Sensorless model predictive speed control method for induction motor

Abstract

The application discloses a sensorless model predictive speed control method of an induction motor, and first, a mathematical model of the induction motor is modeled 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 rotor speed and an estimated value of a magnetic chain of the induction motor through the full-order observer; parameter identification of a stator resistance is introduced into a motor speed estimation and a model prediction module; then, a prediction model is established to predict the stator magnetic chain and the rotor speed at k+1 time to obtain a stator magnetic chain prediction value and a rotor speed prediction value; finally, a reduced-order load torque observer is constructed to perform feedforward compensation on a speed outer ring of a control system to improve the dynamic response of the system. The application solves the problem that sensor faults in the prior art may cause system performance to decrease or even cause system collapse.

Description

Technical Field

[0001] The present 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] The induction motor is a simple motor type. Due to its low cost, easy maintenance, and high reliability, it is widely used in industrial and commercial applications to provide a stable power source. With technological advancements, the demand for motor performance continues to increase, and high-performance AC speed control technology is gradually developing, providing more possibilities for the application of induction motors.

[0003] In recent years, model predictive control (MPC), as an advanced control strategy, has garnered widespread attention in the field of motor control. Applying MPC to induction motors can achieve higher levels of dynamic performance, accuracy, and stability, thereby meeting ever-increasing industrial demands. Traditional MPC (model predictive torque control), MPC (model predictive flux control), and MPC (model predictive current control) all employ a dual closed-loop structure consisting of an outer speed control loop and an inner model predictive control loop. The speed loop parameters require adjustment, increasing system complexity. Model Predictive Direct Speed ​​Control (MPDSC) eliminates the speed loop and adopts a single-loop control structure, improving the system's dynamic response.

[0004] In AC motor speed control systems, sensors are required to determine the motor speed for negative feedback regulation. However, sensors present a number of challenges. For example, sensor failure can lead to system performance degradation or even system crash. Sensor installation also incurs significant costs, and some specific scenarios may not be suitable for sensor installation. Consequently, sensorless control technology has become a 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 the estimated value of the induction motor rotor speed and the estimated value of the flux linkage 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: Build a prediction model k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[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] 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 The stator voltage component below the shaft.

[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: 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, according to the mathematical model of induction motor and the design principle of full-order adaptive observer, we have:

[0022]

[0023] where:

[0024] G is the feedback gain matrix;

[0025] Step 2.5, using the Routh-Hurwitz stability criterion, we get the sufficient and necessary 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. Assume =0,

[0028] We get a range of feedback matrix selection that can ensure the stability of the full-order observer:

[0029]

[0030] From the formula, we can see that , is always true, introduce the adjustment coefficients a and b, so that

[0031]

[0032] The new feedback matrix is:

[0033]

[0034] Step 2.6, the state error equation of the system is obtained by subtracting the equation of the full-order observer of the induction motor from the state equation of the induction motor. According to the Lyapunov stability theorem, the specific equation of the speed adaptive law is derived, which realizes the accurate estimation of the speed. The speed adaptive law is simplified as:

[0035]

[0036] where, is the estimated speed, is the phase stator current error, is the phase stator current error, is the estimated rotor flux of phase, is the estimated rotor flux of phase, and are the proportional coefficient and integral coefficient, respectively.

[0037] Step 3 is implemented as follows:

[0038] Step 3.1: Taking the stator resistance as a time-varying parameter, the state equations of the induction motor and the full-order adaptive observer are subtracted to obtain the state error equation, as shown below:

[0039]

[0040]

[0041] Step 3.2: By defining the Lyapunov function and using the Lyapunov stability law, the stator resistance adaptation rate is obtained. The PI regulator is used to quickly and easily adjust the stator resistance. The final stator resistance adaptation rate is: .

