Sensorless model predictive torque control method for induction motor

Abstract

The application discloses a sensorless model predictive torque control method of an induction motor, and first models a mathematical model of the induction motor based on a two-phase static coordinate system to obtain an induction motor mathematical model; a full-order observer is constructed to obtain an estimated value of a rotating speed and an estimated value of a magnetic flux through the full-order observer; then, an adaptive rate of a stator resistance is derived, and parameter identification of the stator resistance is introduced into a motor rotating speed estimation and a model prediction module; a prediction model is established, the estimated value of the rotating speed and the estimated value of the magnetic flux of the induction motor are taken as inputs of the prediction model to obtain a stator magnetic flux prediction value and an electromagnetic torque prediction value; finally, a reduced-order load torque observer is constructed to perform feedforward compensation on a speed outer loop of a control system. The application is used to solve the technical problem in the sensorless model predictive torque control of the induction motor, and improves the rotating speed dynamic response, load response and tracking performance of the induction motor.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-performance induction motor control, and particularly relates to an induction motor sensorless model predictive torque control method. BACKGROUND

[0002] An induction motor is a simple structure of motor type. Due to its low cost, easy maintenance, high reliability and other advantages, the induction motor is widely used in industrial and commercial fields to provide stable power source. With the progress of science and technology, the demand for motor performance is continuously improved, and high-performance AC speed regulation control technology is gradually developed, which provides more possibilities for the application field of induction motors.

[0003] In recent years, model predictive control as an advanced control strategy has received widespread attention in the field of motor control. By applying model predictive control to induction motors, higher levels of dynamic performance, accuracy and stability can be achieved to meet the increasing industrial demand.

[0004] In the AC motor speed regulation system, sensors are needed to derive the motor speed for negative feedback regulation of the system, but sensors can cause a series of problems, such as sensor failure that can cause system performance to decline or even system crash, and sensor installation requires a certain cost, and some special scenarios may not be suitable for installing sensors. Therefore, sensorless control technology has become a research hotspot. SUMMARY

[0005] The purpose of the present application is to provide an induction motor sensorless model predictive torque control method to solve the technical problems in induction motor sensorless model predictive torque control and improve the speed dynamic response, load response and tracking performance of the induction motor.

[0006] The technical solution adopted by the present application is an induction motor sensorless model predictive torque control method, which is implemented according to the following steps:

[0007] Step 1, model the mathematical model of the induction motor based on the two-phase stationary coordinate system to obtain the mathematical model of the induction motor;

[0008] Step 2, construct a full-order observer to obtain the estimated value of the speed and the estimated value of the flux linkage through the full-order observer;

[0009] Step 3, derive the adaptive rate of the stator resistance and introduce the parameter identification of the stator resistance into the motor speed estimation and model prediction modules;

[0010] Step 4, establish a prediction model, the estimated value of the induction motor speed and the estimated value of the flux linkage are used as the input of the prediction model to obtain the predicted value of the stator flux linkage and the predicted value of the electromagnetic torque;

[0011] Step 5: Construct a reduced-order load torque observer to compensate the reference torque signal given value output by the PI controller, perform feedforward compensation on the control system speed outer loop, and improve the dynamic response of the system.

[0012] The present invention is also characterized in that:

[0013] Step 1 is implemented as follows:

[0014] In the two-phase stationary coordinate system, the mathematical model of the induction motor is:

[0015]

[0016] Among them, R s is the stator resistance, σ is the magnetic leakage coefficient, L s is the stator inductance, T r is the rotor time constant, L m is the mutual inductance, L r is the rotor inductance, ω r is the electric rotor speed, i s is the stator current, ψ r is the rotor flux vector, u sα is the stator voltage component under the α axis, u sβ is the stator voltage component under the β axis.

[0017] Step 2 is implemented as follows:

[0018] Step 2.1, design a state observer as an adjustable model based on the mathematical model of the induction motor;

[0019] Step 2.2: Confirm that the controlled object is observable and reconstruct the state equation of the observer based on the input and output of the controlled object;

[0020] Step 2.3, based on the idea of ​​model reference adaptation, the induction motor itself is used as the reference model, and the constructed full-order observer is used as the adjustable model. Since there is always a certain difference in the initial state of the two, there will be state errors, which will also lead to output errors. The idea of ​​feedback design is introduced to use the output error As negative feedback compensation to the differential equation of the state vector, the output error approaches zero quickly, causing the input error to also approach zero;

[0021] Step 2.4: Based on the mathematical model of the induction motor and the design principle of the full-order adaptive observer, we can obtain:

[0022]

[0023] Where:

[0024] G is a feedback gain matrix

[0025] Step 2.5, the feedback gain matrix is designed according to the requirements of pole configuration. It is assumed that the poles of the full-order adaptive observer are k times of the poles of the induction motor, and the feedback matrix is obtained by combining the characteristic equations of the two. However, this configuration method is relatively complex. According to the feedback matrix obtained, the pole plot is drawn, and it is found that the poles of the observer are distributed on the left side of the poles of the motor, and the poles gradually move away from the real axis and the imaginary axis with the increase of the speed, which will lead to the instability of the system. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used,

