Sensorless model predictive direct speed control method for induction motor

Abstract

The application discloses a sensorless model predictive direct speed control method of an induction motor, and first, establishes a mathematical model of the induction motor in a two-phase static coordinate system by taking stator current and rotor flux as state variables; a sliding mode observer is constructed to obtain an estimated value of the rotating speed and an estimated value of the flux; then, an adaptive rate of the stator resistance is derived based on the sliding mode observer; a predicted value of the stator flux and a predicted value of the rotating speed are obtained; the predicted model is corrected, and the stator resistance identification value is brought back to the stator flux equation to update the predicted value of the stator flux in real time; finally, a cost function is constructed to finally realize the optimal control performance of the induction motor. The application can effectively suppress the prediction error caused by parameter mismatch, and improve the dynamic, steady-state performance, prediction accuracy and robustness performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-performance induction motors, and in particular relates to a sensorless model prediction direct speed control method for induction motors. Background Art

[0002] Induction motors are widely used in industrial and agricultural production due to their simple structure, high reliability, and low cost. With technological advancements, market demands for higher motor performance are increasing. High-performance AC speed control technology has been extensively studied by scholars, and model predictive control has become an important research branch.

[0003] Most current research on model predictive control (MPC) focuses on current, torque, and flux control. However, the inherent cascade structure limits the dynamic response of the motor, necessitating improvements to dual-loop MPC schemes. MPC combines the advantages of MPC and direct speed control, overcoming the limitations of the cascade structure and achieving highly dynamic speed control.

[0004] Compared to vector control, sensorless model predictive control of induction motors requires estimating both the motor speed and the stator flux. Furthermore, compared to general sensorless methods, another difficulty with sensorless model predictive control is the integration of estimation and prediction. Summary of the Invention

[0005] The present invention aims to provide a sensorless model predictive direct speed control method for an induction motor, which can effectively suppress the prediction error caused by parameter mismatch and improve its dynamic and steady-state performance, prediction accuracy and robustness.

[0006] The technical solution adopted by the present invention is a sensorless model predictive direct speed control method for an induction motor, which is specifically implemented according to the following steps:

[0007] Step 1: Using the stator current and rotor flux as state variables, establish a mathematical model of the induction motor in a two-phase stationary coordinate system;

[0008] Step 2: Construct a sliding mode observer to obtain the estimated values ​​of the speed and flux;

[0009] Step 3: Derivation of the adaptive rate of the stator resistance based on the sliding mode observer;

[0010] Step 4: Obtain the stator flux prediction value and the speed prediction value;

[0011] Step 5: Modify the prediction model and bring the stator resistance identification value back into the stator flux equation to update the stator flux prediction value in real time;

[0012] Step 6, the construction of cost function is carried out, and finally the optimal control performance of the induction motor is realized.

[0013] The application is also characterized in that,

[0014] Step 1 is implemented according to the following steps:

[0015] The mathematical model of the induction motor is:

[0016]

[0017]

[0018] Among them, is the stator resistance, is the leakage coefficient, is the stator inductance, is the rotor time constant, , is the mutual inductance, is the rotor inductance, is the rotor speed, , is the stator current, is the rotor flux vector, , is the shaft stator voltage component, is the shaft stator voltage component;

[0019] Let:

[0020]

[0021]

[0022]

[0023] .

[0024] Step 2 is implemented according to the following steps:

[0025] Step 201, according to the mathematical model of the induction motor in two-phase static Coordinate system, and the mathematical model and the sliding mode variable structure control theory to build sliding mode observer state equation as follows:

[0026]

[0027] Where, is the sliding mode gain matrix,

[0028]

[0029] Select the stator current error as the sliding surface:

[0030]

[0031] for Axis stator current error value, for Axis stator current error value, is the sliding surface, and the final sliding mode observer equation is written as:

[0032]

[0033] Step 202: Subtract the mathematical model of the induction motor from the mathematical model of the sliding mode observer, and construct a sliding mode gain matrix using the Lyapunov stability theorem.

