A PMSM Control Method Based on Smith Predictor Compensation

Abstract

The present invention relates to a PMSM control method based on Smith prediction compensation, comprising the following steps: Step 1: Establish a PMSM mathematical model including a disturbance term; Step 2: Introduce a Smith predictor compensator into the PMSM mathematical model, and use a time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object, so as to obtain a Smith predictor compensator with full-parameter adaptability; the time-varying model adaptive prediction method is: first add a time-varying link, input the control quantity, and make the error between the two output quantities approach 0 to obtain the corresponding adaptive law; Step 3: Use a feedforward compensation controller based on sliding mode control to perform feedforward compensation on the output. The present invention uses a time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object, providing accurate parameters for Smith prediction compensation; by designing a sliding mode feedforward controller and combining it with Smith prediction compensation, the overall stability of the system is ensured.

Description

Technical Field

[0001] The present invention relates to the field of servo motor control, and particularly to a PMSM control method based on Smith predictor compensation. Background Art

[0002] In an AC servo system, due to the advantages of high torque density, smooth torque, and high operating speed of the permanent magnet synchronous motor (PMSM for short), PMSM has become the best choice for high-performance AC servo drives.

[0003] In a permanent magnet synchronous motor servo control system, from the perspective of the mathematical model, the inverter can be regarded as a delay link, and this delay link seriously affects the control accuracy and stability margin of the servo system. How to overcome the influence of this delay link on the system performance has always been a hot topic in servo system control.

[0004] In traditional methods for approximating the delay link, the most common one is to perform Taylor expansion on the delay link and approximate it as a first-order inertial link. This approximation method linearizes the delay link and simplifies the design complexity, but it can only be used in occasions with low accuracy requirements and cannot meet the high-precision occasions that require completely overcoming the delay effect. Therefore, in order to improve the approximation accuracy, some scholars have proposed various approximation methods such as Pade approximation and DFR approximation (Direct Frequency Response Approximation) for the delay link. Compared with the first-order inertial link, the numerator and denominator of the transfer function of Pade approximation and DFR approximation are of the same order and are closer to the delay link. However, the disadvantages of these two approximation methods are that the differential order is too high and it is easy to generate vibrations. Moreover, no matter how high the precision of the approximation is, there is still an error compared with the real delay link. For different input signals, the approximation effect is also different, so the delay link cannot be completely replaced.

[0005] In order to completely overcome the influence of the delay effect of the inverter in the servo system, it is necessary to introduce a Smith predictor compensator in the feedback path. The traditional Smith predictor compensator consists of a delay link and a controlled object model. By canceling the original delay link in the denominator of the closed-loop transfer function, the overall stability of the control system is ensured. This method has a simple principle and is easy to implement. Compared with linearizing and approximating the delay link, it can completely overcome the delay effect in a real sense. However, the biggest problem of the traditional Smith predictor compensator is that it requires accurate parameters of the controlled object model, while the parameters are unknown or uncertain in practical applications. Inaccurate parameters will not only reduce the compensation effect of the Smith predictor compensator but also destroy the stability of the system.

[0006] Therefore, how to overcome the influence of parameter uncertainty on the compensation effect of the Smith predictor compensator is a technical problem that those skilled in the art urgently need to solve. Summary of the Invention

[0007] The present invention provides a PMSM control method based on Smith predictor compensation to solve the above technical problems.

[0008] To solve the above technical problems, the present invention provides a PMSM control method based on Smith predictor compensation, including the following steps:

[0009] Step 1: Establish a PMSM mathematical model including a disturbance term;

[0010] Step 2: Introduce a Smith predictor compensator into the PMSM mathematical model, and use a time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object to obtain a Smith predictor compensator with full parameter adaptability; the time-varying model adaptive prediction method is: first add a time-varying link, input the control quantity, and make the error between the two output quantities approach 0 to obtain the corresponding adaptive law;

[0011] Step 3: Use a feedforward compensation controller based on sliding mode control to perform feedforward compensation on the output.

[0012] Preferably, vector control is adopted in the d-q axis coordinate system, and under the condition of making i d = 0, the PMSM mathematical model including a disturbance term is:

[0013]

[0014] Among them, y is the angular position output, ω is the angular velocity output, i q is the q-axis current, u q is the q-axis voltage, d is a Gaussian white noise disturbance with a mean of 0, J is the moment of inertia, B is the viscous friction coefficient, K t is the torque coefficient, K e is the back electromotive force coefficient, R is the stator resistance, and L is the stator inductance.