[0026] The sufficient and necessary condition for ensuring the stability of the full-order observer is obtained:

[0027]

[0028] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4=0, a feedback matrix selection range that can ensure the stability of the full-order observer is obtained:

[0029]

[0030] From the formula, it can be seen that g1≥0 and g3≥0 are always true. The adjustment coefficients a and b are introduced, so that

[0031] a≥0,b≥0

[0032] The new feedback matrix is obtained as follows:

[0033]

[0034] Step 2.6, according to the Lyapunov stability theorem, the specific equation of the speed adaptive law can be derived, and the accurate estimation of the speed can be realized. The speed adaptive law can be simplified as:

[0035]

[0036] Step 3 is implemented according to the following steps:

[0037] Step 3.1, if the stator resistance is taken as a time-varying parameter, the state error equation is obtained by subtracting the state equation of the full-order adaptive observer from the state equation of the induction motor, as shown below:

[0038]

[0039]

[0040] Step 3.2, the stator resistance adaptive rate is obtained from the Lyapunov stability law by defining the Lyapunov function, in order to improve the estimation speed of the stator resistance, a PI regulator is usually used to facilitate and fast realization of adjustment, and the final stator resistance adaptive rate is:

[0041]

[0042] Step 4 is implemented according to the following steps:

[0043] Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux linkage and speed are estimated by the full-order observer;

[0044] Step 4.2, the stator flux linkage prediction value and the stator current prediction value at k+1 time are obtained based on the forward Euler discretization formula:

[0045]

[0046] In the formula, T s is the system sampling period, ψ s (k+1) is the predicted stator flux linkage component at k+1 time, i s (k) and are the stator current vector components at k time, u s (k) is the stator voltage vector component at k time;

[0047] Step 4.3, in the induction motor model predictive control system, the stator flux linkage usually needs to be estimated to realize predictive control, and the conversion relationship between the stator flux linkage and the rotor flux linkage is:

[0048]

[0049] Step 4.4, in the induction motor mathematical model, the state variables i s and ψ s are selected, and it is considered that the motor speed is constant in a very short time, then the k+1 stator current prediction value is obtained after the forward Euler discretization of the stator current differential equation, and can be expressed as:

[0050]

[0051] In the formula:

[0052] Step 4.4, according to the stator flux linkage prediction value at k+1 time and the stator current prediction value at k+1 time, the electromagnetic torque prediction value at k+1 time is obtained, and the electromagnetic torque prediction value at k+1 time is:

[0053]

[0054] Wherein, p is the number of motor pole pairs, is the imaginary part of the complex number, is the predicted value of stator flux at time k+1, is the predicted value of the stator current at time k+1.

[0055] Step 4.5: The cost function of the constructed induction motor sensorless model predictive torque control is

[0056]

[0057] in, represents the reference torque, is the given stator flux amplitude, λ1 is related to the electromagnetic torque, λ2 is the weight coefficient of the flux term, is the predicted value of electromagnetic torque at time k+1, is the absolute value of the stator flux prediction value at time k+1

[0058] λ1 is related to the electromagnetic torque and is defined as:

[0059]

[0060] The weight coefficient of the magnetic flux term is λ2, which is expressed as follows:

[0061]

[0062] Step 5 is implemented as follows:

[0063] Step 5.1, control period T s Small, it is usually considered that the load torque does not change within a control cycle, T L The derivative of is 0, and the equation of motion of the induction motor is:

[0064]

[0065] Step 5.2: When the dimension of the state vector estimated by the state observer is smaller than the dimension of the state vector of the controlled object, it is called a reduced-order state observer. The reduced-order state observer is constructed based on the motion equation of the induction motor as follows:

[0066]

[0067] ω r Motor mechanical angular velocity, J Motor inertia, T e Electromagnetic torque, k1, k2 are matrix gain coefficients, To estimate the motor mechanical angular velocity, To estimate the load torque, n p is the number of motor pole pairs

[0068] Step 5.3, according to the designed reduced order state observer, the characteristic equation of the observer is obtained, the appropriate poles a1, a2 are selected, and the values of k1, k2 are solved by the characteristic equation of the observer, the feedback gain matrix is constructed, and the estimated value of the load torque is obtained;

[0069]

[0070] Step 5.4, the load torque is superimposed on the torque output by the torque regulator to the model predictive torque control algorithm.