[0034] , the mathematical model of the motor is subtracted from the mathematical model of the sliding mode observer to obtain the following error state equation:

[0035]

[0036] The Lyapunov function is constructed using the stator current error as follows:

[0037]

[0038] in, The stator current error is The axis weight, The rotor flux error is The axis's weight;

[0039] Derivative of the Lyapunov function above:

[0040]

[0041] According to the state equation of the induction motor in the two-phase stationary coordinate system in step 1, the expression of the rotor flux is as follows:

[0042]

[0043] When the system enters steady state, The sliding mode gain matrix is ​​zero, and the observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as:

[0044]

[0045] Then the rotor flux observation error can be obtained by subtracting the rotor flux observation value from the rotor flux expression:

[0046]

[0047] Substitute the above rotor flux observation error equation into the derived Lyapunov function:

[0048]

[0049] According to the Lyapunov stability theorem, when When the system is stable, in order to simplify the calculation process and feedback matrix form, let , and guarantee , then:

[0050]

[0051] when When it is large enough, the system is stable. From the above formula, we know that the range of sliding mode gain is:

[0052]

[0053] The sliding mode gain is selected as follows:

[0054]

[0055] The Lyapunov function is then defined using the rotor flux observation error term:

[0056]

[0057] Derivative of the above formula:

[0058]

[0059] According to the Lyapunov stability theorem, the range of sliding mode feedback gain to ensure system stability is expressed as:

[0060]

[0061] The sliding mode gain is selected as follows:

[0062]

[0063] The final sliding mode gain is as follows

[0064]

[0065] From the formula Constantly true, the introduction of adjustment coefficient :

[0066]

[0067] The new gain matrix elements are:

[0068]

[0069] Step 203, according to Lyapunov stability theorem, design Lyapunov function, derive the speed adaptive rate specific equation, thus realizing the accurate estimation of speed:

[0070] The Lyapunov function is defined as follows:

[0071]

[0072] In the formula, is a normal number, so as to ensure ;

[0073] The condition of system asymptotic stability is that the Lyapunov function is positive definite and At this time

[0074] Stator current error Tends to 0, and the estimated speed tends to the actual speed ;

[0075] The derivative of the defined Lyapunov function is:

[0076]

[0077] The state equation after difference in step 202 is substituted into the above formula, and the estimated speed is finally derived as follows:

[0078]

[0079] Step 3 is implemented according to the following steps:

[0080] PI regulator is adopted to realize the adjustment conveniently and quickly, and the final stator resistance adaptive rate is obtained:

[0081] .

[0082] Step 4 is implemented according to the following steps:

[0083] Step 401: Obtain the stator flux according to the rotor and stator flux conversion formula, and then calculate the stator flux according to the two-phase stationary state of the induction motor. The mathematical model in the coordinate system is used to obtain the stator flux state equation and the stator flux estimation value is calculated:

[0084] The stator flux is calculated from the stator current and the rotor flux:

[0085]

[0086] According to the two-phase stationary induction motor The mathematical model in the coordinate system is based on the stator flux The state variable is expressed as:

[0087]

[0088] Step 402: The stator flux state equation obtained in step 401 is obtained by using the forward Euler discretization formula. The predicted value of stator flux and stator current at the moment;

[0089] The forward Euler discretization formula is:

[0090]

[0091] get The predicted value of stator flux at time

[0092]

[0093] In the formula is the system sampling period, for The stator flux component predicted at each moment, Hewei The stator current vector component at time , for The stator voltage vector component at time , is the stator resistance;

[0094] The stator current differential equation is obtained after forward Euler discretization The predicted value of stator current is expressed as:

[0095]

[0096] Where:

[0097] Step 403: The predicted value of stator flux at time The stator current prediction value at time t is obtained The predicted value of electromagnetic torque at time , The predicted value of electromagnetic torque at the moment is:

[0098]

[0099] in, is the number of motor pole pairs, is the imaginary part of the complex number, for k Predicted value of stator current at time +1;

[0100] Step 404: Based on the motion equation of the induction motor, the forward Euler discretization formula is used to obtain Predicted speed at the moment:

[0101] The equation of motion is as follows:

[0102]

[0103] get The predicted speed at this moment is as follows:

[0104] .

[0105] Step 5 is implemented as follows:

[0106] Step 501: The sliding mode observer in step 2 The term is used as the last term of the stator flux prediction value to constrain and modify the prediction model, and at the same time the stator resistance estimation value in step 3 is Bringing it back into the stator flux equation and updating the stator flux prediction value in real time not only improves the accuracy of the prediction, but also updates the prediction model in real time and reduces the prediction error;

[0107] The predicted stator flux after correction and with updated stator resistance is as follows

[0108]

[0109] Step 502: Based on the corrected stator flux prediction value and stator current prediction value , according to the motor electromagnetic torque and motor motion equation, the corrected The electromagnetic torque prediction value at the moment and the corrected The predicted speed values ​​at each moment are:

[0110]

[0111] .

