Sensorless model prediction speed control method for induction motor

Abstract

The invention discloses a sensorless model prediction speed control method for an induction motor, and the method comprises the steps: carrying out the modeling of a mathematical model of the induction motor based on a two-phase static coordinate system, and obtaining a mathematical model of the induction motor; constructing a full-order observer, and obtaining an estimated value of the rotating speed of the rotor of the induction motor and an estimated value of the flux linkage through the full-order observer; parameter identification of stator resistance is introduced into a motor rotating speed estimation and model prediction module; establishing a prediction model, predicting the stator flux linkage and the rotating speed at the k + 1 moment, and obtaining a stator flux linkage prediction value and a rotating speed prediction value; and finally, constructing a reduced order load torque observer, carrying out feedforward compensation on a speed outer ring of the control system, and improving the dynamic response of the system. According to the invention, the problem in the prior art that the system performance is reduced and even the system crashes due to sensor faults is solved.

Description

Technical Field

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

[0002] Induction motor is a type of motor with a simple structure. Due to its advantages such as low cost, easy maintenance and high reliability, induction motor is widely used in industrial and commercial fields to provide a stable power source. With the advancement of science and technology, the demand for motor performance is constantly increasing, and high-performance AC speed control technology is also gradually developing, providing more possibilities for the expansion of the application field of induction motor.

[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 ever-increasing industrial needs. 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 used to eliminate the speed loop and adopt a single-loop control structure to improve the dynamic response speed of the system.

[0004] In the AC motor speed control system, sensors are needed to obtain the motor speed for negative feedback regulation of the system. However, sensors bring a series of problems. For example, sensor failure may cause system performance degradation or even system crash. Sensor installation also requires a certain cost. Some special scenarios may not be suitable for installing sensors. Therefore, sensorless control technology has become a major research hotspot. Summary of the invention

[0005] The purpose of the present invention is to provide a sensorless model predictive speed control method for an induction motor, which solves the problem in the prior art that sensor failure may cause system performance degradation or even system crash.

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

[0007] 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;

[0008] Step 2: construct a full-order observer, and obtain an estimated value of the rotor speed and the flux linkage of the induction motor through the full-order observer;

[0009] Step 3: Introduce the parameter identification of stator resistance into the motor speed estimation and model prediction module;

[0010] Step 4: Establish a prediction model to predict the stator flux and speed at time k+1 to obtain the stator flux prediction value and the speed prediction value;

[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 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 with reference to 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 according to the input and output of the controlled object;

[0020] Step 2.3: Take the induction motor itself as the reference model and the constructed full-order observer as the adjustable model, introduce the idea of ​​feedback design, and 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:

[0022]

[0023] Where:

[0024] G is the feedback gain matrix;

[0025] Step 2.5: Using the Routh-Hurwitz stability criterion, we obtain the necessary and sufficient conditions to ensure the stability of the full-order observer:

[0026]

[0027] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4 = 0, we can get a feedback matrix selection range that can ensure the stability of the full-order observer:

[0028]

[0029] From the formula, we can see that g1≥0, g3≥0 always holds true. By introducing adjustment coefficients a and b,

[0030] a≥0,b≥0

[0031] The new feedback matrix is ​​obtained as:

[0032]

[0033] Step 2.6, subtract the equation of the induction motor full-order observer from the induction motor state equation to obtain the system state error equation. According to Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate estimation of the speed, and the speed adaptive law is simplified to:

[0034]

[0035] in, is the estimated value of the rotation speed, is the stator current error of phase a, is the β-phase stator current error, is the estimated rotor flux of phase a, is the estimated rotor flux of the β phase, k p and k i are the proportional coefficient and the integral coefficient respectively.