[0071] The induction motor sensorless model predictive torque control method of the application introduces a full-order observer to estimate the speed and flux of the motor. The performance of the observer and the model predictive control is improved by predicting the flux and torque through the prediction model and introducing a stator resistance parameter identification module to update the stator resistance in real time. The dynamic response, load response and tracking performance of the motor are improved by introducing a load torque observer to compensate for the electromagnetic torque. The load torque observer is constructed according to the motion equation of the induction motor and the principle of the reduced order observer, and the rate of change of the load torque is considered to be zero in a sampling period. The load torque observer and the torque output by the torque regulator are superimposed on the model predictive torque control algorithm. This can improve the dynamic response of the system. The cost function is a tool to evaluate the error between the given value and the predicted value in the model predictive torque control, and is closely related to the best switching state selected by the control system. In addition, the selection of the cost function is an important factor in judging the effect of the model predictive torque control. If the cost function is not selected properly, it will directly affect the selection of the best switching state, causing the control system to select inappropriate switching states as the best switching state, thereby affecting the control performance of the induction motor. Setting the torque prediction value, the speed prediction value and the flux prediction value as the cost function can control the torque, speed and flux of the motor at the same time, and improve the dynamic and steady-state performance of the motor. In summary, the application introduces a full-order observer to estimate the speed and flux of the motor. The performance of the observer and the model predictive control is improved by predicting the speed, flux and torque through the prediction model, introducing a stator resistance parameter identification module to update the stator resistance in real time, and introducing a load torque observer to compensate for the electromagnetic torque, thereby improving the dynamic response, load response and tracking performance of the motor. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 The control block diagram of the application is shown in Figure 1.

[0073] Figure 2 The principle block diagram of the full-order adaptive observer in the application is shown in Figure 2.

[0074] Figure 3 The basic voltage vector block diagram of the two-level inverter in the application is shown in Figure 3.

[0075] Figure 4 Two-level voltage source inverter block diagram in the application. DETAILED DESCRIPTION

[0076] The application will be described in detail below with reference to the drawings and specific embodiments.

[0077] The sensorless model predictive torque control method of the induction motor in the application combines Figure 1 , and is implemented according to the following steps:

[0078] Step 1, model the mathematical model of the induction motor based on the two-phase stationary coordinate system to obtain the mathematical model of the induction motor;

[0079] Step 1 is implemented according to the following steps:

[0080] The mathematical model of the induction motor in the two-phase stationary coordinate system is:

[0081]

[0082] where R is the stator resistance, σ is the leakage coefficient, L is the stator inductance, T is the rotor time constant, s L is the mutual inductance, L is the rotor inductance, ω is the electrical rotor speed, s i is the stator current, ψ is the rotor flux vector, r u is the stator voltage component in the α-axis, and u is the stator voltage component in the β-axis. m r r s r sα sβ

[0083] Step 2, according to the mathematical model of the induction motor obtained in step 1, taking the stator current and the rotor flux as state variables, constructing a full-order observer, and obtaining the estimated value of the speed and the estimated value of the flux through the full-order observer;

[0084] In combination with Figures 2-4 , step 2 is implemented according to the following steps:

[0085] Step 2.1, referring to the mathematical model of the induction motor, designing a state observer as an adjustable model;

[0086] Step 2.2, confirming that the controlled object is observable, and reconstructing the state equation of the observer according to the input and output quantities of the controlled object;

[0087] ​​​​​​​​​​Step 2.3. According to the idea of model reference adaptive, the induction motor itself is taken as the reference model and the constructed full-order observer is taken as the adjustable model. Since there is always a certain difference between the initial states of the two, there will be a state error, which will also cause an output error. The idea of feedback design is introduced to use the output error as the negative feedback compensation to the differential equation of the state vector, so that the output error quickly approaches zero, resulting in the input error also approaching zero.

[0088] Step 2.4. According to the mathematical model of the induction motor and the design principle of the full-order adaptive observer, we have:

[0089]

[0090] In the formula:

[0091] G is the feedback gain matrix

[0092] Step 2.5. The feedback gain matrix is designed according to the requirements of pole placement. Assuming that the poles of the full-order adaptive observer are k times of the poles of the induction motor, the feedback matrix is obtained by combining the characteristic equations of the two. However, this configuration method is complex. According to the obtained feedback matrix, the pole plot is drawn, and it is found that the poles of the observer are distributed on the left side of the motor poles, and the poles gradually move away from the real axis and the imaginary axis as the speed increases, which will lead to system instability. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used,

[0093] to obtain the sufficient and necessary conditions for ensuring the stability of the full-order observer:

[0094]

[0095] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4=0, a feedback matrix selection range that can ensure the stability of the full-order observer is obtained:

[0096]

[0097] From the formula, it can be seen that g1≥0 and g3≥0 are always true. The adjustment coefficients a and b are introduced to make

[0098] a≥0, b≥0

[0099] The new feedback matrix is obtained as:

[0100]

[0101] Step 2.6. According to the Lyapunov stability theorem, the specific equation of the speed adaptive law can be derived, which realizes the accurate estimation of the speed. The speed adaptive law can be simplified as:

[0102]

[0103] Step 3, the adaptive rate of the stator resistance is derived based on the full-order observer, and the parameter identification of the stator resistance is introduced into the motor speed estimation and model prediction module, so as to improve the robustness of the system;

[0104] Step 3 is implemented according to the following steps:

[0105] Step 3.1, if the stator resistance is taken as a time-varying parameter, the state error equation is obtained by subtracting the state equation of the induction motor from the state equation of the full-order adaptive observer, as shown below:

[0106]

[0107]

[0108] Step 3.2, the stator resistance adaptive rate is derived from the Lyapunov stability law by defining the Lyapunov function, and in order to improve the estimation speed of the stator resistance, a PI regulator is usually used to facilitate and quickly realize the adjustment, and the final stator resistance adaptive rate is obtained as:

[0109]

[0110] Step 4, a prediction model is established according to the mathematical model of the induction motor obtained in step 1, the estimated value of the induction motor speed and the estimated value of the flux obtained in step 2 are taken as the input of the prediction model, the stator flux and the electromagnetic torque at k+1 time are predicted, and the predicted value of the stator flux and the predicted value of the electromagnetic torque are obtained;

[0111] Step 4 is implemented according to the following steps:

[0112] Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux and the speed are estimated by the full-order observer;

[0113] Step 4.2, the predicted value of the stator flux and the predicted value of the stator current at k+1 time are obtained based on the forward Euler discretization formula:

[0114]

[0115] In the formula, T s is the sampling period of the system, ψ s (k+1) is the predicted stator flux component at k+1 time, i s (k) and are the stator current vector components at k time, u s (k) is the stator voltage vector component at k time;

[0116] Step 4.3, in the induction motor model predictive control system, the stator flux usually needs to be estimated to realize the predictive control, the conversion relationship between the stator flux and the rotor flux is:

[0117]

[0118] Step 4.4, in the induction motor mathematical model, the state variable i s and ψ s are selected, and it is considered that the motor speed is constant in a very short time, then the stator current differential equation after forward Euler discretization obtains the k+1 stator current prediction value, which can be expressed as:

[0119]

[0120] In the formula:

[0121] Step 4.4, according to the k+1 stator flux prediction value and the k+1 stator current prediction value, the k+1 electromagnetic torque prediction value is obtained, the k+1 electromagnetic torque prediction value is:

[0122]

[0123] Wherein, p is the number of motor pole pairs, is the imaginary part in the complex number, is the k+1 stator flux prediction value, is the k+1 stator current prediction value.

[0124] Step 4.5, the cost function of the induction motor sensorless model predictive torque control is constructed as

[0125]

[0126] Wherein, Indicates the reference torque, is the given stator flux amplitude, λ1 is related to the electromagnetic torque, and λ2 is the weight coefficient of the flux term, is the k+1 electromagnetic torque prediction value, is the absolute value of the k+1 stator flux prediction value

[0127] λ1 is related to the electromagnetic torque, which is defined as:

[0128]

[0129] The weight coefficient of the flux term is λ2, which is expressed by the following formula:

[0130]

[0131] Step 5, according to the induction motor motion equation and the derivative of the load torque in a sampling period is zero, the reduced order load torque observer is constructed, the reference torque signal given value of the PI controller output is compensated, the feedforward compensation is carried out to the speed outer loop of the control system, and the dynamic response of the system is improved.

[0132] Step 5 is specifically implemented according to the following steps:

[0133] Step 5.1, control period T s It is generally considered that the load torque does not change in a control period, T L The motion equation of the induction motor is:

[0134]

[0135] Step 5.2, when the dimension of the state observer estimated state vector is less than the dimension of the state vector of the controlled object, it is called a reduced order state observer. According to the motion equation of the induction motor, the reduced order state observer is constructed as:

[0136]

[0137] ω r Motor mechanical angular velocity, J motor inertia, T e Electromagnetic torque, k1, k2 are matrix gain coefficients, is the estimated motor mechanical angular velocity, is the estimated load torque, n p is the number of motor pole pairs

[0138] Step 5.3, according to the designed reduced order state observer, the characteristic equation of the observer is obtained, the appropriate poles a1, a2 are selected, and the values of k1, k2 are obtained by solving the characteristic equation of the observer. The feedback gain matrix is constructed, and the estimated value of the load torque is obtained.

[0139]

[0140]

[0141] Step 5.4, the load torque is superimposed with the torque output by the torque regulator to the model predictive torque control algorithm.

[0142] Embodiment 1

[0143] The induction motor sensorless model predictive torque control method of the application combines Figure 1 , and is specifically implemented according to the following steps:

[0144] Step 1, the mathematical model of the induction motor is modeled based on the two-phase stationary coordinate system, and the mathematical model of the induction motor is obtained.

[0145] Step 2, based on the induction motor mathematical model obtained in step 1, the stator current and rotor flux are taken as state variables, and a full-order observer is constructed, and the estimated value of the speed and the estimated value of the flux are obtained through the full-order observer;

[0146] Step 3, based on the full-order 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, and the robustness of the system is improved;

[0147] Step 4, according to the induction motor mathematical model obtained in step 1, a prediction model is established, and the induction motor speed estimation value and flux estimation value obtained in step 2 are taken as the input of the prediction model, and the stator flux and electromagnetic torque at k+1 time are predicted to obtain the stator flux prediction value and electromagnetic torque prediction value;

[0148] Step 5, according to the induction motor motion equation and the derivative of the load torque being zero in a sampling period, a reduced-order load torque observer is constructed, and the reference torque signal given value output by the PI controller is compensated, and the speed outer loop of the control system is feedforward compensated, and the dynamic response of the system is improved.