[0112] Step 6 is implemented as follows:

[0113] The cost function is constructed based on the corrected stator flux prediction value and the corrected speed prediction value obtained in step 5. The cost function of the model prediction direct speed control is composed of two different physical dimensions: stator flux and rotor speed, so a weight coefficient needs to be added. To balance these two dimensions, the specific cost function is constructed as follows:

[0114]

[0115] in, is a given stator flux amplitude, for k The absolute value of the stator flux prediction value at time +1. is the weight coefficient of the magnetic linkage term, is the weight coefficient of the speed term;

[0116] The weight coefficient of the magnetic linkage term is , expressed by the following formula:

[0117]

[0118] is the reference speed term;

[0119] For a two-level voltage source inverter, first predict the speed under the action of the basic voltage vector , stator flux , ; Then calculate the corresponding cost function based on the predicted value; Finally, select the voltage vector that minimizes the cost function as the optimal output of the converter.

[0120] The beneficial effects of the present invention are that the induction motor sensorless model predictive direct speed control method designs a new sliding mode gain matrix and introduces a sliding mode function to k +1 moment stator flux prediction value is corrected to improve the control performance of model predictive control, thereby improving the operating performance of the motor. Model predictive speed control is introduced. Traditional model predictive torque control, model predictive flux control, and model predictive current control all use a double closed-loop structure of speed outer loop control plus model predictive inner loop control. The speed loop parameters need to be adjusted, which increases the complexity of the system. Model Predictive Direct Speed ​​Control (MPDSC) is adopted to eliminate the speed loop and adopt a single-loop control structure to improve the dynamic response speed of the system. k The stator resistance identification value is introduced into the stator flux prediction value at time +1 and updated in real time kThe present invention improves the robustness of sensorless model-based direct speed control of induction motors, can update important motor-related parameters in real time, and effectively improves prediction accuracy and motor control capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] Figure 1 This is a flow chart of the sensorless model predictive direct speed control method for an induction motor according to the present invention;

[0122] Figure 2 This is a block diagram of the principle of a sliding mode observer in the sensorless model predictive direct speed control method for an induction motor according to the present invention;

[0123] Figure 3 The basic voltage vector block diagram of the two-level inverter in the sensorless model predictive direct speed control method of the induction motor of the present invention is shown in FIG.

[0124] Figure 4 This is a block diagram of a two-level voltage source inverter in the sensorless model predictive direct speed control method for an induction motor according to the present invention. DETAILED DESCRIPTION

[0125] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0126] The sensorless model prediction direct speed control method of the induction motor of the present invention is as follows: Figure 1 As shown, please follow the steps below:

[0127] Step 1: Using the stator current and rotor flux as state variables, establish a mathematical model of the induction motor in a two-phase stationary coordinate system;

[0128] Step 1 is implemented as follows:

[0129] The mathematical model of an induction motor is:

[0130]

[0131]

[0132] in, is the stator resistance, is the magnetic flux leakage coefficient, is the stator inductance, is the rotor time constant, , For mutual induction, is the rotor inductance, is the rotor speed, , is the stator current, is the rotor flux vector, , for Shaft stator voltage component, for Shaft stator voltage component;

[0133] For the convenience of calculation, let:

[0134]

[0135]

[0136]

[0137] ; ; ; ; ; .

[0138] Step 2: Based on the mathematical model of the induction motor in the two-phase stationary coordinate system obtained in Step 1, a sliding mode observer is constructed with the stator current and the rotor flux as state variables, and a sliding mode gain matrix is ​​designed. The estimated values ​​of the speed and the flux are obtained through the sliding mode observer.

[0139] Combine Figure 2 , step 2 is implemented according to the following steps:

[0140] Step 201: According to the two-phase stationary state of the induction motor The mathematical model in the coordinate system, as well as the state equation of the sliding mode observer constructed by the mathematical model and sliding mode variable structure control theory are as follows:

[0141]

[0142] Where, is the sliding mode gain matrix,

[0143]

[0144] Select the stator current error as the sliding surface:

[0145]

[0146] for Axis stator current error value, for Axis stator current error value, is the sliding surface, and the final sliding mode observer equation is written as:

[0147]

[0148] Step 202: Subtract the mathematical model of the induction motor from the mathematical model of the sliding mode observer, and construct a sliding mode gain matrix using the Lyapunov stability theorem.