[0036] Step 3 is implemented as follows:

[0037] Step 3.1, taking the stator resistance as a time-varying parameter, the state equation of the induction motor and the full-order adaptive observer are subtracted to obtain the state error equation, as shown below:

[0038]

[0039]

[0040] Step 3.2, by defining the Lyapunov function, the stator resistance adaptation rate is obtained by the Lyapunov stability law, and the PI regulator is used to quickly and conveniently adjust the final stator resistance adaptation rate:

[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 and speed are estimated by the full-order observer;

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

[0045]

[0046] 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 are the stator current vector components at time k, u s (k) is the stator voltage vector component at time k;

[0047] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted, and the conversion relationship between the rotor flux and the stator flux is:

[0048]

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

[0050]

[0051] Where: is the stator resistance identified in step 302;

[0052] Step 4.5: According to the predicted value of stator flux at time k+1 and the predicted value of stator current at time k+1, the predicted value of electromagnetic torque at time k+1 is obtained. The predicted value of electromagnetic torque at time k+1 is:

[0053]

[0054] 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 stator current at time k+1;

[0055] Step 4.6: According to the motion equation of the induction motor, the predicted speed value at time k+1 is obtained:

[0056]

[0057] Step 4.7: Get the estimated speed according to step 2.6 Substitute into the formula in step 4.6 to get the speed prediction value According to step 4.2, the predicted value of magnetic flux is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0058]

[0059] in, is a given stator flux amplitude, ω r * Referring to the speed term, λ1 is the weight coefficient of the flux term, and λ2 is the weight coefficient of the speed term. is the absolute value of the stator flux prediction value at time k+1;

[0060] The weight coefficient of the magnetic flux term is λ1, which is expressed by the following formula:

[0061]

[0062] Finally, r * is the reference speed term.

[0063] Step 5 is implemented according to the following steps:

[0064] Step 5.1, the motion equation of the induction motor is:

[0065]

[0066] 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 according to the motion equation of the induction motor as follows:

[0067]

[0068] ω r Motor mechanical angular velocity, J Motor inertia, T e Electromagnetic torque, k1, k2 are matrix gain coefficients, To estimate the motor speed, n p is the number of motor pole pairs, To estimate the load torque;

[0069] Step 5.3, according to the designed reduced-order state observer, the characteristic equation of the observer is:

[0070]

[0071] Step 5.4 Select the appropriate desired pole a1a2 to keep the system stable. Solve the observer characteristic equation to obtain the values ​​of k1 and k2, construct the feedback gain matrix, and obtain the estimated value of the load torque;

[0072] s 2 -(a1+a2)s+a1a2=0

[0073]

[0074] Step 5.5: Feedback the load torque and the torque output by the torque regulator to step 4.6 to obtain the speed prediction value at time k+1. Substitute the stator resistance identified in step 3.2 into step 4.4 to obtain the speed prediction value at time k+1. This can update the motor parameters in real time, making the model prediction speed control more accurate.

[0075] The beneficial effect of the present invention is that the sensorless model prediction speed control method of the induction motor predicts and controls the speed and flux through the prediction model, and the dynamic response speed of the system is improved by the model prediction speed control. The stator resistance parameter identification module is introduced to update the stator resistance in real time, and the performance of the observer and the model prediction control is improved. The load torque observer is introduced to compensate the electromagnetic torque, and the speed dynamic response, load response and tracking performance of the motor are improved. The load torque observer is introduced, and the change rate of the load torque can be considered to be zero within a sampling period. The load torque observer is constructed according to the motion equation of the induction motor and the principle of reduced-order observer. The torque output by the load torque observer and the torque regulator is superimposed on the model prediction torque control algorithm. In this way, the dynamic response of the system can be improved. Model prediction speed control is introduced. Traditional model prediction torque control, model prediction flux control, and model prediction current control all adopt a double closed-loop structure of speed outer loop control plus model prediction inner loop control. The speed loop parameters need to be adjusted, which increases the complexity of the system. The model prediction direct speed control (MPDSC) is adopted, the speed loop is omitted, and a single-loop control structure is adopted to improve the dynamic response speed of the system. The cost function is a tool for evaluating the error between the given value and the predicted value in the model predictive torque control, so the cost function is closely related to the optimal switching state selected by the control system. In addition, whether the cost function is selected appropriately 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 optimal switching state, causing the control system to use an inappropriate switching state as the optimal switching state, thereby affecting the control performance of the induction motor. Setting the speed prediction value and the flux prediction value as the cost function can control the speed, flux and speed of the motor at the same time, thereby improving the dynamic and steady-state performance of the motor. It can be understood that the beneficial effects of the second to fourth aspects can be found in the relevant description of the first aspect, and will not be repeated here. In summary, the present invention introduces a full-order observer to estimate the speed and flux of the motor. The speed and flux are predicted and controlled by the prediction model, and the model prediction direct speed control is adopted, the speed loop is omitted, and the single-loop control structure is adopted to improve the dynamic response speed of the system. The optimal switching state is obtained by the cost function, thereby improving the dynamic and steady-state performance of the system and reducing current pulsation and switching loss. The stator resistance parameter identification module is introduced to update the stator resistance in real time, improving the performance of the observer and model predictive control. The load torque observer is introduced to compensate the electromagnetic torque, improving the speed dynamic response, load response and tracking performance of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 A control block diagram of a sensorless model predictive speed control method for an induction motor according to the present invention;