[0015] Preferably, the method for estimating the delay time by using the time-varying model adaptive prediction method includes: connecting a time-varying delay link in parallel at both ends of the delay link Input the same control quantity u r to the two delay links, and by comparing the error e q between the two output quantities u and τ to adjust the delay time of the time-varying delay link until the error approaches 0, and at this time Approaching the true delay time, the estimated value of the delay time is calculated The adaptive law of

[0016] Preferably, the output error e of the two delay links is defined τ as:

[0017]

[0018] Take the Lyapunov function V τ and its derivative:

[0019]

[0020]

[0021] where k τ is the estimated parameter of the delay time. From the above formula, we can get:

[0022]

[0023]

[0024] The estimated value of the delay time is calculated The adaptive law of, and introduce the adaptive law into the delay link of the Smith predictor compensator.

[0025] Preferably, calculate the adaptive law of the controlled object model parameters, and introduce the adaptive law of the controlled object model parameters into the Smith predictor compensator,

[0026]

[0027] where e ω is the error between the actual speed output and the time-varying model speed output, is the estimated value of the controlled object model parameters, and μ1 and μ2 are the estimated parameters of the model parameters respectively.

[0028] Preferably, in the calculation of the control quantity of the feedforward compensation controller, there is an advanced prediction of the position output, and the quadratic compensation prediction position lead value is adopted.

[0029] Preferably, the predicted position lead value y(t + τ) after quadratic compensation is:

[0030] y(t + τ) = (1 - 2p + p 2 )y0 + (2 - p)y,

[0031] where y is the actual position output, y0 is the predicted position lead value without compensation, and p is the delay operator. Preferably, the position output tracks the delay signal of the given input:

[0032] e = r(t - τ) - y,

[0033] where r is the given input signal;

[0034] Define the linear sliding mode surface s:

[0035]

[0036] where c is the parameter of the linear sliding mode surface;

[0037] Calculate the feedforward control quantity u of the sliding mode feedforward controller f as:

[0038]

[0039] where u pid is the output of the PID controller, D = max(|d|), which is the maximum amplitude of the Gaussian white noise perturbation, and k s is the decay coefficient of the Lyapunov function.

[0040] Compared with the prior art, the PMSM control method based on Smith predictive compensation provided by the present invention has the following advantages:

[0041] 1. The present invention uses a time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object, providing accurate parameters for Smith predictive compensation; by designing a sliding mode feedforward controller and combining it with Smith predictive compensation, the overall stability of the system is ensured;

[0042] 2. The present invention provides a position output lead amount for the controller through "secondary compensation position output lead prediction", so that when passing through the delay link, the delay effect can be offset, and a timely control quantity can be input to the controlled object. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is the structural block diagram of the simplified mathematical model of PMSM in a specific embodiment of the present invention;

[0044] Figure 2 is the schematic diagram of the ideal Smith predictive compensator in a specific embodiment of the present invention;

[0045] Figure 3 is the schematic diagram of the delay time estimation structure in a specific embodiment of the present invention;

[0046] Figure 4 is the curve diagram of the delay time estimation in a specific embodiment of the present invention;

[0047] Figure 5Schematic diagram of the controlled object model parameter estimation structure in a specific embodiment of the present invention;

[0048] Figure 6 Schematic diagram of the full-parameter adaptive Smith prediction compensation structure in a specific embodiment of the present invention;

[0049] Figure 7 Comparison diagram of the predicted position lead value and the actual position output in a specific embodiment of the present invention;

[0050] Figure 8a Comparison diagram of the predicted position lead value before and after compensation in a specific embodiment of the present invention;

[0051] Figure 8b Comparison diagram of the predicted error of the position lead value before and after compensation in a specific embodiment of the present invention;

[0052] Figure 9 Comparison diagram of the predicted error of the position lead value after multiple compensations in a specific embodiment of the present invention;

[0053] Figure 10 Schematic diagram of the FPASPC + SMFC structure in a specific embodiment of the present invention;

[0054] Figure 11 Effect diagram of the estimation of the model parameter K in a specific embodiment of the present invention;

[0055] Figure 12 Effect diagram of the estimation of the model parameter α in a specific embodiment of the present invention;