[0149] Embodiment 2

[0150] The induction motor sensorless model predictive torque control method of the application combines Figure 1 , and is specifically implemented according to the following steps:

[0151] Step 1, based on the mathematical model of the induction motor in the two-phase stationary coordinate system, the mathematical model of the induction motor is obtained;

[0152] Step 2, based on the induction motor mathematical model obtained in step 1, the stator current and rotor flux are taken as state variables, and a full-order observer is constructed, and the estimated value of the speed and the estimated value of the flux are obtained through the full-order observer;

[0153] Step 3, based on the full-order 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, and the robustness of the system is improved;

[0154] Step 4, according to the induction motor mathematical model obtained in step 1, a prediction model is established, and the induction motor speed estimation value and flux estimation value obtained in step 2 are taken as the input of the prediction model, and the stator flux and electromagnetic torque at k+1 time are predicted to obtain the stator flux prediction value and electromagnetic torque prediction value;

[0155] Step 5, according to the induction motor motion equation and the derivative of the load torque being zero in a sampling period, a reduced-order load torque observer is constructed, and the reference torque signal given value output by the PI controller is compensated, and the speed outer loop of the control system is feedforward compensated, and the dynamic response of the system is improved.

[0156] Step 1 is implemented according to the following steps:

[0157] The mathematical model of the induction motor in the two-phase stationary coordinate system is:

[0158]

[0159] where R is the stator resistance, σ is the leakage coefficient, L is the stator inductance, T is the rotor time constant, s s L is the mutual inductance, L is the rotor inductance, ω is the electrical rotor speed, r m i is the stator current, ψ is the rotor flux vector, r r u is the stator voltage component in the α-axis, and u is the stator voltage component in the β-axis. s r sα sβ

[0160] Step 2, according to the mathematical model of the induction motor obtained in step 1, taking the stator current and the rotor flux as state variables, a full-order observer is constructed, and the estimated value of the speed and the estimated value of the flux are obtained through the full-order observer;

[0161] Step 2 is implemented according to the following steps:

[0162] Step 2.1, referring to the mathematical model of the induction motor, a state observer is designed as an adjustable model;

[0163] Step 2.2, confirm the controllable object is observable, and reconstruct the state equation of the observer according to the input and output of the controllable object;

[0164] Step 2.3, according to the idea of model reference self-adaptation, taking the induction motor itself as the reference model and the constructed full-order observer as the adjustable model, since there is always a certain difference between the initial states of the two, there will be a state error, which will also lead to an output error, the idea of feedback design is introduced, and the output error is used as a negative feedback compensation to the differential equation of the state vector, so that the output error quickly approaches zero, leading to the input error also approaching zero;

[0165] Step 2.4, according to the mathematical model of the induction motor and the design principle of the full-order adaptive observer, we can get:

[0166]

[0167] In the formula: ​​​​​​​​​​

[0168] G is the feedback gain matrix

[0169] Step 2.5. Design the feedback gain matrix according to the requirements of pole configuration. Assuming that the poles of the full-order adaptive observer are k times the poles of the induction motor, the feedback matrix is ​​obtained by combining the characteristic equations of the two. However, this configuration method is relatively complicated. When the pole diagram is drawn based on the obtained feedback matrix, it is found that the poles of the observer are distributed to the left of the motor poles. As the speed increases, the poles gradually move away from the real axis and the imaginary axis, which will cause system instability. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used.

[0170] The necessary and sufficient conditions to ensure the stability of the full-order observer are obtained:

[0171]

[0172] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4 = 0, we can obtain a range of feedback matrices that can ensure the stability of the full-order observer:

[0173]

[0174] From the formula, we can see that g1≥0, g3≥0 always holds true. By introducing the adjustment coefficients a and b,

[0175] a≥0,b≥0

[0176] The new feedback matrix is ​​obtained as:

[0177]

[0178] Step 2.6: Based on Lyapunov's stability theorem, the specific equation of the speed adaptation law can be derived, thereby achieving accurate estimation of the speed. The speed adaptation law can be simplified to:

[0179]

[0180] Step 3: Based on the full-order 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;

[0181] Step 4: Establish a prediction model based on the mathematical model of the induction motor obtained in step 1, use the estimated speed value and flux linkage value of the induction motor obtained in step 2 as inputs of the prediction model, predict the stator flux linkage and electromagnetic torque at time k+1, and obtain the stator flux linkage predicted value and electromagnetic torque predicted value;

[0182] Step 4 is implemented as follows:

[0183] Step 4.1, based on the mathematical model of the induction motor in the two-phase stationary coordinate system, estimate the stator flux and speed using a full-order observer;

[0184] Step 4.2: Based on the forward Euler discretization formula, the predicted stator flux and stator current at time k+1 are obtained:

[0185]

[0186] Where T s is the system sampling period, ψ s (k+1) is the stator flux component predicted at time k+1, i s (k) and is the stator current vector component at time k, u s (k) is the stator voltage vector component at time k;

[0187] Step 4.3: In the induction motor model predictive control system, it is usually necessary to estimate the stator flux and implement predictive control based on this. The conversion relationship between the stator flux and the rotor flux is:

[0188]

[0189] Step 4.4: Select the state variable i in the induction motor mathematical model s and ψ s , and assuming that the motor speed is constant in a very short time, the stator current differential equation is obtained after forward Euler discretization to obtain the k+1 stator current prediction value, which can be expressed as:

[0190]

[0191] Where:

[0192] Step 4.4: Based on the predicted value of the stator flux at time k+1 and the predicted value of the stator current at time k+1, the predicted value of the electromagnetic torque at time k+1 is obtained. The predicted value of the electromagnetic torque at time k+1 is:

[0193]

[0194] Where p is the number of motor pole pairs, is the imaginary part of the complex number, is the predicted value of stator flux at time k+1, is the predicted value of the stator current at time k+1.