[0077] Figure 2 The principle block diagram of the full-order adaptive observer in the sensorless model predictive speed control method of the induction motor of the present invention is

[0078] Figure 3 It is a basic voltage vector block diagram of a two-level inverter in the sensorless model predictive speed control method of an induction motor of the present invention. DETAILED DESCRIPTION

[0079] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0080] The mathematical model of the induction motor is obtained by modeling the induction motor in the two-phase stationary coordinate system. According to the mathematical model of the induction motor in the stationary coordinate system, the stator current and rotor flux are selected as state variables to design the full-order observer. A new feedback matrix design method is adopted. The Routh-Hurwitz stability criterion is used to obtain the necessary and sufficient conditions to ensure the stability of the full-order observer. The adjustment coefficient is introduced to obtain the improved feedback matrix. The speed adaptation rate is obtained according to the Lyapunov stability theorem. The stator resistance parameter identification is introduced to update the motor parameters in real time to improve the robustness of the model predictive control. The model predictive speed control is adopted to eliminate the speed outer loop and simplify the system structure. A model predictive direct speed control method with only one control loop is proposed. The dynamic response of the system is improved by introducing the stator flux error and speed error in the cost function. The speed and flux are estimated by the designed full-order adaptive observer and fed back to the model predictive speed controller. Assuming that the current moment is k, the stator flux and speed at k+1 are predicted to obtain the stator flux prediction value and speed prediction value. Since the model predictive speed control directly controls the motor speed and flux, changes in load torque during motor operation will cause system instability. In order to solve this problem, a reduced-order load torque observer is introduced to improve the load response and tracking performance of the motor.

[0081] The sensorless model prediction speed control method of the induction motor of the present invention is combined with Figure 1 , follow the steps below:

[0082] 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;

[0083] Step 1 is implemented as follows:

[0084] In the two-phase stationary coordinate system, the mathematical model of the induction motor is:

[0085]

[0086] Among them, R s is the stator resistance, σ is the leakage coefficient, Ls 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.

[0087] 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 rotor speed and the flux of the induction motor are obtained through the full-order observer;

[0088] Combination Figure 2-3 , step 2 is implemented according to the following steps:

[0089] Step 2.1, design a state observer as an adjustable model with reference to the mathematical model of the induction motor;

[0090] Step 2.2: Confirm that the controlled object is observable, and reconstruct the state equation of the observer according to the input and output of the controlled object;

[0091] Step 2.3, according to 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 between the initial states 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;

[0092] Step 2.4: Based on the mathematical model of the induction motor and the design principle of the full-order adaptive observer:

[0093]

[0094] Where:

[0095] G is the feedback gain matrix;

[0096] 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. 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 system instability. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used to obtain the necessary and sufficient conditions for ensuring the stability of the full-order observer:

[0097]

[0098] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4 = 0, we can get a feedback matrix selection range that can ensure the stability of the full-order observer:

[0099]

[0100] From the formula, we can see that g1≥0, g3≥0 always holds true. By introducing adjustment coefficients a and b,

[0101] a≥0,b≥0

[0102] The new feedback matrix is ​​obtained as:

[0103]

[0104] Step 2.6, subtract the equation of the induction motor full-order observer from the induction motor state equation to obtain the system state error equation. According to Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate estimation of the speed, and the speed adaptive law is simplified to:

[0105]

[0106] in, is the estimated value of the rotation speed, is the stator current error of phase a, is the β-phase stator current error, is the estimated rotor flux of phase a, is the estimated rotor flux of the β phase, k p and k i are the proportional coefficient and the integral coefficient respectively.