[0056] Figure 13 Effect diagram of the prediction of the position lead value in a specific embodiment of the present invention;

[0057] Figure 14 Comparison diagram of the position responses of FPASPC + SMFC and TSPC in a specific embodiment of the present invention;

[0058] Figure 15 Comparison diagram of the position response errors of FPASPC + SMFC and TSPC in a specific embodiment of the present invention;

[0059] Figure 16 Comparison diagram of the position responses of FPASPC + SMFC and TSPC + DFRA in a specific embodiment of the present invention;

[0060] Figure 17 Comparison diagram of the position response errors of FPASPC + SMFC and TSPC + DFRA in a specific embodiment of the present invention;

[0061] Figure 18This is the position response comparison diagram of FPASPC+SMFC and TSPC+MRAC in a specific embodiment of the present invention;

[0062] Figure 19 This is the position response error comparison diagram of FPASPC+SMFC and TSPC+MRAC in a specific embodiment of the present invention;

[0063] Figure 20 This is the position response comparison diagram of FPASPC+SMFC and ISPC+ADC in a specific embodiment of the present invention;

[0064] Figure 21 This is the position response error comparison diagram of FPASPC+SMFC and ISPC+ADC in a specific embodiment of the present invention;

[0065] Figure 22 This is the position response comparison diagram of FPASPC+SMFC and ASPTDCC in a specific embodiment of the present invention;

[0066] Figure 23 This is the position response error comparison diagram of FPASPC+SMFC and ASPTDCC in a specific embodiment of the present invention. Specific Embodiment

[0067] In order to more elaborately describe the technical solutions of the above invention, specific embodiments are listed below to prove the technical effects; it should be emphasized that these embodiments are used to illustrate the present invention and are not limited to restricting the scope of the present invention.

[0068] The PMSM control method based on Smith prediction compensation provided by the present invention includes the following steps:

[0069] Step 1: Establish a PMSM mathematical model including disturbance terms;

[0070] Step 2: Introduce a Smith prediction compensator into the PMSM mathematical model, and use the time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object to obtain a Smith prediction compensator with full parameter adaptability; the time-varying model adaptive prediction method is: first add a time-varying link, input the control quantity, and make the error between the two output quantities approach 0 to obtain the corresponding adaptive law;

[0071] Step 3: Use a feedforward compensation controller based on sliding mode control to perform feedforward compensation on the output.

[0072] The present invention uses the time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object, providing accurate parameters for Smith prediction compensation; by designing a sliding mode feedforward controller and combining it with Smith prediction compensation, the overall stability of the system is ensured.

[0073] In some embodiments, vector control is adopted in the d-q axis coordinate system. Under the condition that i d = 0, the mathematical model of the PMSM with disturbance terms is as follows:

[0074]

[0075] where y is the angular position output, ω is the angular velocity output, T e is the excitation torque, i q is the q-axis current, u q is the q-axis voltage, d is the Gaussian white noise disturbance with a mean of 0, J is the moment of inertia, B is the viscous friction coefficient, K t is the torque coefficient, K e is the back electromotive force coefficient, R is the stator resistance, and L is the stator inductance.

[0076] It can be seen from Equation (1) that in the mathematical model of the PMSM, the closed-loop transfer function of ω and u q + d can be simplified as:

[0077]

[0078] where:

[0079]

[0080] Therefore, the simplified mathematical model of the PMSM is as shown in Figure 1 Figure.

[0081] In an actual control system, the inverter is an important current converter. However, there is a delay in the response of the inverter, and the delay link has a serious impact on the stability of the control system. Therefore, a Smith predictor compensator is introduced into the control system to compensate for the influence of the delay link on the system stability.

[0082] On the premise of not considering the disturbance, after introducing the PID controller, the inverter, and the ideal Smith predictor compensator, the structural block diagram is as shown in Figure 2 Figure.

[0083] where r is the given input signal, G pid is the transfer function of the PID controller, u r is the input control quantity of the inverter, e -τs is the transfer function of the delay link of the inverter, τ is the delay time of the inverter, generally half of the period of the triangular carrier signal for generating the SPWM (Pulse Width Modulation) wave, τ * , K * , α *They are the parameters of the Smith predictor compensator respectively.