[0195] Step 4.5: The cost function of the constructed induction motor sensorless model predictive torque control is

[0196]

[0197] wherein, represents a reference torque, is a given stator flux linkage amplitude, λ1 is related to the electromagnetic torque, and λ2 is a weight coefficient of the flux linkage term, is a predicted value of the electromagnetic torque at k+1, is an absolute value of a predicted value of the stator flux linkage at k+1

[0198] λ1 is related to the electromagnetic torque and is defined as:

[0199]

[0200] the weight coefficient of the flux linkage term is λ2 and is represented by the following formula:

[0201]

[0202] Step 5, according to the induction motor motion equation and the derivative of the load torque being zero in a sampling period, a reduced-order load torque observer is constructed to compensate for the given value of the reference torque signal output by the PI controller, to perform feedforward compensation on the speed outer loop of the control system and to improve the dynamic response of the system.

[0203] Step 5 is implemented according to the following steps:

[0204] Step 5.1, control period T s is small, it is generally considered that the load torque does not change in a control period, T L The motion equation of the induction motor is:

[0205]

[0206] Step 5.2, when the dimension of the state vector estimated by the state observer is less than the dimension of the state vector of the controlled object, it is called a reduced-order state observer. According to the motion equation of the induction motor, the reduced-order state observer is constructed as:

[0207]

[0208] ω r motor mechanical angular velocity, J motor inertia, T e electromagnetic torque, k1, k2 are matrix gain coefficients, is an estimated motor mechanical angular velocity, is an estimated load torque, n p is the number of motor pole pairs

[0209] Step 5.3, according to the designed reduced-order state observer, the characteristic equation of the observer is obtained, appropriate poles a1, a2 are selected, and the values of k1, k2 are solved by combining the characteristic equation of the observer, a feedback gain matrix is constructed, and an estimated value of the load torque is obtained;

[0210]

[0211] Step 5.4: Superimpose the load torque and the torque output by the torque regulator into the model predictive torque control algorithm.

[0212] Example 3

[0213] The sensorless model predictive torque control method of the induction motor of the present invention is combined with Figure 1 , specifically follow the steps below:

[0214] Step 1: Modeling a mathematical model of the induction motor based on a two-phase stationary coordinate system to obtain a mathematical model of the induction motor;

[0215] Step 2: Based on the mathematical model of the induction motor obtained in step 1, a full-order observer is constructed with the stator current and the rotor flux as state variables, and an estimated value of the speed and the estimated value of the flux are obtained through the full-order observer;

[0216] Step 3: Based on the full-order 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;

[0217] Step 4: Establish a prediction model based on the mathematical model of the induction motor obtained in step 1, use the estimated speed value and flux linkage value of the induction motor obtained in step 2 as inputs of the prediction model, predict the stator flux linkage and electromagnetic torque at time k+1, and obtain the stator flux linkage predicted value and electromagnetic torque predicted value;

[0218] Step 5: Based on the motion equation of the induction motor and the load torque derivative being zero within a sampling period, a reduced-order load torque observer is constructed to compensate the reference torque signal given value output by the PI controller, perform feedforward compensation on the control system speed outer loop, and improve the dynamic response of the system.

[0219] Step 1 is implemented as follows:

[0220] In the two-phase stationary coordinate system, the mathematical model of the induction motor is:

[0221]

[0222] Among them, R s is the stator resistance, σ is the magnetic leakage coefficient, L s is the stator inductance, T r is the rotor time constant, L m is the mutual inductance, L r is the rotor inductance, ω r is the electric rotor speed, is ψ is the stator current, r ψ is the rotor flux vector, u sα u is the stator voltage component on the α axis, sβ u is the stator voltage component on the β axis.

