CN117997188A - Self-adaptive high-order terminal sliding mode observer and sensorless control method of permanent magnet synchronous motor based on same - Google Patents
Self-adaptive high-order terminal sliding mode observer and sensorless control method of permanent magnet synchronous motor based on same Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/22—Current control, e.g. using a current control loop
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
- H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
- H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters
- H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation
- H02P27/085—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation wherein the PWM mode is adapted on the running conditions of the motor, e.g. the switching frequency
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/14—Electronic commutators
- H02P6/16—Circuit arrangements for detecting position
- H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
- H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings
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- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
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Abstract
本发明公开了一种自适应高阶终端滑模观测器、及基于此观测器的永磁同步电机无传感器控制方法，主要步骤为：1、建立永磁同步电机在α‑β两相静止坐标系下的电流估计误差状态方程并设计非线性二阶系统；2、基于系统中的状态变量设计非奇异终端滑模面；3、根据上述系统和滑模面设计高阶滑模控制律；4、设计自适应律；5、构造自适应高阶终端滑模观测器；6、设计转速控制器；7、设计无传感器控制系统。本发明的优点：一，构造非奇异终端滑模面，使得电流观测误差在有限时间收敛到零，避免奇异问题；二，采用高阶滑模控制律，降低抖振；三、设计的自适应律无需计算所估计变量的界限便可实现估计变量的实时高精度估计，降低滑模观测器的估计抖振。
The present invention discloses an adaptive high-order terminal sliding mode observer and a sensorless control method for a permanent magnet synchronous motor based on the observer, and the main steps are: 1. Establishing the current estimation error state equation of the permanent magnet synchronous motor in the α-β two-phase stationary coordinate system and designing a nonlinear second-order system; 2. Designing a non-singular terminal sliding mode surface based on the state variables in the system; 3. Designing a high-order sliding mode control law according to the above system and the sliding mode surface; 4. Designing an adaptive law; 5. Constructing an adaptive high-order terminal sliding mode observer; 6. Designing a speed controller; 7. Designing a sensorless control system. The advantages of the present invention are: 1. Constructing a non-singular terminal sliding mode surface so that the current observation error converges to zero in a finite time to avoid singular problems; 2. Using a high-order sliding mode control law to reduce jitter; 3. The designed adaptive law can realize real-time high-precision estimation of the estimated variable without calculating the limit of the estimated variable, thereby reducing the estimated jitter of the sliding mode observer.
Description
Technical Field
The invention belongs to the field of permanent magnet synchronous motor control, relates to a sensorless control method of a permanent magnet synchronous motor, and particularly relates to a self-adaptive high-order terminal sliding mode observer and a sensorless control method of a permanent magnet synchronous motor based on the observer.
Background
In recent years, the permanent magnet synchronous motor has the advantages of small volume, high power density, high efficiency, energy conservation and the like, and is widely used in the fields of household appliances, wind power generation, industrial automation, aerospace, electric automobiles and the like. Permanent magnet synchronous motors are a complex system, however, susceptible to disturbances from various factors. Therefore, in designing a control strategy for a permanent magnet synchronous motor, strong coupling and non-linearity problems between multiple variables need to be considered. In order to achieve effective vector control, it is necessary to accurately measure rotor position and speed, and to transform and feedback the voltage vector. For this reason, it is often necessary to install some additional mechanical sensors on the motor shaft to obtain these measurement information. However, when the mechanical sensor works in some occasions such as aerospace, wind power generation and the like, the service life is greatly influenced, so that the reliability of the whole control system is reduced; second, high precision sensors are also expensive. Therefore, the research on high-precision sensorless control is a problem to be solved in the motor control neighborhood in the future.
Current sensorless control research is largely divided into two types: saliency-based studies and model-based approaches. Saliency-based methods are typically used in control systems for motors at zero low speed; model-based methods are typically used for medium-high speed control systems when the back EMF of the motor is large. The common control method based on the model comprises a sliding mode observer method, a model reference self-adaptive system and an extended Kalman filtering method, and the sliding mode observer method has the advantages of low requirements on the accuracy of a motor mathematical model, simple realization, strong robustness and the like, so that the sliding mode observer method is widely paid attention to by researchers. However, since the sliding mode observer has a high-frequency switching term, an estimation buffeting problem is inevitably caused, and therefore, the sliding mode observer with smaller buffeting needs to be designed to improve the estimation accuracy of back electromotive force.