[0084] From Figure 2 it can be seen that under ideal conditions, that is, τ * = τ, K * = K, α * = α, the closed-loop transfer function of the Smith predictor compensation system is:

[0085]

[0086] From Equation (4), it can be seen that after introducing the Smith predictor compensator, the delay link in the denominator of the closed-loop transfer function is canceled, becoming a series connection of a closed-loop function and a delay link, eliminating the influence of the delay link on the system stability.

[0087] Of course, the Smith predictor compensator analyzed above achieves an ideal effect when the inverter delay time and the controlled object model parameters are both known. However, in practical applications, these parameters are very likely to be unknown. Therefore, this application proposes a time-varying model adaptive prediction method to estimate the delay time and the controlled object model parameters.

[0088] In some embodiments, the method for estimating the delay time using the time-varying model adaptive prediction method includes: connecting a time-varying delay link in parallel at both ends of the delay link inputting the same control quantity u r to the two delay links, and by comparing the error e q between and τ of the two output quantities u to adjust the delay time of the time-varying delay link until the error approaches 0, at this time approaches the true delay time, and the estimated value of the delay time is calculated

[0089] Specifically, the schematic diagram of the delay time estimation structure is as shown in Figure 3 Figure.

[0090] From Figure 3 it can be seen that the output error e τ of the two delay links is defined as:

[0091]

[0092] Take the Lyapunov function V τ and its derivative:

[0093]

[0094]

[0095] Among them, k τ is the delay time estimation parameter. Therefore, from equations (5) and (7), we can obtain:

[0096]

[0097]

[0098] Through equation (9), the estimated value of the delay time can be obtained, and the adaptive law can be obtained, so as to obtain the accurate delay time and introduce it into the delay link of the Smith predictor compensator. If the estimated delay time is 0.02, the curve of the estimator is as Figure 4 shown.

[0099] From Figure 4 it can be seen that the estimated value almost increases synchronously with time, converges to the actual value and remains stable. Therefore, the estimated curve of the delay time can be approximated to the functional relationship in equation (10):

[0100]

[0101] And the response of the system is after t > τ. Therefore, when it comes to in the following text, it is simplified to that is, the delay time τ is known.

[0102] In addition to estimating the delay time of the inverter, the accurate estimation of the mathematical model parameters of the controlled object is also very important. This application also uses the time-varying model adaptive prediction method to predict the model parameters of the controlled object, and its structure block diagram is as Figure 5 shown.

[0103] Among them, ω0 is the speed output of the time-varying model, and e ω is the error between the actual speed output and the speed output of the time-varying model, u0 is the input quantity of the time-varying model, is the estimated value of the model parameters of the controlled object.

[0104] From Figure 5 it can be seen that the speed output error e ω of the two models is defined as:

[0105] e ω = ω - ω0 (11)

[0106] It is known that both the controlled object model and the time-varying model are first-order inertia links:

[0107]

[0108] Take the Lyapunov function V ω and its derivative:

[0109]

[0110]

[0111] According to equations (11), (12), and (14), it can be obtained that:

[0112]

[0113]

[0114] Replace both K and α in equation (16) with the estimated values It can be obtained that:

[0115]

[0116] Define the estimated value error It can be obtained that Take the Lyapunov function V Kα :

[0117]

[0118] where μ1 and μ2 are respectively the adaptive law parameters of the model parameters. In some embodiments, the adaptive law of the controlled object model parameters:

[0119]

[0120] Therefore, it can be obtained that V Kα The derivative of is:

[0121]

[0122] As can be seen from equation (20), by introducing both the delay time and the adaptive law of the controlled object model parameters into the Smith predictor compensator, a fully parameter adaptive Smith predictor compensator can be obtained, as Figure 6 shown.

[0123] Since the parameter estimation is inaccurate during the convergence process, it will affect the compensation accuracy of the Smith predictor compensator and the stability of the system. Therefore, this application proposes a feedforward compensation controller based on sliding mode control, abbreviated as a sliding mode feedforward controller. However, due to the existence of the delay link, there will be an over-forecast of the position output in the calculation of the control quantity. Therefore, it is crucial to design a prediction method for the position output lead value y(t + τ).

[0124] Preferably, when there is an over-forecast of the position output in the calculation of the control quantity of the feedforward compensation controller, a quadratic compensation is used to predict the position lead value.