[0042] Step 4 is implemented as follows:

[0043] 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;

[0044] Step 4.2: Based on the forward Euler discretization formula, we get The predicted values ​​of stator flux and stator current at time:

[0045] Where, 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 ;

[0046] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted. The conversion relationship between the rotor flux and the stator flux is:

[0047]

[0048] 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 is expressed as:

[0049]

[0050] Where: , is the stator resistance identified in step 3.2;

[0051] Step 4.5: Based on the predicted value of stator flux at time k+1 and 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:

[0052]

[0053] 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;

[0054] Step 4.6: Based on the motion equation of the induction motor, we get Predicted speed at this moment:

[0055]

[0056] Step 4.7: Get the estimated speed according to step 2.6 Substitute this into the formula in step 4.6 to get the predicted speed value According to step 4.2, the predicted magnetic flux is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0057]

[0058] in, is a given stator flux amplitude, Reference speed term, is the weight coefficient of the magnetic linkage term, is the weight coefficient of the velocity term, is the absolute value of the stator flux prediction value at time k+1;

[0059] The weight coefficient of the magnetic linkage term is , expressed by the following formula:

[0060]

[0061] at last, is the reference speed term.

[0062] Step 5 is implemented as follows:

[0063] Step 5.1. 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] Motor mechanical angular velocity, Motor inertia, electromagnetic torque, is the matrix gain coefficient, To estimate the motor speed, is the number of motor pole pairs, To estimate the load torque;

[0068] Step 5.3: According to the designed reduced-order state observer, the characteristic equation of the observer is:

[0069]

[0070] Step 5.4 Select the appropriate desired extreme point , so that the system remains stable. Solving it together with the observer characteristic equation yields The value of is used to construct the feedback gain matrix and obtain the estimated value of the load torque;

[0071]

[0072]

[0073] Step 5.5: Feed the load torque and the torque output by the torque regulator back to step 4.6 to obtain The predicted speed value at the moment is obtained by substituting the stator resistance identified in step 3.2 into step 4.4. The speed prediction value at each moment can update the motor parameters in real time, making the model prediction speed control more accurate.

[0074] The present invention provides a sensorless model predictive speed control method for an induction motor. This method uses a predictive model to predict speed and flux linkage, improving the system's dynamic response speed. A 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. A load torque observer is introduced to compensate for electromagnetic torque, improving the motor's speed dynamic response, load response, and tracking performance. The load torque observer is constructed based on the induction motor's equation of motion and the principle of reduced-order observers, assuming the rate of change of the load torque is zero within a sampling period. The load torque observer is constructed based on the induction motor's equation of motion and the principle of reduced-order observers. The torque output by the load torque observer and the torque regulator are superimposed on the model predictive torque control algorithm, improving the system's dynamic response. Model predictive speed control is introduced. Traditional model predictive torque control, model predictive flux control, and model predictive current control all employ a dual closed-loop structure consisting of an outer speed control loop and an inner model predictive control loop. The speed loop parameters require adjustment, increasing system complexity. Model predictive direct speed control (MPDSC) eliminates the speed loop and adopts a single-loop control structure, improving the system's dynamic response speed. The cost function is a tool for evaluating the error between the given and predicted values ​​in model-predictive torque control. Therefore, the cost function is closely related to the optimal switching state selected by the control system. Furthermore, the appropriateness of the cost function selection is a crucial factor in determining the effectiveness of model-predictive torque control. An inappropriate cost function directly impacts the selection of the optimal switching state, causing the control system to select an inappropriate switching state as the optimal switching state, thereby impacting the induction motor's control performance. Setting the predicted speed and flux values ​​as cost functions allows for simultaneous control of the motor's speed, flux, and dynamic and steady-state performance. It is understood that the beneficial effects of aspects 2 through 4 above can be found in the relevant description of aspect 1 above and are not further elaborated here. In summary, the present invention introduces a full-order observer to estimate the motor's speed and flux. By using a predictive model to predict and control the speed and flux, and employing model-predictive direct speed control, the speed loop is eliminated, a single-loop control structure is adopted, and the system's dynamic response speed is improved. By using the cost function to obtain the optimal switching state, the system's dynamic and steady-state performance is improved, reducing current ripple and switching losses. A 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. A load torque observer is introduced to compensate for electromagnetic torque, improving the motor's speed dynamic response, load response, and tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 A control block diagram of the sensorless model predictive speed control method for an induction motor according to the present invention;

[0076] Figure 2 This is a block diagram of the principle of the full-order adaptive observer in the sensorless model predictive speed control method of the induction motor of the present invention.