Disclosure of Invention
In order to reduce the observation buffeting of back electromotive force in sensorless control of a permanent magnet synchronous motor and improve the estimation precision of the rotor position and the rotating speed, the invention provides a self-adaptive high-order terminal sliding mode observer and a sensorless control method of the permanent magnet synchronous motor based on the observer, which comprises the following steps:
Step 1, establishing a current state and an observer equation of the surface-mounted permanent magnet synchronous motor under an alpha-beta two-phase static coordinate system, calculating a state equation of a current estimation error and designing a nonlinear second-order system taking the current estimation error as a state variable;
Step 2, designing a nonsingular terminal sliding mode surface based on state variables in a system;
step 3, designing a high-order terminal sliding mode control law according to the nonlinear second-order system and the nonsingular terminal sliding surface;
step 4, designing a self-adaptive law;
Step 5, combining the self-adaptive law with a high-order terminal sliding mode control law, and designing a self-adaptive high-order terminal sliding mode observer;
Step 6, designing a rotating speed controller;
and 7, designing a sensorless control strategy of the permanent magnet synchronous motor, and completing sensorless control of the permanent magnet synchronous motor.
Further, in the step 1, the current state equation of the permanent magnet synchronous motor in the α - β two-phase stationary coordinate system is:
In the above formula, i α、iβ、uα、uβ is the stator current and voltage of α and β phases, R s is the stator resistance, L s is the equivalent inductance of the stator winding on the α and β axes, and E α、Eβ is the back electromotive force of the α and β phases, and satisfies the following conditions:
In the above description, ψ f is the rotor flux, ω e is the rotor electrical angular velocity, θ e is the rotor position electrical angle;
To obtain an estimate of the extended back emf, a current state observer equation is constructed as:
In the above-mentioned method, the step of, The stator current observation values of the alpha and beta axes are shown, and V α、Vβ is a sliding mode control law;
and taking the difference between the current state observer equation and the current state equation under the static coordinate system to obtain a stator current estimation error state equation, wherein the stator current estimation error state equation is as follows:
In the above-mentioned method, the step of, Stator current estimation errors for the α, β axes;
According to the error equation, considering that the system state variables have no coupling relation in the alpha and beta axes, a nonlinear second-order system taking the current estimation error as the state variable can be designed as follows:
In the above formula, x 1、x2 is a system state; i、/> and/> Respectively a stator current value, an observed value and an observed error value in a nonlinear second-order system; /(I)Control law for the required design in a nonlinear second-order system,/>Sliding mode control law derivative for any axis of alpha and beta; /(I)Is the back electromotive force derivative of any one of alpha phase and beta phase, wherein/(E 1、e2 are constants greater than zero.
Further, in the step 2, the non-singular terminal sliding surface is:
in the above formula, n is a constant greater than zero, 1 < m < 2, "α＝sgn(·)|·|α", sgn (·) is a sign function; it should be noted that in the conventional terminal sliding surface s=x 1+bx2 p/q, b is a coefficient of the state variable x 2, b >0, q > p >0, p, q are odd numbers, and when x 2 =0, Singular phenomena can occur, and the non-singular terminal sliding die surface designed by the design effectively solves the problem.
Further, in the step 3, the higher-order terminal sliding mode control law is:
In the above-mentioned method, the step of, For equivalent control law, the system state can be located on the sliding mode surface,/>To approach the control law, the system state can be accelerated to reach the sliding mode surfaceTo switch control laws, compensation of discontinuous control can be used to keep the system state from leaving the slip plane; a. k is the gain of the approach control law and the switching control law and a >0,/>, respectivelyWhen the system state reaches the sliding mode surface, k-sgn(s) is equivalent to the derivative of the counter electromotive force of the motor, so that the counter electromotive force can be obtained by integrating k-sgn(s), and buffeting caused by the fact that a switching function k-sgn(s) is directly equivalent to the counter electromotive force in a traditional sliding mode observer is reduced;
in addition, the state variable indexes in the high-order terminal sliding mode control law are all larger than 0, and no singular point exists, so that the system is nonsingular, and can be converged to the original point in a limited time through stability demonstration.
Further, in the step 4, as shown in fig. 2, the function expression of the adaptive law is:
In the above formula, k (t) is an adaptive gain, k 0(t)、k1 (t) is an auxiliary intermediate variable, κ 0、κ1 is an adaptive law parameter, and κ 0>0,κ1 >0 respectively.