[0107] 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 to improve the robustness of the system;

[0108] Step 3 is implemented as follows:

[0109] Step 3.1, taking the stator resistance as a time-varying parameter, the state equation of the induction motor and the full-order adaptive observer are subtracted to obtain the state error equation, as shown below:

[0110]

[0111]

[0112] Step 3.2: By defining the Lyapunov function, the stator resistance adaptation rate is obtained by 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:

[0113]

[0114] 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 estimated value of the induction motor obtained in step 2 as inputs of the prediction model, predict the stator flux linkage and speed at time k+1, and obtain the stator flux linkage predicted value and speed predicted value;

[0115] Step 4 is implemented according to the following steps:

[0116] Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux and speed are estimated by the full-order observer;

[0117] Step 4.2: Based on the forward Euler discretization formula, the predicted value of the stator flux and the predicted value of the stator current at time k+1 are obtained:

[0118]

[0119] 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 are the stator current vector components at time k, u s (k) is the stator voltage vector component at time k;

[0120] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted, and the conversion relationship between the rotor flux and the stator flux is:

[0121]

[0122] Step 4.4: Select the state variable i in the mathematical model of the induction motor s and ψ s, and the motor speed is considered to be constant in a very short time, then the stator current differential equation is obtained after forward Euler discretization to obtain the k+1 stator current prediction value, which is expressed as:

[0123]

[0124] Where: is the stator resistance identified in step 302;

[0125] Step 4.5: According to the predicted value of stator flux at time k+1 and the predicted value of stator current at time k+1, the predicted value of electromagnetic torque at time k+1 is obtained. The predicted value of electromagnetic torque at time k+1 is:

[0126]

[0127] 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 stator current at time k+1;

[0128] Step 4.6: According to the motion equation of the induction motor, the predicted speed value at time k+1 is obtained:

[0129]

[0130] Step 4.7: Get the estimated speed according to step 2.6 Substitute into the formula in step 4.6 to get the speed prediction value According to step 4.2, the predicted value of magnetic flux is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0131]

[0132] in, is a given stator flux amplitude, ω r * Referring to the speed term, λ1 is the weight coefficient of the flux term, and λ2 is the weight coefficient of the speed term. is the absolute value of the stator flux prediction value at time k+1;

[0133] The weight coefficient of the magnetic flux term is λ1, which is expressed by the following formula:

[0134]

[0135] Finally, r *It is the reference speed term, and its influence is determined by the weight coefficient λ2, which is generally obtained through simulation and experimental debugging.

[0136] Step 5: According to 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.

[0137] Step 5 is implemented according to the following steps:

[0138] Step 5.1, control period T s It is usually considered that the load torque does not change within a control cycle. L The derivative of is 0, and the equation of motion of the induction motor is:

[0139]

[0140] 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 according to the motion equation of the induction motor as follows:

[0141]

[0142] ω r Motor mechanical angular velocity, J Motor inertia, T e Electromagnetic torque, k1, k2 are matrix gain coefficients, To estimate the motor speed, n p is the number of motor pole pairs, To estimate the load torque;

[0143] Step 5.3: According to the designed reduced-order state observer, the characteristic equation of the observer is

[0144]

[0145] Step 5.4 Select the appropriate desired pole a1a2 to keep the system stable. Solve the observer characteristic equation to obtain the values ​​of k1 and k2, construct the feedback gain matrix, and obtain the estimated value of the load torque;

[0146] s 2 -(a1+a2)s+a1a2=0

[0147]

[0148] Step 5.5: Feedback the load torque and the torque output by the torque regulator to step 4.6 to obtain the speed prediction value at time k+1. Substitute the stator resistance identified in step 3.2 into step 4.4 to obtain the speed prediction value at time k+1. This can update the motor parameters in real time, making the model prediction speed control more accurate.