[0149] Considering the stability and accuracy of the system and the fact that the speed is a constant within a sampling period, it is assumed that the error between the identified speed and the true speed can be ignored, that is, , the mathematical model of the motor is subtracted from the mathematical model of the sliding mode observer to obtain the following error state equation:

[0150]

[0151] The Lyapunov function is constructed using the stator current error as follows:

[0152]

[0153] in, The stator current error is The axis weight, The rotor flux error is The weight of the axis;

[0154] Derivative of the Lyapunov function above:

[0155]

[0156] According to the state equation of the induction motor in the two-phase stationary coordinate system in step 1, the expression of the rotor flux is as follows:

[0157]

[0158] When the system enters steady state, The sliding mode gain matrix is ​​zero, and the observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as:

[0159]

[0160] Then the rotor flux observation error can be obtained by subtracting the rotor flux observation value from the rotor flux expression:

[0161]

[0162] Substitute the above rotor flux observation error equation into the derived Lyapunov function:

[0163]

[0164] According to the Lyapunov stability theorem, when When the system is stable, in order to simplify the calculation process and feedback matrix form, let , and guarantee , then:

[0165]

[0166] when When it is large enough, the system is stable. From the above formula, we know that the range of sliding mode gain is:

[0167]

[0168] The sliding mode gain is selected as follows:

[0169]

[0170] The Lyapunov function is then defined using the rotor flux observation error term:

[0171]

[0172] Derivative of the above formula:

[0173]

[0174] According to the Lyapunov stability theorem, the range of sliding mode feedback gain to ensure system stability is expressed as:

[0175]

[0176] The sliding mode gain is selected as follows:

[0177]

[0178] The final sliding mode gain is as follows

[0179]

[0180] From the formula we can see Constantly established, introducing adjustment coefficient :

[0181]

[0182] The elements of the new gain matrix are:

[0183]

[0184] Step 203: Based on the Lyapunov stability theorem, a Lyapunov function is designed to derive a specific equation for the speed adaptation rate, thereby achieving accurate estimation of the speed:

[0185] The Lyapunov function is defined as follows:

[0186]

[0187] Where, is a positive number, thus ensuring ;

[0188] The conditions for the system to be asymptotically stable are that the Lyapunov function is positive definite and ,at this time

[0189] Stator current error It tends to 0, and the estimated speed tends to the actual speed ;

[0190] Taking the derivative of the defined Lyapunov function, we get:

[0191]

[0192] Substituting the state equation after the difference in step 202 into the above equation, the estimated speed is derived as follows:

[0193]

[0194] Step 3: Based on the sliding mode observer, the adaptive rate of the stator resistance is derived, and the parameter identification of the stator resistance is introduced into the motor speed estimation and model prediction module to improve the robustness of the system;

[0195] Combine Figure 3 、 Figure 4 , step 3 is implemented as follows:

[0196] Based on the differential equation in step 203, the stator resistance adaptation rate is obtained by defining the Lyapunov function and the Lyapunov stability law. In order to improve the estimation speed of the stator resistance, a PI regulator is usually used to facilitate and quickly implement the adjustment. The final stator resistance adaptation rate is:

[0197] .

[0198] Step 4: Establish a prediction model based on the mathematical model of the induction motor obtained in step 1, and use the estimated speed value and flux linkage value of the induction motor obtained in step 2 as the input of the prediction model. k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[0199] Step 4 is implemented as follows:

[0200] Step 401: Obtain the stator flux according to the rotor and stator flux conversion formula, and then calculate the stator flux according to the two-phase stationary state of the induction motor. The mathematical model in the coordinate system is used to obtain the stator flux state equation and the stator flux estimation value is calculated:

[0201] The stator flux is calculated from the stator current and the rotor flux:

[0202]

[0203] According to the two-phase stationary induction motor The mathematical model in the coordinate system is based on the stator flux The state variable is expressed as:

[0204]

[0205] Step 402: The stator flux state equation obtained in step 401 is obtained by using the forward Euler discretization formula. The predicted value of stator flux and stator current at the moment;

[0206] The forward Euler discretization formula is:

[0207]

[0208] get The predicted value of stator flux at time

[0209]

[0210] In the formula is the system sampling period, for The stator flux component predicted at each moment, Hewei The stator current vector component at time , for The stator voltage vector component at time , is the stator resistance;

[0211] Selecting State Variables in the Mathematical Model of an Induction Motor and , and assuming that the motor speed is constant in a very short time, the stator current differential equation is obtained after forward Euler discretization The predicted value of stator current is expressed as:

[0212]

[0213] In the formula:

[0214] Step 403, according to the stator flux prediction value at the moment and the stator current prediction value at the moment, obtain the electromagnetic torque prediction value at the moment, the electromagnetic torque prediction value at the moment is:

[0215]

[0216] Wherein, is the number of motor pole pairs, is the imaginary part of the complex number, is k the stator current prediction value at the moment;

[0217] Step 404, according to the motion equation of the induction motor, the forward Euler discrete formula is obtained the speed prediction value at the moment:

[0218] The motion equation is as follows:

[0219]

[0220] obtain the speed prediction value at the moment is as follows:

[0221] .