Further, in the step 5, the functional expression of the adaptive high-order terminal sliding mode observer is:
In the above formula, k α(t)、kβ (t) is the switching control law gain of the sliding mode observer on the alpha and beta axes respectively, a is the approaching control law gain, wherein k α(t)≥0,kβ (t) is equal to or more than 0, a >0, t and n are constants larger than zero, 1 < m < 2, Is stator current observation value of alpha and beta axes,/>For the stator current estimation errors of the alpha and beta axes, u α、uβ is the stator voltage of the alpha and beta phases, R s is the stator resistance, L s is the equivalent inductance of the stator winding on the alpha and beta axes, and S α、sβ is the nonsingular terminal sliding mode surface of the alpha and beta axes;
In addition, the extraction of the rotor position and the rotating speed is realized by adopting a phase-locked loop technology, and the counter electromotive force observed by an observer is used as the input of the phase-locked loop, so that an error signal can be obtained as follows:
Wherein epsilon is an error input signal of a PI controller in a phase-locked loop, E α、Eβ is counter electromotive force of alpha phase and beta phase respectively, For rotor position estimation, E σ is an auxiliary intermediate variable, and E σ＝ψfωe; the parameters of the PI controller in the phase-locked loop are reasonably adjusted, so that the accurate estimation of the rotor position and the rotating speed can be realized.
Further, in the step 6, the functional expression of the PI controller in the rotation speed ring is:
iq＝Kpωeq+∫Kiωeqdt
In the above formula, K p and K i are the proportional gain and the integral gain of the PI controller, ω eq is the error between the rotation speed given value and the actual value, and ω eq can be expressed as:
ωeq＝ωref-ωe
Where ω ref is the given rotational speed and ω e is the estimated rotational speed.
Further, in step 7, as shown in fig. 1, the whole control strategy adopts a vector control strategy, the motor output torque is controlled by a torque current component i q, the outer rotating speed ring and the inner current ring are both tracked and controlled by PI controllers, and the adaptive high-order sliding mode observer and phase-locked loop technology are utilized to replace the use of a sensor in the traditional vector control, and at the moment, the rotor position and the rotating speed are both obtained by a designed algorithm.
The invention has the beneficial effects that:
1) The nonsingular terminal sliding mode surface constructed by the invention can enable the current observation error to be converged to zero in a limited time, so that the singular problem is avoided;
2) The buffeting is reduced by adopting a high-order sliding mode control law;
3) The designed self-adaptive law can realize real-time high-precision estimation of the back electromotive force without calculating the limit of the estimated variable, thereby reducing the estimation buffeting of the sliding mode observer.
Drawings
Table 1 is parameters of the permanent magnet synchronous motor;
FIG. 1 is a block diagram of a sensorless control system of a permanent magnet synchronous motor of a self-adaptive high-order terminal sliding mode observer;
FIG. 2 is an adaptive law block diagram;
FIG. 3 is a diagram of simulation results of the rotor speed estimation and its error for the higher order terminal sliding mode observer;
FIG. 4 is a diagram of simulation results of rotor position estimates and their errors for a high-order terminal sliding mode observer;
FIG. 5 is a diagram of simulation results of the rotor speed estimation and its error for the adaptive high-order terminal sliding mode observer;
fig. 6 is a diagram of simulation results of rotor position estimation and its error for an adaptive high-order terminal sliding mode observer.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The following description of the embodiments of the invention is provided with reference to specific embodiments, but is intended to be exemplary of the invention.
The system structure diagram of the self-adaptive high-order terminal sliding mode observer is shown in fig. 1, and the motor parameters in simulation are shown in table 1.