[0125] From Figure 6 it can be seen that:

[0126]

[0127] As can be seen from the above description of the delay time estimation, the delay time estimation value is known Therefore, the estimated value of the controlled object model parameters is substituted into Equation (21). Defining the predicted position lead value at this time as y0, the differential equation can be obtained as follows:

[0128]

[0129] However, during the convergence process of estimating the controlled object model parameters, the parameter estimation value is inaccurate. Therefore, the directly predicted position lead value is also inaccurate, as Figure 7 shown

[0130] As Figure 7 can be seen, there are errors in the amplitude, mean, and phase of the predicted position lead value curve. Therefore, it is necessary to compensate the predicted value; otherwise, it will cause a deviation in the calculated feedforward control quantity

[0131] This application proposes a "position lead value compensation prediction method". Defining the predicted position lead value after n compensations as y n , y n The error obtained by subtracting the delay value from the actual position output is denoted as e yn . y n and e yn The recurrence formulas are shown in Equations (23) and (24) as follows:

[0132] e yn = y - y n (t - τ) (23)

[0133] y n+1 = y n + e yn (24)

[0134] Define the delay operator p:[[ID=�5]]

[0135] py = y(t - τ) (25)

[0136] From Equations (23)-(25), the formulas for the predicted position lead value y1 and the prediction error e y1 after one compensation can be obtained as follows:

[0137] e y0 = y - py0 (26)

[0138] y1 = y0 + e y0

[0139] = (1 - p)y0 + y (27)

[0140] e y1 = y - py1

[0141] = (1 - p)y - (p - p 2 )y0 (28)

[0142] The comparison of the predicted position lead value after one - time compensation with that without compensation is as Figure 8a and 8b shown.

[0143] From Figure 8a it can be seen that after one - time compensation, the amplitude and mean value of y1 are almost the same as the actual position output y, and the phase difference is only one delay time. Compared with the uncompensated y0, the prediction effect has been significantly improved. And from Figure 8b it can be seen that the error e y1 of y1 after delay and the actual position output, compared with the error e y0 without compensation, the order of magnitude also drops from 10 0 to 10 -2 . The prediction error is almost eliminated through compensation. However, it can also be seen that after one - time compensation, all errors cannot be completely eliminated. Therefore, the method of multiple compensations can be adopted. Define the objective function J yn for measuring the total error, compare the total errors of multiple compensations, and thus select the number of compensations with the smallest total error:

[0144]

[0145] where T is the total running time. The comparison of the total error after multiple compensations is as Figure 9 shown.

[0146] From Figure 9 it can be seen that the total error is the smallest when compensating twice. Therefore, this application adopts "the predicted position lead value of secondary compensation" to provide the most accurate parameters for the controller design:

[0147] y(t + τ) = (1 - 2p + p 2 )y0+(2 - p)y (30).

[0148] In addition, in the delay system of this application, a delay signal for the position output to track the given input is also designed:

[0149] e = r(t - τ)-y (31)

[0150] This application adopts the sliding - mode control method to design the feed - forward control quantity, which has strong robustness to parameter uncertainties. Define the linear sliding - mode surface s:

[0151]

[0152] Among them, c is the parameter of the linear sliding mode surface;

[0153]

[0154]

[0155]

[0156]

[0157] k s is the decay coefficient of the Lyapunov function;

[0158] According to Equation (36), it can be obtained that:

[0159]

[0160]

[0161] From Figure 2 it can be known that:

[0162] u q = u r (t - τ) (39)

[0163] Therefore, according to Equations (38) and (39), it can be obtained that:

[0164]

[0165] Since y(t + τ) can be calculated by Equation (30), substituting the estimated values of the model parameters gives:

[0166]

[0167] Define the output of the PID controller as u pid , and add the nonlinear feedforward compensation amount u f in front of the inverter, so that the total control amount of the control system satisfies Equation (41), that is:

[0168] u pid + u f + d = u r (42)

[0169] Finally, the feedforward control amount based on sliding mode control is obtained as:

[0170]

[0171] However, the disturbance d belongs to Gaussian white noise and cannot be accurately predicted. Therefore, u f is redesigned as:

[0172]

[0173] Among them, D = max(|d|), which is the maximum amplitude of Gaussian white noise perturbation. Since dsgn(s) > -max(|d|), then D + dsgn(s) > 0.

[0174] When and both approximate the exact value, the derivative of the Lyapunov function is:

[0175]

[0176] In summary, the complete structural schematic diagram of FPASPC + SMFC is obtained, as shown in Figure 10 shown.