[0223] Step 2, according to the induction motor mathematical model obtained in step 1, the stator current and the rotor flux are taken as the state variables, and a full-order observer is constructed to obtain the estimated value of the speed and the estimated value of the flux through the full-order observer;

[0224] Step 2 is implemented according to the following steps:

[0225] Step 2.1, refer to the induction motor mathematical model to design a state observer as an adjustable model;

[0226] Step 2.2, confirm the controllable object is observable, and reconstruct the state equation of the observer according to the input and output of the controllable object;

[0227] Step 2.3, according to the idea of model reference self-adaptation, take the induction motor itself as the reference model and the constructed full-order observer as the adjustable model, because there is always a certain difference between the initial states of the two, there will be a state error, which will also lead to an output error, introduce the idea of feedback design, use the output error as a negative feedback compensation to the differential equation of the state vector, so that the output error quickly approaches zero, leading to the input error also approaching zero;

[0228] Step 2.4, according to the mathematical model of the induction motor and the design principle of the full-order adaptive observer, we can get:

[0229]

[0230] In the formula:

[0231] G is the feedback gain matrix

[0232] Step 2.5, design the feedback gain matrix according to the requirement of pole placement. Assume that the poles of the full-order adaptive observer are k times of the poles of the induction motor, and the feedback matrix is obtained by combining the characteristic equations of the two. However, this configuration method is relatively complex, and according to the obtained feedback matrix, it is found that the poles of the observer are distributed on the left side of the poles of the motor, and the poles gradually move away from the real axis and the imaginary axis as the speed increases, which will lead to system instability. In order to ensure the stability of the full-order observer, use the Routh-Hurwitz stability criterion,

[0233] get the sufficient and necessary condition to ensure the stability of the full-order observer:

[0234]

[0235] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4=0, a feedback matrix selection range that can guarantee the stability of the full-order observer is obtained:

[0236]

[0237] From the formula, g1≥0 and g3≥0 are always true. Introduce adjustment coefficients a and b, so that

[0238] a≥0,b≥0

[0239] The new feedback matrix is obtained as follows:

[0240]

[0241] Step 2.6, according to Lyapunov stability theorem, the specific equation of speed adaptive law can be derived, so as to realize accurate estimation of speed. The speed adaptive law can be simplified as:

[0242]

[0243] Step 3, based on the full-order observer, the adaptive rate of stator resistance is derived, 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;

[0244] Step 3 is implemented according to the following steps:

[0245] Step 3.1, if the stator resistance is regarded as a time-varying parameter, the state error equation is obtained by subtracting the state equation of the induction motor from the full-order adaptive observer, as shown below:

[0246]

[0247]

[0248] Step 3.2, by defining Lyapunov function, the stator resistance adaptive rate is obtained from Lyapunov stability theorem. In order to improve the estimation speed of stator resistance, PI regulator is usually used to realize adjustment conveniently and quickly, and the final stator resistance adaptive rate is obtained as:

[0249]

[0250] Step 4, according to the mathematical model of induction motor obtained in step 1, a prediction model is established, and the estimated value of induction motor speed and flux obtained in step 2 is used as the input of the prediction model. The stator flux and electromagnetic torque at k+1 time are predicted to obtain the predicted value of stator flux and electromagnetic torque;

[0251] Step 4 is specifically implemented according to the following steps:

[0252] Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux linkage and speed are estimated by the full-order observer;

[0253] Step 4.2, based on the forward Euler discretization formula, the stator flux linkage prediction value and the stator current prediction value at k+1 time are obtained:

[0254]

[0255] In the formula, T s is the system sampling period, ψ s (k+1) is the predicted stator flux linkage component at k+1 time, i s (k) and are the stator current vector components at k time, u s (k) is the stator voltage vector component at k time;

[0256] Step 4.3, in the induction motor model predictive control system, the stator flux linkage usually needs to be estimated to realize the predictive control on this basis, and the conversion relationship between the stator flux linkage and the rotor flux linkage is:

[0257]

[0258] Step 4.4, in the induction motor mathematical model, the state variables i s and ψ s are selected, and it is considered that the motor speed is a constant value in a very short time, so that the k+1 stator current prediction value is obtained after the forward Euler discretization of the stator current differential equation, which can be expressed as:

[0259]

[0260] In the formula:

[0261] Step 4.4, according to the stator flux linkage prediction value at k+1 time and the stator current prediction value at k+1 time, the electromagnetic torque prediction value at k+1 time is obtained, and the electromagnetic torque prediction value at k+1 time is:

[0262]

[0263] In the formula, p is the number of motor pole pairs, is the imaginary part in the complex number, is the stator flux linkage prediction value at k+1 time, is the stator current prediction value at k+1 time.

[0264] Step 4.5, the cost function of the induction motor sensorless model predictive torque control constructed is

[0265]

[0266] wherein, represents the reference torque, is the given stator flux magnitude, λ1 is related to the electromagnetic torque, and λ2 is the weight coefficient of the flux term, is the electromagnetic torque prediction value at k+1, is the absolute value of the stator flux prediction value at k+1

[0267] λ1 is related to the electromagnetic torque and is defined as:

[0268]

[0269] The weight coefficient of the flux term is λ2 and is represented by the following formula:

[0270]

[0271] Step 5, according to the induction motor motion equation and the load torque derivative being zero in one sampling period, a reduced-order load torque observer is constructed to compensate the reference torque signal given value output by the PI controller, to perform feedforward compensation on the speed outer loop of the control system, and to improve the dynamic response of the system.