Table 1 parameters of permanent magnet synchronous motor for simulation
A self-adaptive high-order terminal sliding mode observer and a permanent magnet synchronous motor sensorless control method based on the observer are provided, wherein the realization process of the method is as follows:
in the step 1, the current state equation of the permanent magnet synchronous motor under the alpha-beta two-phase static coordinate system is as follows:
In the above formula, i α、iβ、uα、uβ is the stator current and voltage of α and β phases, R s is the stator resistance, L s is the equivalent inductance of the stator winding on the α and β axes, and E α、Eβ is the back electromotive force of the α and β phases, and satisfies the following conditions:
In the above description, ψ f is the rotor flux, ω e is the rotor electrical angular velocity, θ e is the rotor position electrical angle;
To obtain an estimate of the extended back emf, a current state observer equation is constructed as:
In the above-mentioned method, the step of, The stator current observation values of the alpha and beta axes are shown, and V α、Vβ is a sliding mode control law;
and taking the difference between the current state observer equation and the current state equation under the static coordinate system to obtain a stator current error state equation:
In the above-mentioned method, the step of, Stator current estimation errors for the α, β axes;
According to the error equation, considering that the system state variables have no coupling relation in the alpha and beta axes, a nonlinear second-order system taking the current estimation error as the state variable can be designed as follows:
In the above formula, x 1、x2 is a system state; i、/> and/> Respectively a stator current value, an observed value and an observed error value in a nonlinear second-order system; /(I)Control law for the required design in a nonlinear second-order system,/>Sliding mode control law derivative for any axis of alpha and beta; /(I)Is the derivative of back electromotive force of any one of alpha phase and beta phase and/>E 1、e2 are constants greater than zero.
In the step2, the nonsingular terminal sliding mode surface is as follows:
In the above formula, n is a constant greater than zero, 1 < m < 2, "α＝sgn(·)|·|α", sgn (·) is a sign function; it should be noted that in the conventional terminal sliding surface s=x 1+bx2 p/q, b is a coefficient of the state variable x 2, b >0, g > p >0, p, q are odd numbers, and when x 2 =0, Singular phenomena can occur, and the non-singular terminal sliding die surface designed by the design effectively solves the problem.
In the step 3, the higher-order terminal sliding mode control lawThe method comprises the following steps:
In the above-mentioned method, the step of, For equivalent control law, the system state can be located on the sliding mode surface,/>To approach the control law, the system state can be accelerated to reach the sliding mode surfaceTo switch control laws, compensation of discontinuous control can be used to keep the system state from leaving the slip plane; a. k is the gain of the approach control law and the switching control law and a >0,/>, respectivelyWhen the system state reaches the sliding mode surface, k-sgn(s) is equivalent to the derivative of the counter electromotive force of the motor, so that the counter electromotive force can be obtained by integrating k-sgn(s), and buffeting caused by the fact that a switching function k-sgn(s) is directly equivalent to the counter electromotive force in a traditional sliding mode observer is reduced;
in addition, the state variable indexes in the high-order terminal sliding mode control law are all larger than 0, and no singular point exists, so that the system is nonsingular, and can be converged to the original point in a limited time through stability demonstration.
In the step 4, the function expression of the adaptive law is:
In the above formula, k (t) is an adaptive gain, k 0(t)、k1 (t) is an auxiliary intermediate variable, κ 0、κ1 is an adaptive law parameter, and κ 0>0,κ1 >0 respectively.
In the step 5, the functional expression of the adaptive high-order terminal sliding mode observer is:
In the above formula, k α(t)、kβ (t) is the switching control law gain of the sliding mode observer on the alpha and beta axes respectively, a is the approaching control law gain, wherein k α(t)≥0,kβ (t) is equal to or more than 0, a > theta, t and n are constants larger than zero, 1 < m < 2, Is stator current observation value of alpha and beta axes,/>For the stator current estimation errors of the alpha and beta axes, u α、uβ is the stator voltage of the alpha and beta phases, R s is the stator resistance, L s is the equivalent inductance of the stator winding on the alpha and beta axes, and s α、sβ is the nonsingular terminal sliding mode surface of the alpha and beta axes;
In addition, the extraction of the rotor position and the rotating speed is realized by adopting a phase-locked loop technology, and the counter electromotive force observed by an observer is used as the input of the phase-locked loop, so that an error signal can be obtained as follows:
Wherein epsilon is an error input signal of a PI controller in a phase-locked loop, E α、Eβ is counter electromotive force of alpha phase and beta phase respectively, For rotor position estimation, E σ is an auxiliary intermediate variable, and E σ＝ψfωe; the parameters of the PI controller in the phase-locked loop are reasonably adjusted, so that the accurate estimation of the rotor position and the rotating speed can be realized.
In the step 6, the functional expression of the PI controller in the rotation speed ring is:
iq＝Kpωeq+∫Kiωeqdt
In the above formula, K p and K i are the proportional gain and the integral gain of the PI controller, ω eq is the error between the rotation speed given value and the actual value, and ω eq can be expressed as:
ωeq＝ωref-ωe
Where ω ref is the given rotational speed and ω e is the estimated rotational speed.