[0177] To verify the correctness of the control method proposed in the application, a control system model is built in MATLAB / Simulink and compared with five comparative examples. Comparative example 1 is traditional Smith predictive compensation (Traditional Smith Predictive Compensation), abbreviated as TSPC; Comparative example 2 is traditional Smith predictive compensation + DFR approximation (Traditional Smith Prediction Compensation + Direct Frequency Response Approximation), abbreviated as TSPC + DFRA; Comparative example 3 is traditional Smith predictive compensation + model reference adaptive control (Traditional Smith Predictive Compensation + Model Reference Adaptive Control), abbreviated as TSPC + MRAC; Comparative example 4 is improved Smith predictive compensation + anti-disturbance control (Improved Smith Predictor Compensation + Anti-disturbance Control), abbreviated as ISPC + ADC; Comparative example 5 is adaptive Smith predictive time-varying delay compensation control (Adaptive Smith Predictive Time-varying Delay Compensation Control), abbreviated as ASPTDCC. However, considering that in the published literature on Smith predictive compensators, most are considered to be in an ideal state, which does not match the situation studied in this application. Therefore, in the simulation comparison, all models are run under the condition of uncertain parameters, so it is inevitable that the ideal effects in the previous literature cannot be fully reproduced, which is a normal situation.

[0178] In the simulation of this application, the PID controller uses a P controller, and its proportional gain is designed by pole placement. The model parameters and controller parameters are shown in Table 1:

[0179] Table 1 Model Parameters and Controller Parameters

[0180] Parameter Numerical value Parameter Numerical value Stator inductance L (H) 0.01869 Stator resistance R (Ω) 4.78 Moment of inertia J (kgm2) 0.57 Viscous friction coefficient B (Ns / m) 0.0065 Torque coefficient Kt (Nm / A) 1.6 Back electromotive force coefficient Ke (Vs / m) 1.6 Delay time τ (s) 0.02 Proportional gain Kp of P controller 30 Delay time estimation parameter kτ 500 Model parameter estimation parameter kω 100 Model parameter estimation parameter μ1 100 Model parameter estimation parameter μ2 350 Linear sliding mode surface parameter c 5 Reaching law parameter k 5 Variance of Gaussian white noise perturbation d 50 Feedforward control perturbation term parameter D 50

[0181] According to the parameters in Table 1, the actual model parameters can be obtained:

[0182]

[0183] Based on the parameters in Table 1 and Equation (46), a Simulink model is established.

[0184] When a sine signal is input, the delay time estimation effect of FPASPC+SMFC is as Figure 5 shown, while the effect of model parameter estimation and predicted position lead value is as Figures 11 - 13 shown.

[0185] From Figure 11 , 12 , it can be seen that the parameter estimation of FPASPC+SMFC has a short start time, fast speed, high estimation accuracy, and stable final value convergence. From Figure 13 , it can be seen that the predicted position lead value after secondary compensation is very accurate in terms of amplitude, mean value, and phase, with fast prediction speed and good stability. Especially from the local graph, it can be seen that the predicted lead value is completely parallel to the actual value and exactly leads by a delay time of 0.02 s. The simulation image proves that the time-varying model adaptive prediction method and the "position lead value compensation prediction method" proposed in this application can still obtain accurate model parameters and position lead values under the initial conditions of unknown parameters, providing optimal parameters for the calculation of control quantities.

[0186] The comparison effect between FPASPC+SMFC of this application and Comparative Example 1 (TSPC) is as Figure 14 , Figure 15 shown. From Figure 14 , it can be seen that under the condition of uncertain parameters, although the traditional Smith prediction compensation TSPC does not show instability, the compensation effect will decrease significantly. The first maximum value of the position response of TSPC is 1.173° at 1.654 s, with a phase lag of 0.084 s from the given input delay signal, and there is also an error of 17.3% in amplitude. While the first maximum value of FPASPC+SMFC is 0.9918° at 1.601 s, with a phase lag of only 0.031 s from the given input delay signal, and the amplitude error is only 0.82%. From Figure 15It can be seen that the error of FPASPC+SMFC remains between -0.01° and 0.01°, and the order of magnitude is within the range of 10 -2 ° interval. While TSPC always has an obvious sine waveform on the error image, and the maximum error is -0.4522°, which is 45 times the steady-state error of FPASPC+SMFC. It can be seen from this that compared with TSPC, FPASPC+SMFC has a faster tracking speed, higher steady-state accuracy and smaller error.