[0077] Figure 3 This is a basic voltage vector block diagram of a two-level inverter in the sensorless model predictive speed control method for an induction motor according to the present invention. DETAILED DESCRIPTION

[0078] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] The induction motor is modeled according to the two-phase stationary coordinate system to obtain the mathematical model of the induction motor; based on 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. By introducing the stator flux error and speed error in the cost function, the dynamic response of the system is improved. 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 Moment, then The stator flux and speed are predicted at each moment to obtain predicted stator flux and speed values. Since model-predictive speed control directly controls the motor speed and flux, changes in load torque during motor operation can lead to system instability. To address this issue, a reduced-order load torque observer is introduced to improve the motor's load response and tracking performance.

[0080] The sensorless model prediction speed control method of the induction motor of the present invention is combined with Figure 1 , specifically follow the steps below:

[0081] 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;

[0082] Step 1 is implemented as follows:

[0083] In the two-phase stationary coordinate system, the mathematical model of the induction motor is:

[0084]

[0085] 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 The stator voltage component below the shaft.

[0086] 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;

[0087] Combine Figure 2~Figure 3 , step 2 is implemented according to the following steps:

[0088] Step 2.1, design a state observer as an adjustable model based on the mathematical model of the induction motor;

[0089] 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;

[0090] 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 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;

[0091] 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:

[0092]

[0093] Where:

[0094] G is the feedback gain matrix;

[0095] Step 2.5, design the feedback gain matrix according to the pole configuration requirements. Assume that the poles of the full-order adaptive observer are the poles of the induction motor. times, and combining the characteristic equations of the two yields the feedback matrix. However, this configuration method is relatively complex. Drawing a pole diagram based on the obtained feedback matrix reveals that the observer's poles are distributed to the left of the motor's poles. As the speed increases, the poles gradually move away from the real and imaginary axes, which can lead to system instability. To ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used to derive the necessary and sufficient conditions for ensuring the stability of the full-order observer:

[0096]

[0097] There are three equations and four unknowns in the condition, so the solution is not unique. =0,

[0098] The selection range of the feedback matrix that can ensure the stability of the full-order observer is obtained:

[0099]

[0100] From the formula we can see , Always holds true, introduce adjustment coefficients a and b, so

[0101]

[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. Based on Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate speed estimation. The speed adaptive law is simplified to:

[0105]

[0106] in, is the estimated value of the rotational speed, for Phase stator current error, for Phase stator current error, for Phase estimated rotor flux, for Phase estimated rotor flux, and are the proportional coefficient and the integral coefficient respectively.

[0107] 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;

[0108] Step 3 is implemented as follows:

[0109] Step 3.1: Taking the stator resistance as a time-varying parameter, the state equations 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 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:

[0113]

[0114] Step 4: Establish a prediction model based on the mathematical model of the induction motor obtained in step 1, and use the estimated speed value and flux linkage value of the induction motor obtained in step 2 as the input of the prediction model. k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[0115] Step 4 is implemented as follows:

[0116] 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;

[0117] Step 4.2: Based on the forward Euler discretization formula, we get The predicted values ​​of stator flux and stator current at the moment:

[0118]

[0119] Where, 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 ;

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

[0121]

[0122] 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 is expressed as:

[0123]

[0124] Where: , is the stator resistance identified in step 3.2;

[0125] Step 4.5: Based on the predicted value of stator flux at time k+1 and 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:

[0126]

[0127] 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;

[0128] Step 4.6: Based on the motion equation of the induction motor, we get Predicted speed at the moment:

[0129]

[0130] Step 4.7: Get the estimated speed according to step 2.6 Substitute this into the formula in step 4.6 to get the predicted speed value According to step 4.2, the predicted 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, Reference speed term, is the weight coefficient of the magnetic linkage term, is the weight coefficient of the velocity term, for k The absolute value of the stator flux prediction value at time +1;

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

[0134]

[0135] at last, is the reference speed term, and its influence is determined by the weight coefficient Decide, It is usually obtained through simulation and experimental debugging.

[0136] 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.

[0137] Step 5 is implemented as follows:

[0138] 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:

[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 based on the motion equation of the induction motor as follows:

[0141]

[0142] Motor mechanical angular velocity, Motor inertia, electromagnetic torque, is the matrix gain coefficient, To estimate the motor speed, 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 , so that the system remains stable. The value of is solved together with the observer characteristic equation, the feedback gain matrix is constructed, and the estimated value of the load torque is obtained;

[0146]

[0147]

[0148] Step 5.5, the load torque and the torque feedback of the torque regulator output are fed back to step 4.6 to obtain the speed prediction value at the moment, and the stator resistance identified in step 3.2 is brought into step 4.4 to obtain the speed prediction value at the moment, so that the motor parameters can be updated in real time, and the model predictive speed control is more accurate.