[0222] Step 5, according to the stator flux prediction value at the moment k obtained in step 4, introduce the same sliding mode function as in step 2 as the constraint term of the stator flux prediction value, modify the prediction model, and at the same time bring the stator resistance identification value back to the stator flux equation to update the stator flux prediction value in real time, improve the accuracy of the prediction model;

[0223] Step 5 is implemented according to the following steps:

[0224] Step 501, the sliding mode observer term in step 2 is taken as the last term of the stator flux prediction value, which is constrained, and the prediction model is modified, and at the same time, the stator resistance estimation value in step 3 is brought back to the stator flux equation and the stator flux prediction value is updated in real time, which not only improves the accuracy of the prediction, but also updates the prediction model in real time and reduces the prediction error;

[0225] The modified stator flux prediction value with the stator resistance update is as follows

[0226]

[0227] Step 502: Based on the corrected stator flux prediction value and stator current prediction value , according to the motor electromagnetic torque and motor motion equation, the corrected The electromagnetic torque prediction value at the moment and the corrected The predicted speed values ​​at each moment are:

[0228]

[0229] .

[0230] Step 6: Based on the principle of model predictive direct speed control (MPDSC), the cost function is constructed using the corrected stator flux prediction value obtained in step 5 and the rotor speed prediction value in step 4. A weight coefficient is added to balance the two physical dimensions, and the voltage vector output that minimizes the cost function is selected to ultimately achieve the optimal control performance of the induction motor.

[0231] Step 6 is implemented as follows:

[0232] The cost function is constructed based on the corrected stator flux prediction value and the corrected speed prediction value obtained in step 5. The cost function of the model prediction direct speed control is composed of two different physical dimensions: stator flux and rotor speed, so a weight coefficient needs to be added. To balance these two dimensions, the specific cost function is constructed as follows:

[0233]

[0234] in, is a given stator flux amplitude, for k The absolute value of the stator flux prediction value at time +1. is the weight coefficient of the magnetic linkage term, is the weight coefficient of the speed term;

[0235] The weight coefficient of the magnetic linkage term is , expressed by the following formula:

[0236]

[0237] is the reference speed term, and its influence is determined by the weight coefficient Decide. It is usually obtained through simulation and experimental debugging.

[0238] The cost function is a tool used to evaluate the similarity between the predicted and reference values, so the cost function directly determines the selected optimal vector and thus the control performance of the induction motor.

[0239] For a two-level voltage source inverter, first predict the speed under the action of the basic voltage vector , stator flux , ; Then calculate the corresponding cost function based on the predicted value; Finally, select the voltage vector that minimizes the cost function as the optimal output of the converter.

[0240] Example 1

[0241] The sensorless model prediction direct speed control method of the induction motor of the present invention is as follows: Figure 1 As shown, please follow the steps below:

[0242] Step 1: Using the stator current and rotor flux as state variables, establish a mathematical model of the induction motor in a two-phase stationary coordinate system;

[0243] Step 2: Using the stator current and rotor flux as state variables, construct a sliding mode observer and design a sliding mode gain matrix. The estimated values ​​of the speed and flux are obtained through the sliding mode observer.

[0244] Step 3: Based on the sliding mode observer, the adaptive rate of the stator resistance is derived, and the parameter identification of the stator resistance is introduced into the motor speed estimation and model prediction module to improve the robustness of the system;

[0245] Step 4: k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[0246] Step 5: Modify the prediction model and bring the stator resistance identification value back into the stator flux equation to update the stator flux prediction value in real time, thereby improving the accuracy of the prediction model.

[0247] Step 6: Construct the cost function to ultimately achieve the optimal control performance of the induction motor.

[0248] Example 2

[0249] The sensorless model prediction direct speed control method of the induction motor of the present invention is as follows: Figure 1 As shown, please follow the steps below:

[0250] Step 1: Using the stator current and rotor flux as state variables, establish a mathematical model of the induction motor in a two-phase stationary coordinate system;

[0251] Step 2: Based on the mathematical model of the induction motor in the two-phase stationary coordinate system obtained in Step 1, a sliding mode observer is constructed with the stator current and the rotor flux as state variables, and a sliding mode gain matrix is ​​designed. The estimated values ​​of the speed and the flux are obtained through the sliding mode observer.