[0187] The comparison effect between the FPASPC+SMFC of the present application and Comparative Example 2 (TSPC+DFRA) is as Figure 16 、 Figure 17 shown. It can be seen from Figure 16 、 Figure 17 that when the parameters are uncertain, using the DFR approximation method to replace the delay link will make the system unstable and divergent, and the position response and error will reach 10 26 . It can be shown from this that only by using the real delay link in the Smith predictor compensation can the optimal effect be achieved. The difficulty of the delay link lies in the estimation of the delay time. Therefore, it is necessary to introduce the time-varying model adaptive prediction method proposed in the present application to better use the delay link to compensate for the influence of the inverter on the system stability.

[0188] The comparison effect between the FPASPC+SMFC of the present application and Comparative Example 3 (TSPC+MRAC) is as Figure 18 、 Figure 19 shown. It can be seen from Figure 18 、 Figure 19 that compared with TSPC, after introducing the model reference adaptive, even under the condition of uncertain parameters, the effect of non-linear control is better than that of traditional linear control. At 4.483 s, TSPC+MRAC reaches the first minimum value of -1.073°, the phase leads by 0.227 s, and the error is only 7.3%, and the tracking effect is better than that of TSPC. However, compared with the method proposed in the present application, FPASPC+SMFC reaches the first minimum value of -0.9908° at 4.724 s, the phase lags by 0.014 s, and the error is only 0.92%, which has a smaller phase error and amplitude error than TSPC+MRAC. And TSPC+MRAC has two other problems. It can be seen from Figure 18 that in the startup stage, TSPC+MRAC has huge phase and amplitude deviations, which are due to the inaccurate reference model parameters and different from the actual parameters of the controlled object. In order to make the actual output consistent with the reference output, a huge adjustment deviation is caused. When t>2.832 s, the error of TSPC+MRAC stabilizes between -0.2892° and 0.2317°, and the order of magnitude is within the range of 10 -1Within the range of °, it is 20 times the steady-state error of FPASPC+SMFC. It can be seen from this that even with the adoption of non-linear control, due to inaccurate parameters and the lack of effective vibration suppression, the control accuracy still cannot reach the optimal level.

[0189] The comparison effect between the FPASPC+SMFC of this application and Comparative Example 4 (ISPC+ADC) is as Figure 20 , Figure 21 shown. It can be seen from Figure 20 , Figure 21 that, compared with TSPC, by introducing a filter and anti-interference control in the Smith predictor compensator, ISPC+ADC strengthens the robustness and the response error also becomes significantly smaller. At 1.559 s, ISPC+ADC reaches the first maximum value of 1.002°, with a phase lead of 0.011 s and an error of only 0.2%. Compared with TSPC+MRAC, due to the anti-interference control, even for a classical linear system, it can achieve a better control effect than an adaptive system. It can be seen from Figure 21 that although at 1.559 s, the phase error and amplitude error are of the same order of magnitude as the method proposed in this application, from the overall position error, the steady-state error of ISPC+ADC is ±0.08°, while the steady-state error of FPASPC+SMFC is ±0.01°, and the former is 8 times the latter. The disadvantage of ISPC+ADC is that it is necessary to design the inverse transfer function of the controlled object model, and the inverse transfer function of the delay link is the lead link. It is very difficult to achieve lead prediction without an effective prediction algorithm. Secondly, although the second-order system in the disturbance observer will approach 1 as t→∞ according to the final value theorem. However, the second-order system is a phase-lagging integral link, and for the random noise of high-frequency vibration, the second-order system will have the same effect as a filter on the input, resulting in a huge deviation between the observed value and the actual value.

[0190] The comparison effect between the FPASPC+SMFC of this application and Comparative Example 5 (ASPTDCC) is as Figure 22 , Figure 23 shown. It can be seen from Figure 22 , Figure 23 that ASPTDCC realizes the adaptive adjustment of the delay time by introducing a multiplier and an integrator, and the response curve shows severe fluctuations during the start-up stage. However, after entering the steady state, even if the delay time and the controlled object model are inaccurate, the steady-state error is still very small, indicating that ASPTDCC has strong adaptability. At 4.755 s, ASPTDCC reaches the first minimum value of -1.023°, with a phase lag of 0.045° and an error of 2.3%. Compared with the method proposed in this application, the order of magnitude of the phase error is quite the same, but the error ratio is relatively large. It can be seen from Figure 23It can be seen that the steady-state error of ASPTDCC is within ±0.05°, which is five times that of FPASPC+SMFC. Thus, it can be known that the biggest drawback of ASPTDCC is the large fluctuation during the startup phase. The main reason is that the integrator and multiplier will make the error e(s) larger, and then it will become even larger through integration and multiplication. Therefore, it is very difficult to adjust the integrator well, otherwise divergence is very likely to occur.