Claims

1. A sensorless model predictive torque control method for an induction motor, characterized in that: Please follow the steps below to implement: Step 1: Modeling a mathematical model of the induction motor based on a two-phase stationary coordinate system to obtain a mathematical model of the induction motor; The step 1 is specifically implemented according to the following steps: In the two-phase stationary coordinate system, the mathematical model of the 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 electric rotor speed, , is the stator current, is the rotor flux vector, , for The stator voltage component below the shaft, for stator voltage component below the shaft; Step 2: Construct a full-order observer and obtain the estimated values ​​of the speed and flux linkage through the full-order observer; The speed adaptation law is: ； Step 3: derive the adaptive rate of the stator resistance and introduce the parameter identification of the stator resistance into the motor speed estimation and model prediction module; The step 3 is specifically implemented according to the following steps: Step 3.1: If the stator resistance is used as a time-varying parameter, the state error equation is obtained by subtracting the state equations of the induction motor and the full-order adaptive observer, as shown below: Step 3.2: By defining the Lyapunov function, the stator resistance adaptation rate is obtained from the Lyapunov stability law. 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: ； Step 4: Establish a prediction model, use the estimated value of the induction motor speed and the estimated value of the flux as inputs to obtain the predicted value of the stator flux and the predicted value of the electromagnetic torque; The step 4 is specifically implemented according to the following steps: Step 4.1, based on the mathematical model of the induction motor in the two-phase stationary coordinate system, estimate the stator flux and speed using a full-order observer; Step 4.2: Based on the forward Euler discretization formula, we get The predicted values ​​of stator flux and stator current at the moment: 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 components at time ; Step 4.3: In the induction motor model predictive control system, it is usually necessary to estimate the stator flux and implement predictive control based on this. The conversion relationship between the stator flux and the rotor flux is: Step 4.

4. Select state variables in the induction motor mathematical model 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 can be expressed as: Where: Step 4.5, according to 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 The predicted value of stator flux at time +1, for k Predicted value of stator current at time +1; Step 4.6: The cost function of the constructed sensorless model for predictive torque control of the induction motor is in, represents the reference torque, is a given stator flux amplitude, Related to electromagnetic torque, is the weight coefficient of the magnetic linkage term, for k The predicted value of electromagnetic torque at time +1, for k The absolute value of the stator flux prediction value at time +1; Related to the electromagnetic torque, it is defined as: The weight coefficient of the magnetic linkage term is , expressed by the following formula: Step 5: Construct a reduced-order load torque observer to compensate the reference torque signal given by the PI controller, perform feedforward compensation on the control system speed outer loop, and improve the dynamic response of the system; The step 5 is specifically implemented according to the following steps: Step 5.1, control cycle Small, it is usually considered that the load torque does not change within a control cycle. The derivative of is 0, and the equation of motion of the induction motor is: Step 5.2: When the dimension of the state vector estimated by the state observer is smaller than the dimension of the state vector of the controlled object, it is called a reduced-order state observer. The reduced-order state observer is constructed based on the motion equation of the induction motor as follows: Motor mechanical angular velocity, Motor inertia, electromagnetic torque, is the matrix gain coefficient, To estimate the motor mechanical angular velocity, To estimate the load torque, is the number of motor pole pairs; Step 5.3: According to the designed reduced-order state observer, obtain the characteristic equation of the observer and select the appropriate poles , and the characteristic equation of the observer are solved to obtain The value of is used to construct the feedback gain matrix and obtain the estimated value of the load torque; Step 5.4: Superimpose the load torque estimate and the torque output by the torque regulator into the model predictive torque control algorithm.

2. The sensorless model predictive torque control method for an induction motor according to claim 1, wherein: The step 2 is specifically implemented according to the following steps: Step 2.1, design a state observer as an adjustable model based on the mathematical model of the induction motor; Step 2.2: Confirm that the controlled object is observable and reconstruct the state equation of the observer based on the input and output of the controlled object; Step 2.3, based on the idea of ​​model reference adaptation, the induction motor itself is used as the reference model, the constructed full-order observer is used as the adjustable model, the idea of ​​feedback design is introduced, and the output error is used to As negative feedback compensation to the differential equation of the state vector, the output error approaches zero quickly, causing the input error to also approach zero; Step 2.4: Based on the mathematical model of the induction motor and the design principle of the full-order adaptive observer, we can obtain: Where: G is the feedback gain matrix; Step 2.5: Design the feedback gain matrix according to the pole configuration requirements, assuming that the poles of the full-order adaptive observer are the poles of the induction motor. times, and the feedback matrix is ​​obtained by combining the characteristic equations of the two. However, this configuration method is relatively complicated. According to the obtained feedback matrix, the pole diagram is drawn and it is found that the poles of the observer are distributed on the left side of the motor poles. As the speed increases, the poles gradually move away from the real axis and the imaginary axis, which will cause the system to be unstable. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used. The necessary and sufficient conditions to ensure the stability of the full-order observer are obtained: There are three equations and four unknowns in the condition, so the solution is not unique. Suppose =0, The selection range of the feedback matrix that can ensure the stability of the full-order observer is obtained: From the formula we can see , Always holds true, introduce adjustment coefficients a and b, so The new feedback matrix is ​​obtained as: Step 2.6: Based on Lyapunov's stability theorem, the specific equation of the speed adaptation law can be derived, thereby achieving accurate estimation of the speed.

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