[0252] Step 3: Based on the sliding mode observer, the adaptive rate of the stator resistance is derived, and the parameter identification of the stator resistance is introduced into the motor speed estimation and model prediction module to improve the robustness of the system;

[0253] Step 3 is implemented as follows:

[0254] The PI regulator is used to quickly and easily adjust the stator resistance, and the final adaptive rate of the stator resistance is:

[0255] .

[0256] Step 4: k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[0257] Step 5: Modify the prediction model and bring the stator resistance identification value back into the stator flux equation to update the stator flux prediction value in real time, thereby improving the accuracy of the prediction model.

[0258] Step 5 is implemented as follows:

[0259] Step 501: The sliding mode observer in step 2 The term is used as the last term of the stator flux prediction value to constrain and modify the prediction model, and at the same time the stator resistance estimation value in step 3 is Bringing it back into the stator flux equation and updating the stator flux prediction value in real time not only improves the accuracy of the prediction, but also updates the prediction model in real time and reduces the prediction error;

[0260] The predicted stator flux after correction and with updated stator resistance is as follows

[0261]

[0262] Step 502: Based on the corrected stator flux prediction value and stator current prediction value , according to the motor electromagnetic torque and motor motion equation, the corrected The electromagnetic torque prediction value at the moment and the corrected The predicted speed values ​​at each moment are:

[0263]

[0264] .

[0265] Step 6, the construction of the cost function is carried out, and finally the optimal control performance of the induction motor is realized.

[0266] Embodiment 3

[0267] The induction motor sensorless model predictive direct speed control method of the present application is shown in the flow chart as Figure 1 The following steps are implemented in detail:

[0268] Step 1, the stator current and the rotor flux linkage are taken as the state variables, and the mathematical model of the induction motor in the two-phase stationary coordinate system is established;

[0269] Step 1 is implemented in detail as follows:

[0270] The mathematical model of the induction motor is:

[0271]

[0272]

[0273] wherein, is the stator resistance, is the leakage coefficient, is the stator inductance, is the rotor time constant, , is the mutual inductance, is the rotor inductance, is the rotor speed, , is the stator current, is the rotor flux linkage vector, , is the axis stator voltage component, is the axis stator voltage component;

[0274] For the convenience of calculation, let:

[0275]

[0276]

[0277]

[0278] ;

[0279] ;

[0280] ;

[0281] ;

[0282] ;

[0283] .

[0284] Step 2: Based on the mathematical model of the induction motor in the two-phase stationary coordinate system obtained in Step 1, a sliding mode observer is constructed with the stator current and the rotor flux as state variables, and a sliding mode gain matrix is ​​designed. The estimated values ​​of the speed and the flux are obtained through the sliding mode observer.

[0285] Step 2 is implemented as follows:

[0286] Step 201: According to the two-phase stationary state of the induction motor The mathematical model in the coordinate system, as well as the state equation of the sliding mode observer constructed by the mathematical model and sliding mode variable structure control theory are as follows:

[0287]

[0288] Where, is the sliding mode gain matrix,

[0289]

[0290] Select the stator current error as the sliding surface:

[0291]

[0292] for Axis stator current error value, for Axis stator current error value, is the sliding surface, and the final sliding mode observer equation is written as:

[0293]

[0294] Step 202: Subtract the mathematical model of the induction motor from the mathematical model of the sliding mode observer, and construct a sliding mode gain matrix using the Lyapunov stability theorem.

[0295] , the mathematical model of the motor is subtracted from the mathematical model of the sliding mode observer to obtain the following error state equation:

[0296]

[0297] The Lyapunov function is constructed using the stator current error as follows:

[0298]

[0299] in, The stator current error is The axis weight, The rotor flux error is The weight of the axis;

[0300] Derivative of the Lyapunov function above:

[0301]

[0302] According to the state equation of the induction motor in the two-phase stationary coordinate system in step 1, the expression of the rotor flux is as follows:

[0303]

[0304] When the system enters steady state, The sliding mode gain matrix is ​​zero, and the observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as:

[0305]

[0306] Then the rotor flux observation error can be obtained by subtracting the rotor flux observation value from the rotor flux expression:

[0307]

[0308] Substitute the above rotor flux observation error equation into the derived Lyapunov function:

[0309]

[0310] According to the Lyapunov stability theorem, when When the system is stable, in order to simplify the calculation process and feedback matrix form, let , and guarantee , then:

[0311]

[0312] when When it is large enough, the system is stable. From the above formula, we know that the range of sliding mode gain is:

[0313]

[0314] The sliding mode gain is selected as follows:

[0315]

[0316] The Lyapunov function is then defined using the rotor flux observation error term:

[0317]

[0318] Derivative of the above formula:

[0319]

[0320] According to the Lyapunov stability theorem, the range of sliding mode feedback gain to ensure system stability is expressed as:

[0321]

[0322] The sliding mode gain is selected as follows:

[0323]

[0324] The final sliding mode gain is as follows

[0325]

[0326] From the formula we can see Constantly established, introducing adjustment coefficient :

[0327]

[0328] The elements of the new gain matrix are:

[0329]

[0330] Step 203: Based on the Lyapunov stability theorem, a Lyapunov function is designed to derive a specific equation for the speed adaptation rate, thereby achieving accurate estimation of the speed:

[0331] The Lyapunov function is defined as follows:

[0332]

[0333] Where, is a positive number, thus ensuring ;

[0334] The conditions for the system to be asymptotically stable are that the Lyapunov function is positive definite and ,at this time

[0335] Stator current error is a tendency to 0, and the estimated speed tends to the actual speed ;

[0336] Taking the derivative of the defined Lyapunov function, we have:

[0337]

[0338] Substitute the state equation after the difference in step 202 into the above formula, and finally derive the estimated speed as follows:

[0339]

[0340] Step 3, based on the sliding mode observer to derive the adaptive rate of stator resistance, and the parameter identification of stator resistance is introduced into the motor speed estimation and model prediction module, to improve the robustness of the system;

[0341] Step 3 is implemented according to the following steps:

[0342] PI regulator is adopted to realize the adjustment conveniently and quickly, and the final adaptive rate of stator resistance is obtained as:

[0343] .

[0344] Step 4, the stator flux and speed at time t+1 are predicted to obtain the predicted value of stator flux and speed; k

[0345] Step 5, the prediction model is corrected, and the identified value of stator resistance is brought back to the stator flux equation to update the predicted value of stator flux in real time, which improves the accuracy of the prediction model;

[0346] Step 6, the cost function is constructed to finally realize the optimal control performance of the induction motor.​

Claims

1. A sensorless model predictive direct speed control method for an induction motor, characterized in that: Please follow the steps below to implement: Step 1: Using the stator current and rotor flux as state variables, establish a mathematical model of the induction motor in a two-phase stationary coordinate system; The step 1 is specifically implemented according to the following steps: The mathematical model of an induction motor is: in, ; ; ; is the stator resistance, is the magnetic flux leakage coefficient, is the stator inductance, is the rotor time constant, , For mutual induction, is the rotor inductance, is the rotor speed, , is the stator current, is the rotor flux vector, , for Shaft stator voltage component, for Shaft stator voltage component; make: ； ； ； ； ； ； ； ； Step 2: Construct a sliding mode observer to obtain the estimated values ​​of the speed and flux; The estimated speeds are as follows: ； Step 3: Derivation of the adaptive rate of the stator resistance based on the sliding mode observer; The step 3 is specifically implemented according to the following steps: The PI regulator is used to quickly and easily adjust the stator resistance, and the final adaptive rate of the stator resistance is: ； Step 4: Obtain the stator flux prediction value and the speed prediction value; The step 4 is specifically implemented according to the following steps: Step 401: Obtain the stator flux according to the rotor and stator flux conversion formula, and then calculate the stator flux according to the two-phase stationary state of the induction motor. The mathematical model in the coordinate system is used to obtain the stator flux state equation and the stator flux estimation value is calculated: The stator flux is calculated from the stator current and the rotor flux: According to the two-phase stationary induction motor The mathematical model in the coordinate system is based on the stator flux The state variable is expressed as: Step 402: The stator flux state equation obtained in step 401 is obtained by using the forward Euler discretization formula. The predicted value of stator flux and stator current at the moment; The forward Euler discretization formula is: get The predicted value of stator flux at time In the formula is the system sampling period, for The stator flux component predicted at each moment, Hewei The stator current vector component at time , for The stator voltage vector component at time , is the stator resistance; The stator current differential equation is obtained after forward Euler discretization The predicted value of stator current is expressed as: Where: Step 403: The predicted value of stator flux at time The stator current prediction value at time t is obtained The predicted value of electromagnetic torque at time , The predicted value of electromagnetic torque at the moment is: in, is the number of motor pole pairs, is the imaginary part of the complex number, for k Predicted value of stator current at time +1; Step 404: Based on the motion equation of the induction motor, the forward Euler discretization formula is used to obtain Predicted speed at the moment: The equation of motion is as follows: get The predicted speed at this moment is as follows: ； Step 5: Modify the prediction model and bring the stator resistance identification value back into the stator flux equation to update the stator flux prediction value in real time; The step 5 is specifically implemented according to the following steps: Step 501: The sliding mode observer in step 2 The term is the last term of the stator flux prediction value, K is the sliding mode gain matrix, constrains, modifies the prediction model, and at the same time converts the stator resistance estimate in step 3 into Bringing it back into the stator flux equation and updating the stator flux prediction value in real time not only improves the accuracy of the prediction, but also updates the prediction model in real time and reduces the prediction error; The corrected stator flux prediction with updated stator resistance is as follows: Step 502: Based on the corrected stator flux prediction value and stator current prediction value , according to the motor electromagnetic torque and motor motion equation, the corrected The electromagnetic torque prediction value at the moment and the corrected The predicted speed values ​​at each moment are: ； Step 6: construct the cost function to ultimately achieve the optimal control performance of the induction motor; The step 6 is specifically implemented according to the following steps: The cost function is constructed based on the corrected stator flux prediction value and the corrected speed prediction value obtained in step 5. The cost function of the model prediction direct speed control is composed of two different physical dimensions: stator flux and rotor speed, so a weight coefficient needs to be added. To balance these two dimensions, the specific cost function is constructed as follows: in, is a given stator flux amplitude, for k The absolute value of the stator flux prediction value at time +1, is the weight coefficient of the magnetic linkage term, is the weight coefficient of the speed term; The weight coefficient of the magnetic linkage term is , expressed by the following formula: is the reference speed term; For a two-level voltage source inverter, first predict the speed under the action of the basic voltage vector , stator flux , ; Then calculate the corresponding cost function based on the predicted value; Finally, select the voltage vector that minimizes the cost function as the optimal output of the converter.