In the step 7, the whole control strategy adopts a vector control strategy, the motor output torque is only controlled by a torque current component i q, the rotating speed outer ring and the current inner ring are both tracked and controlled by a PI controller, and the self-adaptive high-order sliding mode observer and phase-locked loop technology are utilized to replace the use of a sensor in the traditional vector control, so that the rotor position and the rotating speed are obtained by a designed algorithm.
Specifically, at t=0, the motor starts from 0rpm to a given speed of 1000rpm, and at t=0.3 s, the speed drops suddenly to 500rpm, the adaptive high-order terminal sliding mode observer parameters n=0.98, m=1.14, a=1200, κ 0＝100,κ1 =1000 are chosen.
In the control system, a series structure controller is adopted for both the current loop and the rotating speed loop. The current loop adopts two PI controllers, so that current tracking errors of d and q axis currents are stabilized respectively. Although an advanced control technology can be adopted for the current loop in order to improve the tracking precision of the current controller, due to the complexity of the control technology in real-time implementation, the PI controller can well ensure the high tracking precision of the current loop, so the design of the current controller is based on the PI controller, the parameters K p×50,Ki = 2000 in the d-axis current loop controller and the parameters K p＝50,Ki = 2000 in the g-axis current loop controller are selected; in the above step 6, the design of the rotational speed loop controller is also based on the PI controller, and the parameter K p＝0.3,Ki =6 of the controller is selected.
When the position and the rotating speed of the rotor are extracted by using an anti-positive tangent method, the angle is often differentiated to obtain the speed, so that the fluctuation of a speed signal is serious, the phase-locked loop realizes the tracking of the rotating speed by using an angle change rate through a PI controller, and an integral link in the controller enables the speed signal to be smoother, so that the position and the rotating speed of the rotor are extracted by using a phase-locked loop technology, the position electrical angle and the electrical angular speed of the rotor can be accurately estimated by reasonably adjusting parameters of the PI regulator in the phase-locked loop, and PI parameters in the phase-locked loop are set to be K p＝4.98,Ki =0.002.
A self-adaptive high-order terminal sliding mode observer and a sensorless control strategy of the permanent magnet synchronous motor based on the observer are designed, and the control effect of the invention is verified by simulation comparison in a Simulink. Specifically, the initial expected rotating speed of the permanent magnet synchronous motor is set to 1000rpm, and the sudden drop rotating speed working condition is set. Fig. 3 and 4 are diagrams of simulation results of a high-order terminal sliding mode observer, fig. 3 is a diagram of simulation results of a rotor speed estimated value and an error thereof, and fig. 4 is a diagram of simulation results of a rotor position estimated value and an error thereof. Fig. 5 and 6 are simulation result diagrams of the adaptive high-order terminal sliding mode observer, fig. 5 is a simulation result diagram of a rotor speed estimated value and an error thereof, and fig. 6 is a simulation result diagram of a rotor position estimated value and an error thereof.
From simulation results, in comprehensive terms, compared with the high-order terminal sliding mode observer, the self-adaptive high-order terminal sliding mode observer has the advantages that the observed counter electromotive force has smaller buffeting and has better tracking performance on the rotor position and the rotating speed.
The above list of detailed descriptions is only specific to practical embodiments of the present invention, and they are not intended to limit the scope of the present invention, and all equivalent manners or modifications that do not depart from the technical scope of the present invention should be included in the scope of the present invention.
Claims (10)
1. The sensorless control method of the permanent magnet synchronous motor based on the self-adaptive high-order terminal sliding mode observer is characterized by comprising the following steps of:
S1, establishing a current state and an observer equation of the surface-mounted permanent magnet synchronous motor under an alpha-beta two-phase static coordinate system, calculating a state equation of a current estimation error and designing a nonlinear second-order system taking the current estimation error as a state variable;
S2, designing a nonsingular terminal sliding mode surface based on state variables in a system;
s3, designing a high-order terminal sliding mode control law according to the nonlinear second-order system and the nonsingular terminal sliding surface;
s4, designing a self-adaptive law;
s5, combining the self-adaptive law with a high-order terminal sliding mode control law, and designing a self-adaptive high-order terminal sliding mode observer;
S6, designing a rotating speed controller;
S7, designing a sensorless control strategy of the permanent magnet synchronous motor, and completing sensorless control of the permanent magnet synchronous motor.