[0191] In summary, the PMSM control method based on Smith predictor compensation provided by the present invention uses a time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object, providing accurate parameters for Smith predictor compensation, so as to achieve Smith predictor compensation under the condition of unknown parameters; then, by designing a feedforward compensation based on sliding mode and combining it with Smith predictor compensation, the overall stability of the system is ensured; the present application also proposes a "quadratic compensation position output lead value prediction method", and by comparing the delay of the predicted value with the actual value and compensating multiple times, an accurate position output lead value can be obtained. The simulation comparison results prove that for various Smith predictor compensation systems designed under ideal conditions, once the parameters are uncertain, the response tracking effect will decrease significantly, the error will increase, and even unstable results will occur. However, the method proposed by the present application can still achieve high-precision stable tracking, extremely small errors and strong robustness even when the parameters are unknown.

[0192] Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A PMSM control method based on Smith prediction compensation, characterized in that, The method includes the following steps: Step 1: Establish a PMSM mathematical model including a disturbance term; Step 2: Introduce a Smith predictor compensator into the PMSM mathematical model, and use a time-varying model adaptive prediction method to estimate the delay time and the model parameters of the controlled object, so as to obtain a Smith predictor compensator with full-parameter adaptability; the time-varying model adaptive prediction method is: first add a time-varying link, input the control quantity, and make the error between the two output quantities approach 0 to obtain the corresponding adaptive law; Step 3: Use a feedforward compensation controller based on sliding mode control to perform feedforward compensation on the output; Under vector control in the d-q axis coordinate system, let Under the condition of, the mathematical model of PMSM with disturbance terms is as follows: ， Among them, is the angular position output, is the angular velocity output, is the shaft current, is the shaft voltage, is the Gaussian white noise perturbation with a mean of 0, is the moment of inertia, is the viscous friction coefficient, is the torque coefficient, is the back electromotive force coefficient, is the stator resistance, is the stator inductance; The method for estimating the delay time using the time-varying model adaptive prediction method includes: connecting a time-varying delay link in parallel at both ends of the delay link , inputting the same control quantity to the two delay links , by comparing the two output quantities and error to adjust the delay time of the time-varying delay link , until the error approaches 0, at this time approaches the true delay time, and the estimated value of the delay time is calculated adaptive law; Define the output error of two delay links as follows: , Take the Lyapunov function and its derivative: ， ， wherein, is the delay time estimation parameter, and it can be obtained from the above formula: ， ， Calculate the estimated delay time and introduce the adaptation law into the delay link of the Smith predictor compensator.

2. The PMSM control method based on Smith prediction compensation according to claim 1, characterized in that, Calculate the adaptive law of the model parameters of the controlled object, and introduce the adaptive law of the model parameters of the controlled object into the Smith predictor compensator, ， Among them, is the error between the actual speed output and the time-varying model speed output, , are the estimated values of the controlled object model parameters, μ 1 and μ 2 are the model parameter estimation parameters respectively.

3. The PMSM control method based on Smith predictor compensation according to claim 2, characterized in that In the calculation of the control quantity of the feedforward compensation controller, there is a lead prediction of the position output, and a quadratic compensation is used to predict the position lead value.

4. The PMSM control method based on Smith prediction compensation according to claim 3, characterized in that, The predicted position leading value after secondary compensation is as follows: ， Among them, is the actual position output, is the uncompensated predicted position lead value, is the delay operator.

5. The PMSM control method based on Smith predictor compensation according to claim 4, characterized in that The position output tracks the delayed signal of the given input: ， wherein, is a given input signal; Define the linear sliding mode surface s : , Among them, c is the parameter of the linear sliding mode surface; Calculate the feedforward control amount of the sliding mode feedforward controller It is: ， Among them, is the output of the PID controller, , is the maximum amplitude of the Gaussian white noise perturbation, k s is the decay coefficient of the Lyapunov function.

Images