[0149] Example 1

[0150] The sensorless model prediction speed control method of the induction motor of the present invention is combined with Figure 1 , follow the steps below:

[0151] 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;

[0152] 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 rotor speed and the flux of the induction motor are obtained through the full-order observer;

[0153] 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 to improve the robustness of the system;

[0154] 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 estimated value of the induction motor obtained in step 2 as inputs of the prediction model, predict the stator flux linkage and speed at time k+1, and obtain the stator flux linkage predicted value and speed predicted value;

[0155] Step 5: According to 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.

[0156] Example 2

[0157] The sensorless model prediction speed control method of the induction motor of the present invention is combined with Figure 1 , follow the steps below:

[0158] 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;

[0159] Step 1 is implemented as follows:

[0160] In the two-phase stationary coordinate system, the mathematical model of the induction motor is:

[0161]

[0162] Among them, R s is the stator resistance, σ is the 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.

[0163] 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 rotor speed and the flux of the induction motor are obtained through the full-order observer;

[0164] Step 2 is implemented as follows:

[0165] Step 2.1, design a state observer as an adjustable model with reference to the mathematical model of the induction motor;

[0166] Step 2.2: Confirm that the controlled object is observable, and reconstruct the state equation of the observer according to the input and output of the controlled object;

[0167] Step 2.3, according to 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 between the initial states 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;

[0168] Step 2.4: Based on the mathematical model of the induction motor and the design principle of the full-order adaptive observer:

[0169]

[0170] Where:

[0171] G is the feedback gain matrix;

[0172] 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. 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 system instability. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used to obtain the necessary and sufficient conditions for ensuring the stability of the full-order observer:

[0173]

[0174] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4 = 0, we can get a feedback matrix selection range that can ensure the stability of the full-order observer:

[0175]

[0176] From the formula, we can see that g1≥0, g3≥0 always holds true. By introducing adjustment coefficients a and b,

[0177] a≥0,b≥0

[0178] The new feedback matrix is ​​obtained as:

[0179]

[0180] Step 2.6, subtract the equation of the induction motor full-order observer from the induction motor state equation to obtain the system state error equation. According to Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate estimation of the speed, and the speed adaptive law is simplified to:

[0181]

[0182] in, is the estimated value of the rotation speed, is the stator current error of phase a, is the β-phase stator current error, is the estimated rotor flux of phase a, is the estimated rotor flux of the β phase, k p and k i are the proportional coefficient and the integral coefficient respectively.

[0183] 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 to improve the robustness of the system;

[0184] 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 estimated value of the induction motor obtained in step 2 as inputs of the prediction model, predict the stator flux linkage and speed at time k+1, and obtain the stator flux linkage predicted value and speed predicted value;

[0185] Step 4 is implemented according to the following steps:

[0186] Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux and speed are estimated by the full-order observer;

[0187] Step 4.2: Based on the forward Euler discretization formula, the predicted value of the stator flux and the predicted value of the stator current at time k+1 are obtained:

[0188]

[0189] 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 are the stator current vector components at time k, u s (k) is the stator voltage vector component at time k;

[0190] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted, and the conversion relationship between the rotor flux and the stator flux is:

[0191]

[0192] Step 4.4: Select the state variable i in the mathematical model of the induction motor s and ψ s , and the motor speed is considered to be constant in a very short time, then the stator current differential equation is obtained after forward Euler discretization to obtain the k+1 stator current prediction value, which is expressed as:

[0193]

[0194] Where: is the stator resistance identified in step 302;

[0195] Step 4.5: According to the predicted value of stator flux at time k+1 and the predicted value of stator current at time k+1, the predicted value of electromagnetic torque at time k+1 is obtained. The predicted value of electromagnetic torque at time k+1 is:

[0196]

[0197] 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 stator current at time k+1;

[0198] Step 4.6: According to the motion equation of the induction motor, the predicted speed value at time k+1 is obtained:

[0199]

[0200] Step 4.7: Get the estimated speed according to step 2.6 Substitute into the formula in step 4.6 to get the speed prediction value According to step 4.2, the predicted value of magnetic flux is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0201]

[0202] in, is a given stator flux amplitude, ω r * Referring to the speed term, λ1 is the weight coefficient of the flux term, and λ2 is the weight coefficient of the speed term. is the absolute value of the stator flux prediction value at time k+1;

[0203] The weight coefficient of the magnetic flux term is λ1, which is expressed by the following formula:

[0204]

[0205] Finally, r * It is the reference speed term, and its influence is determined by the weight coefficient λ2, which is generally obtained through simulation and experimental debugging.

