrete polynomial of the output characteristic of the servo system respectively; The processing process of the dynamic model F(·) with dead zone nonlinearity for the input u(k) is as follows: The second-order controlled autoregressive model G(q -1 ) for the intermediate variable u m The processing of (k) is as follows: Then we get the Hammerstein model with dead zone nonlinearity, as follows: Where l1 and l2 are the slopes of the linear segments of the dynamic model with dead zone nonlinearity. The parameter to be identified of the Hammerstein model is θ = [a1, a2, b1l1d1, l1b1, b1l2d2, b1l2, b2l1d1, l1b2, b2l2d2, b2l2] T , where a1, a2, b1, b2 are the parameters to be identified in the second-order controlled autoregressive model, which are known quantities in the Hammerstein model, and d1≥0 and d2≤0 are the unknown dead zone parameters within the dead zone range.

5. The high-precision model identification method of the servo system according to claim 4, characterized in that: The linear auxiliary constrained particle swarm algorithm outputs the optimal solution of the parameters to be identified of the Hammerstein model. The dead zone parameters d1 and d2 are calculated according to the optimal solution and are respectively and θ3 represents the third item in the parameter θ to be identified of the Hammerstein model, θ4 represents the fourth item in the parameter θ to be identified of the Hammerstein model, θ5 represents the fifth item in the parameter θ to be identified of the Hammerstein model, and θ6 represents the sixth item in the parameter θ to be identified of the Hammerstein model.

6. The high-precision model identification method for a servo system according to claim 1, characterized in that: The linear auxiliary constraint range of the linear auxiliary constraint particle swarm algorithm is the dead zone range.

7. The high-precision model identification method for a servo system according to claim 6, characterized in that: The method of offline estimating the parameters to be identified of the Hammerstein model using a linear auxiliary constrained particle swarm algorithm according to the objective function includes: Initialize particle positions, particle velocities and fitness functions, set population size, maximum number of iterations and learning factor; During the particle convergence process, the particle position and particle velocity are updated, and it is determined whether the updated particle position exceeds the set linear auxiliary constraint range. If it exceeds, it is forced to be projected to the boundary of the dead zone range; otherwise, forced projection is not performed; The fitness function is calculated repeatedly and the particle position and particle velocity are updated until the objective function converges or the maximum number of iterations is reached, and the optimal solution of the parameters to be identified of the Hammerstein model is obtained.

8. The high-precision model identification method for a servo system according to claim 7, characterized in that: It is determined whether the updated particle position exceeds the set linear auxiliary constraint range. If it exceeds, it is forced to project to the boundary of the dead zone range; otherwise, forced projection is not performed, and the execution is as follows: The dead zone parameter is calculated according to the updated particle position, and it is determined whether the dead zone parameter is within the dead zone range. If the dead zone parameter is less than the dead zone range, the dead zone parameter is projected as the minimum value of the dead zone range. If the dead zone parameter is greater than the dead zone range, the dead zone parameter is projected as the maximum value of the dead zone range. Then, the updated particle position after projection is obtained by reversely solving the projected dead zone parameter. If the dead zone parameter is within the dead zone range, no forced projection is performed, and the updated particle position is directly accepted.

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