[0149] Example 1

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

[0151] 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;

[0152] Step 2, according to the induction motor mathematical model obtained in step 1, taking the stator current and rotor flux as state variables, a full-order observer is constructed, and the estimated value of the induction motor rotor speed and the estimated value of the flux 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, according to the induction motor mathematical model obtained in step 1, a prediction model is established, taking the estimated value of the induction motor speed and the estimated value of the flux obtained in step 2 as the input of the prediction model, to predict the stator flux and the speed at k +1 moment, to obtain the stator flux prediction value and the speed prediction value;

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

[0156] Example 2

[0157] The sensorless model prediction speed control method of the induction motor of the present invention is combined with Figure 1 , specifically 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] 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 The stator voltage component below the shaft.

[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 based on 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 based on the input and output of the controlled object;

[0167] 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 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, we can obtain:

[0169]

[0170] Where:

[0171] G is the feedback gain matrix;

[0172] Step 2.5, design the feedback gain matrix according to the pole configuration requirements. Assume that the poles of the full-order adaptive observer are the poles of the induction motor. times, and combining the characteristic equations of the two yields the feedback matrix. However, this configuration method is relatively complex. Drawing a pole diagram based on the obtained feedback matrix reveals that the observer's poles are distributed to the left of the motor's poles. As the speed increases, the poles gradually move away from the real and imaginary axes, which can lead to system instability. To ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used to derive 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. =0,

[0175] The selection range of the feedback matrix that can ensure the stability of the full-order observer is obtained:

[0176]

[0177] From the formula we can see , Always holds true, introduce adjustment coefficients a and b, so

[0178]

[0179] The new feedback matrix is ​​obtained as:

[0180]

[0181] 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. Based on Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate speed estimation. The speed adaptive law is simplified to:

[0182]

[0183] in, is the estimated value of the rotational speed, for Phase stator current error, for Phase stator current error, for Phase estimated rotor flux, for Phase estimated rotor flux, and are the proportional coefficient and the integral coefficient respectively.

[0184] 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;

[0185] Step 4: Establish a prediction model based on the mathematical model of the induction motor obtained in step 1, and use the estimated speed value and flux linkage value of the induction motor obtained in step 2 as the input of the prediction model. k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[0186] Step 4 is implemented as follows:

[0187] 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;

[0188] Step 4.2: Based on the forward Euler discretization formula, we get The predicted values ​​of stator flux and stator current at the moment:

[0189]

[0190] Where, is the system sampling period, for The stator flux component predicted at each moment, for The stator current vector component at time , for The stator voltage vector components at time ;

[0191] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted. The conversion relationship between the rotor flux and the stator flux is:

[0192]

[0193] 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 is expressed as:

[0194]

[0195] Where: , is the stator resistance identified in step 3.2;

[0196] Step 4.5: Based on the predicted value of stator flux at time k+1 and 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:

[0197]

[0198] 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;

[0199] Step 4.6: Based on the motion equation of the induction motor, we get Predicted speed at the moment:

[0200]

[0201] Step 4.7: Get the estimated speed according to step 2.6 Substitute this into the formula in step 4.6 to get the predicted speed value According to step 4.2, the predicted magnetic flux is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0202]

[0203] in, is a given stator flux amplitude, Reference speed term, is the weight coefficient of the magnetic linkage term, is the weight coefficient of the velocity term, for k The absolute value of the stator flux prediction value at time +1;

[0204] The weight coefficient of the magnetic linkage term is , expressed by the following formula:

[0205]

[0206] at last, is the reference speed term, and its influence is determined by the weight coefficient Decide, It is usually obtained through simulation and experimental debugging.

[0207] 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.