2. The sensorless model predictive direct speed control method for an induction motor according to claim 1, characterized in that: The step 2 is specifically implemented according to the following steps: Step 201: According to the two-phase stationary state of the induction motor The mathematical model in the coordinate system, as well as the state equation of the sliding mode observer constructed by the mathematical model and sliding mode variable structure control theory are as follows: Where, is the sliding mode gain matrix, ； ； ； ； Select the stator current error as the sliding surface: for Axis stator current error value, for Axis stator current error value, is the sliding surface, and the final sliding mode observer equation is written as: Step 202: Subtract the mathematical model of the induction motor from the mathematical model of the sliding mode observer, and construct a sliding mode gain matrix using the Lyapunov stability theorem. , the mathematical model of the motor is subtracted from the mathematical model of the sliding mode observer to obtain the following error state equation: The Lyapunov function is constructed using the stator current error as follows: in, The stator current error is The axis weight, The rotor flux error is The axis's weight; Derivative of the Lyapunov function above: According to the state equation of the induction motor in the two-phase stationary coordinate system in step 1, the expression of the rotor flux is as follows: When the system enters steady state, The sliding mode gain matrix is ​​zero, and the observer model is consistent with the dynamic mathematical model of the induction motor. Therefore, the observed value of the rotor flux is expressed as: Then the rotor flux observation error can be obtained by subtracting the rotor flux observation value from the rotor flux expression: Substitute the above rotor flux observation error equation into the derived Lyapunov function: According to the Lyapunov stability theorem, when When the system is stable, in order to simplify the calculation process and feedback matrix form, let , and guarantee , then: when When it is large enough, the system is stable. From the above formula, we know that the range of sliding mode gain is: The sliding mode gain is selected as follows: The Lyapunov function is then defined using the rotor flux observation error term: Derivative of the above formula: According to the Lyapunov stability theorem, the range of sliding mode feedback gain to ensure system stability is expressed as: The sliding mode gain is selected as follows: The final sliding mode gain is as follows From the formula we can see Constantly established, introducing adjustment coefficient : The elements of the new gain matrix are: Step 203: Based on the Lyapunov stability theorem, a Lyapunov function is designed to derive a specific equation for the speed adaptation rate, thereby achieving accurate estimation of the speed: The Lyapunov function is defined as follows: Where, is a positive number, thus ensuring ; The conditions for the system to be asymptotically stable are that the Lyapunov function is positive definite and ,at this time Stator current error It tends to 0, and the estimated speed tends to the actual speed ; Derivative of the defined Lyapunov function yields: Substitute the state equation after the difference in step 202 into the above equation, simplify it, and finally derive the estimated speed.

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