[0206] Step 5: According to 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.

[0207] Step 5 is implemented according to the following steps:

[0208] Step 5.1, control period T s It is usually considered that the load torque does not change within a control cycle. L The derivative of is 0, and the equation of motion of the induction motor is:

[0209]

[0210] 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 according to the motion equation of the induction motor as follows:

[0211]

[0212] ω r Motor mechanical angular velocity, J Motor inertia, T e Electromagnetic torque, k1, k2 are matrix gain coefficients, To estimate the motor speed, n p is the number of motor pole pairs, To estimate the load torque;

[0213] Step 5.3, according to the designed reduced-order state observer, the characteristic equation of the observer is:

[0214]

[0215] Step 5.4 Select the appropriate desired pole a1a2 to keep the system stable. Solve the observer characteristic equation to obtain the values ​​of k1 and k2, construct the feedback gain matrix, and obtain the estimated value of the load torque;

[0216] s 2 -(a1+a2)s+a1a2=0

[0217]

[0218] Step 5.5: Feedback the load torque and the torque output by the torque regulator to step 4.6 to obtain the speed prediction value at time k+1. Substitute the stator resistance identified in step 3.2 into step 4.4 to obtain the speed prediction value at time k+1. This can update the motor parameters in real time, making the model prediction speed control more accurate.

[0219] Example 3

[0220] The sensorless model prediction speed control method of the induction motor of the present invention is combined with Figure 1 , follow the steps below:

[0221] 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;

[0222] Step 1 is implemented as follows:

[0223] In the two-phase stationary coordinate system, the mathematical model of the induction motor is:

[0224]

[0225] Among them, Rs is the stator resistance, σ is the 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.

[0226] 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 rotor speed and the flux of the induction motor are obtained through the full-order observer;

[0227] Step 2 is implemented as follows:

[0228] Step 2.1, design a state observer as an adjustable model with reference to the mathematical model of the induction motor;

[0229] Step 2.2: Confirm that the controlled object is observable, and reconstruct the state equation of the observer according to the input and output of the controlled object;

[0230] Step 2.3, according to 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 between the initial states 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;

[0231] Step 2.4: Based on the mathematical model of the induction motor and the design principle of the full-order adaptive observer:

[0232]

[0233] Where:

[0234] G is the feedback gain matrix;

[0235] 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. 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 system instability. In order to ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used to obtain the necessary and sufficient conditions for ensuring the stability of the full-order observer:

[0236]

[0237] There are three equations and four unknowns in the condition, so the solution is not unique. Assuming g4 = 0, we can get a feedback matrix selection range that can ensure the stability of the full-order observer:

[0238]

[0239] From the formula, we can see that g1≥0, g3≥0 always holds true. By introducing adjustment coefficients a and b,

[0240] a≥0,b≥0

[0241] The new feedback matrix is ​​obtained as:

[0242]

[0243] Step 2.6, subtract the equation of the induction motor full-order observer from the induction motor state equation to obtain the system state error equation. According to Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate estimation of the speed, and the speed adaptive law is simplified to:

[0244]

[0245] in, is the estimated value of the rotation speed, is the stator current error of phase a, is the β-phase stator current error, is the estimated rotor flux of phase a, is the estimated rotor flux of the β phase, k p and k i are the proportional coefficient and the integral coefficient respectively.