[0208] Step 5 is implemented as follows:

[0209] 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:

[0210]

[0211] 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:

[0212]

[0213] Motor mechanical angular velocity, Motor inertia, electromagnetic torque, is the matrix gain coefficient, To estimate the motor speed, is the number of motor pole pairs, To estimate the load torque;

[0214] Step 5.3: According to the designed reduced-order state observer, the characteristic equation of the observer is:

[0215]

[0216] Step 5.4 Select the appropriate desired extreme point , so that the system remains stable. Solving it together with the observer characteristic equation yields The value of is used to construct the feedback gain matrix and obtain the estimated value of the load torque;

[0217]

[0218]

[0219] Step 5.5, the load torque and torque feedback of the torque regulator output to step 4.6 the rotor speed prediction value at the moment, and the stator resistance identified in step 3.2 is brought into step 4.4 to obtain the rotor speed prediction value at the moment, so that the motor parameters can be updated in real time, so that the model prediction speed control is more accurate.

[0220] Example 3

[0221] The sensorless model predictive speed control method of the induction motor of the application combines Figure 1 , and is specifically implemented according to the following steps:

[0222] 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;

[0223] Step 1 is specifically implemented according to the following steps:

[0224] The mathematical model of the induction motor in the two-phase stationary coordinate system is:

[0225]

[0226] Among them, is the stator resistance, is the leakage coefficient, is the stator inductance, is the rotor time constant, , is the mutual inductance, is the rotor inductance, is the rotor speed, , is the stator current, is the rotor flux vector, , is the stator voltage component in the d-axis, is the stator voltage component in the q-axis.

[0227] Step 2, according to the mathematical model of the induction motor obtained in step 1, taking the stator current and the rotor flux as the state variables, a full-order observer is constructed, and the estimated value of the rotor speed and the estimated value of the flux of the induction motor are obtained through the full-order observer;

[0228] Step 2 is specifically implemented according to the following steps:

[0229] Step 2.1, refer to the induction motor mathematical model to design a state observer as an adjustable model;

[0230] 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;

[0231] 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 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;

[0232] 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:

[0233]

[0234] Where:

[0235] G is the feedback gain matrix;

[0236] Step 2.5, design the feedback gain matrix according to the pole configuration requirements. Assume that the poles of the full-order adaptive observer are the poles of the induction motor. times, and combining the characteristic equations of the two yields the feedback matrix. However, this configuration method is relatively complex. Drawing a pole diagram based on the obtained feedback matrix reveals that the observer's poles are distributed to the left of the motor's poles. As the speed increases, the poles gradually move away from the real and imaginary axes, which can lead to system instability. To ensure the stability of the full-order observer, the Routh-Hurwitz stability criterion is used to derive the necessary and sufficient conditions for ensuring the stability of the full-order observer:

[0237]

[0238] There are three equations and four unknowns in the condition, so the solution is not unique. =0,

[0239] The selection range of the feedback matrix that can ensure the stability of the full-order observer is obtained:

[0240]

[0241] From the formula we can see , Always holds true, introduce adjustment coefficients a and b, so

[0242]

[0243] The new feedback matrix is ​​obtained as:

[0244]

[0245] 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. Based on Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived, thereby achieving accurate speed estimation. The speed adaptive law is simplified to:

[0246]

[0247] in, is the estimated value of the rotational speed, for Phase stator current error, for Phase stator current error, for Phase estimated rotor flux, for Phase estimated rotor flux, and are the proportional coefficient and the integral coefficient respectively.

[0248] 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;

[0249] Step 3 is implemented as follows:

[0250] Step 3.1: Taking the stator resistance as a time-varying parameter, the state equations of the induction motor and the full-order adaptive observer are subtracted to obtain the state error equation, as shown below:

[0251]

[0252]

[0253] 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:

[0254]

[0255] Step 4: Establish a prediction model based on the mathematical model of the induction motor obtained in step 1, and use the estimated speed value and flux linkage value of the induction motor obtained in step 2 as the input of the prediction model. k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value;

[0256] Step 4 is implemented as follows:

[0257] 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;

[0258] Step 4.2: Based on the forward Euler discretization formula, we get The predicted values ​​of stator flux and stator current at the moment:

[0259]

[0260] Where, 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 ;

[0261] Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted. The conversion relationship between the rotor flux and the stator flux is:

[0262]

[0263] 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 is expressed as:

[0264]

[0265] Where: , is the stator resistance identified in step 3.2;

[0266] Step 4.5: Based on the predicted value of stator flux at time k+1 and 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:

[0267]

[0268] 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;