[0246] 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 to improve the robustness of the system;

[0247] Step 3 is implemented as follows:

[0248] Step 3.1, taking the stator resistance as a time-varying parameter, the state equation of the induction motor and the full-order adaptive observer are subtracted to obtain the state error equation, as shown below:

[0249]

[0250]

[0251] Step 3.2: By defining the Lyapunov function, the stator resistance adaptation rate is obtained by 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:

[0252]

[0253] 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 estimated value of the induction motor obtained in step 2 as inputs of the prediction model, predict the stator flux linkage and speed at time k+1, and obtain the stator flux linkage predicted value and speed predicted value;

[0254] Step 4 is implemented according to the following steps:

[0255] Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux and speed are estimated by the full-order observer;

[0256] Step 4.2: Based on the forward Euler discretization formula, the predicted value of the stator flux and the predicted value of the stator current at time k+1 are obtained:

[0257]

[0258] 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 are the stator current vector components at time k, u s (k) is the stator voltage vector component at time k;

[0259] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted, and the conversion relationship between the rotor flux and the stator flux is:

[0260]

[0261] Step 4.4: Select the state variable i in the mathematical model of the induction motor s and ψ s, and the motor speed is considered to be constant in a very short time, then the stator current differential equation is obtained after forward Euler discretization to obtain the k+1 stator current prediction value, which is expressed as:

[0262]

[0263] Where: is the stator resistance identified in step 302;

[0264] Step 4.5: According to the predicted value of stator flux at time k+1 and the predicted value of stator current at time k+1, the predicted value of electromagnetic torque at time k+1 is obtained. The predicted value of electromagnetic torque at time k+1 is:

[0265]

[0266] 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 stator current at time k+1;

[0267] Step 4.6: According to the motion equation of the induction motor, the predicted speed value at time k+1 is obtained:

[0268]

[0269] Step 4.7: Get the estimated speed according to step 2.6 Substitute into the formula in step 4.6 to get the speed prediction value According to step 4.2, the predicted value of magnetic flux is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0270]

[0271] in, is a given stator flux amplitude, ω r * Referring to the speed term, λ1 is the weight coefficient of the flux term, and λ2 is the weight coefficient of the speed term. is the absolute value of the stator flux prediction value at time k+1;

[0272] The weight coefficient of the magnetic flux term is λ1, which is expressed by the following formula:

[0273]

[0274] Finally, r *It is the reference speed term, and its influence is determined by the weight coefficient λ2, which is generally obtained through simulation and experimental debugging.

[0275] Step 5: According to 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.

[0276] The present invention introduces a full-order observer to estimate the speed and flux of the motor. The speed and flux are predicted and controlled by a prediction model, and direct speed control is adopted by model prediction, which eliminates the speed loop and adopts a single-loop control structure to improve the dynamic response speed of the system. The optimal switching state is obtained through a cost function to improve the dynamic and steady-state performance of the system and reduce current pulsation and switching losses. A stator resistance parameter identification module is introduced to update the stator resistance in real time, thereby improving the performance of the observer and model predictive control. A load torque observer is introduced to compensate for the electromagnetic torque, thereby improving the speed dynamic response, load response and tracking performance of the motor.

Claims

1. A sensorless model predictive speed control method for an induction motor, characterized in that: Follow the steps below to implement it: 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; Step 2: construct a full-order observer, and obtain an estimated value of the rotor speed and the flux linkage of the induction motor through the full-order observer; Step 3: Introduce the parameter identification of the stator resistance into the motor speed estimation and model prediction module; Step 4: Establish a prediction model to predict the stator flux and speed at time k+1 to obtain the stator flux prediction value and the speed prediction value; 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.

2. The induction motor sensorless model predictive speed control method according to claim 1, characterized in that: 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: 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.

3. The sensorless model predictive speed control method for an induction motor according to claim 2, characterized in that: The step 2 is specifically implemented according to the following steps: Step 2.1, design a state observer as an adjustable model with reference to 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 according to the input and output of the controlled object; Step 2.3: Take the induction motor itself as the reference model and the constructed full-order observer as the adjustable model, introduce the idea of ​​feedback design, and 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; Step 2.4: Based on the mathematical model of the induction motor and the design principle of the full-order adaptive observer: Where: G is the feedback gain matrix; Step 2.5: Using the Routh-Hurwitz stability criterion, we obtain the necessary and sufficient conditions to ensure the stability of the full-order observer: There are three equations and four unknowns in the conditions, so the solution is not unique. Assuming g4 = 0, we can obtain a feedback matrix selection range that can ensure the stability of the full-order observer: From the formula, we can see that g1≥0, g3≥0 always holds true. By introducing adjustment coefficients a and b, a≥0,b≥0 The new feedback matrix is ​​obtained as: Step 2.6: Subtract the equation of the induction motor full-order observer from the state equation of the induction motor to obtain the state error equation of the system. According to the Lyapunov stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate estimation of the speed. The speed adaptive law is simplified to: in, is the estimated value of the rotation speed, is the stator current error of phase a, is the β-phase stator current error, is the estimated rotor flux of phase a, is the estimated rotor flux of β phase, k p and k i are the proportional coefficient and the integral coefficient respectively.

4. The sensorless model predictive speed control method for an induction motor according to claim 3, characterized in that: The step 3 is specifically implemented according to the following steps: Step 3.1, taking the stator resistance as a time-varying parameter, the state equation of the induction motor and the full-order adaptive observer are subtracted to obtain the state error equation, as shown below: Step 3.2, by defining the Lyapunov function, the stator resistance adaptation rate is obtained by the Lyapunov stability law, and the PI regulator is used to quickly and conveniently adjust the final stator resistance adaptation rate:

5. The induction motor sensorless model predictive speed control method according to claim 4, characterized in that: The step 4 is specifically implemented according to the following steps: Step 4.1, according to the mathematical model of the induction motor in the two-phase stationary coordinate system, the stator flux and speed are estimated by the full-order observer; Step 4.2: Based on the forward Euler discretization formula, the predicted value of the stator flux and the predicted value of the stator current at time k+1 are obtained: 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 are the stator current vector components at time k, u s (k) is the stator voltage vector component at time k; Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted, and the conversion relationship between the rotor flux and the stator flux is: Step 4.4: Select the state variable i in the mathematical model of the induction motor s and ψ s , and the motor speed is considered to be constant in a very short time, then the stator current differential equation is obtained after forward Euler discretization to obtain the k+1 stator current prediction value, which is expressed as: Where: is the stator resistance identified in step 302; Step 4.5: According to the predicted value of stator flux at time k+1 and the predicted value of stator current at time k+1, the predicted value of electromagnetic torque at time k+1 is obtained. The predicted value of electromagnetic torque at time k+1 is: 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 stator current at time k+1; Step 4.6: According to the motion equation of the induction motor, the predicted speed value at time k+1 is obtained: Step 4.7: Get the estimated speed according to step 2.6 Substitute into the formula in step 4.6 to get the speed prediction value According to step 4.2, the predicted value of magnetic flux is obtained The speed prediction value and flux prediction value are used to construct the cost function shown below: in, is a given stator flux amplitude, ω r * Referring to the speed term, λ1 is the weight coefficient of the flux term, and λ2 is the weight coefficient of the speed term. is the absolute value of the stator flux prediction value at time k+1; The weight coefficient of the magnetic flux term is λ1, which is expressed by the following formula: Finally, r * is the reference speed term.

6. The sensorless model predictive speed control method for an induction motor according to claim 5, characterized in that: The step 5 is specifically implemented according to the following steps: Step 5.1, the motion equation 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 according to the motion equation of the induction motor as follows: ω r Motor mechanical angular velocity, J Motor inertia, T e Electromagnetic torque, k1, k2 are matrix gain coefficients, To estimate the motor speed, n p is the number of motor pole pairs, To estimate the load torque; Step 5.3: According to the designed reduced-order state observer, the characteristic equation of the observer is Step 5.4: Select the appropriate desired pole a1a2 to keep the system stable, solve the observer characteristic equation to obtain the values ​​of k1 and k2, construct the feedback gain matrix, and obtain the estimated value of the load torque; <h2 style=";text-align:left;direction:ltr">s<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> -(a1+a2)s+a1a2=0 Step 5.5: Feedback the load torque and the torque output by the torque regulator to step 4.6 to obtain the speed prediction value at time k+1. Substitute the stator resistance identified in step 3.2 into step 4.4 to obtain the speed prediction value at time k+1. This can update the motor parameters in real time, making the model prediction speed control more accurate.

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