[0269] Step 4.6: Based on the motion equation of the induction motor, we get Predicted speed at this moment:

[0270]

[0271] Step 4.7: Get the estimated speed according to step 2.6 Substitute this into the formula in step 4.6 to get the predicted speed value According to step 4.2, the magnetic flux prediction value is obtained. The speed prediction value and flux prediction value are used to construct the cost function shown below:

[0272]

[0273] in, is a given stator flux amplitude, Reference speed term, is the weight coefficient of the magnetic linkage term, is the weight coefficient of the velocity term, for k The absolute value of the stator flux prediction value at time +1;

[0274] The weight coefficient of the magnetic linkage term is , expressed by the following formula:

[0275]

[0276] at last, is the reference speed term, and its influence is determined by the weight coefficient Decide, It is usually obtained through simulation and experimental debugging.

[0277] 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.

[0278] The present invention introduces a full-order observer to estimate the motor's speed and flux. The speed and flux are predictively controlled using a predictive model, and model-predictive direct speed control is adopted, eliminating the speed loop. A single-loop control structure is adopted to improve the system's dynamic response speed. The optimal switching state is obtained through a cost function, thereby improving the system's dynamic and steady-state performance and reducing current pulsation and switching losses. A 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. A load torque observer is introduced to compensate for electromagnetic torque, improving the motor's speed dynamic response, load response, and tracking performance.

Claims

1. A sensorless model predictive speed 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; Step 2: construct a full-order observer, and obtain the estimated value of the induction motor rotor speed and the estimated value of the flux linkage through the full-order observer; 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: 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, we can obtain: Where: G is the feedback gain matrix; Step 2.5: Using the Routh-Hurwitz stability criterion, we can obtain the necessary and sufficient conditions for the stability of the full-order observer: 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: Subtract the equation of the induction motor full-order observer from the induction motor state equation to obtain the system state error equation. Based on Lyapunov's stability theorem, the specific equation of the speed adaptive law is derived. This allows for accurate speed estimation. The speed adaptive law is simplified to: in, is the estimated value of the rotational speed, for Phase stator current error, for Phase stator current error, for Phase estimated rotor flux, for The estimated rotor flux is the estimated value of the flux. and are the proportional coefficient and the integral coefficient respectively; Step 3: Introduce the parameter identification of the stator resistance into the motor speed estimation model prediction module; 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 equations 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 and using the Lyapunov stability law, the stator resistance adaptation rate is obtained. The PI regulator is used to quickly and easily adjust the stator resistance. The final stator resistance adaptation rate is: ； Step 4: Build a prediction model k The stator flux and speed are predicted at time +1 to obtain the stator flux prediction value and the speed prediction value; 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: Where, is the system sampling period, for The stator flux component predicted at each moment, for The stator current vector component at time , for The stator voltage vector components at time ; Step 4.3: For the induction motor model predictive control system, the stator flux is usually predicted. The conversion relationship between the rotor flux and the stator 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 is expressed as: Where: , is the stator resistance identified in step 3.2; Step 4.5: Based on the predicted value of stator flux at time k+1 and 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: Based on the motion equation of the induction motor, we get Predicted speed at this moment: Step 4.7: Get the estimated speed according to step 2.6 Substitute this into the formula in step 4.6 to get the predicted speed value , according to step 4.2, the magnetic flux prediction value 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, Reference speed term, is the weight coefficient of the magnetic linkage term, is the weight coefficient of the velocity term, for k The absolute value of the stator flux prediction value at time +1; The weight coefficient of the magnetic linkage term is , expressed by the following formula: at last, is the reference speed term; 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. 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, is the motor inertia, is the electromagnetic torque, is the matrix gain coefficient, To estimate the motor speed, 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 extreme point 、 , so that the system remains stable, and the observer characteristic equation is solved together to obtain The value of is used to construct the feedback gain matrix and obtain the estimated value of the load torque; Step 5.5: Feed the estimated value of the load torque and the torque output by the torque regulator back to step 4.6 to obtain The predicted speed value at the moment is obtained by substituting the stator resistance identified in step 3.2 into step 4.

4. The current prediction value at each moment and the real-time update of motor parameters make the model prediction speed control more accurate.

2. The sensorless model predictive speed control method for an induction motor according to claim 1, wherein: 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 The stator voltage component below the shaft.

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