2. The sensorless control method of a permanent magnet synchronous motor based on an adaptive high-order terminal sliding mode observer according to claim 1, wherein in S1, the current state equation of the permanent magnet synchronous motor in an α - β two-phase stationary coordinate system is:
In the above formula, i α、iβ、uα、uβ is the stator current and voltage of α and β phases, R s is the stator resistance, L s is the equivalent inductance of the stator winding on the α and β axes, and E α、Eβ is the back electromotive force of the α and β phases, and satisfies the following conditions:
In the above description, ψ f is the rotor flux, ω e is the rotor electrical angular velocity, θ e is the rotor position electrical angle;
the constructed current state observer equation is:
In the above-mentioned method, the step of, The observed values of stator currents of the alpha and beta axes are V α、Vβ which is a sliding mode control law.
3. The sensorless control method of permanent magnet synchronous motor based on the adaptive high-order terminal sliding mode observer according to claim 2, wherein in step S1, the state equation of the calculated current estimation error is specifically as follows:
and taking the difference between the current state observer equation and the current state equation under the static coordinate system to obtain a stator current error state equation:
In the above-mentioned method, the step of, Stator current estimation errors for the α, β axes;
The nonlinear second-order system with current estimation error as state variable is designed as follows:
In the above formula, x 1、x2 is a system state; wherein/> E 1、e2 are constants greater than zero.
4. The sensorless control method of a permanent magnet synchronous motor based on a self-adaptive high-order terminal sliding mode observer according to claim 1, wherein in S2, a nonsingular terminal sliding mode surface is designed as follows:
In the above formula, n is a constant greater than zero, 1 < m < 2, "α＝sgn(·)|·|α", sgn (·) is a sign function.
5. The sensorless control method of permanent magnet synchronous motor based on self-adaptive high-order terminal sliding mode observer according to claim 1, wherein in S3, the high-order terminal sliding mode control law is designed as follows:
In the above-mentioned method, the step of, For equivalent control law, the system state can be located on the sliding mode surface,/>To approach the control law, the system state can be accelerated to reach the sliding mode surfaceTo switch control laws, compensation of discontinuous control can be used to keep the system state from leaving the slip plane; a. k is the gain of the approach control law and the switching control law and a >0,/>, respectivelyWhen the system state reaches the sliding mode surface, k-sgn(s) is equivalent to the derivative of the counter electromotive force of the motor, so that the counter electromotive force can be obtained by integrating k-sgn(s), and buffeting caused by the fact that a switching function k-sgn(s) is directly equivalent to the counter electromotive force in a traditional sliding mode observer is reduced; the state variable indexes in the high-order terminal sliding mode control law are all larger than 0, no singular point exists, and the state variable indexes are nonsingular.
6. The sensorless control method of permanent magnet synchronous motor based on the adaptive high-order terminal sliding mode observer according to claim 5, wherein the adaptive law in S4 is designed as follows:
In the above formula, k (t) is an adaptive gain, k 0(t)、k1 (t) is an auxiliary intermediate variable, and κ 0、κ1 is an adaptive law parameter, and κ 0>0,κ1 >0.
7. The sensorless control method of permanent magnet synchronous motor based on adaptive high-order terminal sliding mode observer according to claim 6, wherein in S5, the adaptive high-order terminal sliding mode observer is designed to:
In the above formula, k α(t)、kβ (t) is the switching control law gain of the sliding mode observer on the alpha and beta axes respectively, a is the approaching control law gain, wherein k α(t)≥0,kβ (t) is equal to or more than 0, a >0, t and n are constants larger than zero, 1 < m < 2, Is stator current observation value of alpha and beta axes,/>For the stator current estimation errors of the alpha and beta axes, u α、uβ is the stator voltage of the alpha and beta phases, R s is the stator resistance, L s is the equivalent inductance of the stator winding on the alpha and beta axes, and S α、sβ is the nonsingular terminal sliding mode surface of the alpha and beta axes;
In addition, the extraction of the rotor position and the rotating speed is realized by adopting a phase-locked loop technology, and the counter electromotive force observed by an observer is used as the input of the phase-locked loop, so that an error signal can be obtained as follows:
Wherein epsilon is an error input signal of a PI controller in a phase-locked loop, E α、Eβ is counter electromotive force of alpha phase and beta phase respectively, For rotor position estimation, E σ is an auxiliary intermediate variable, and E σ＝ψfωe; the parameters of the PI controller in the phase-locked loop are reasonably adjusted, so that the accurate estimation of the rotor position and the rotating speed can be realized.
8. The sensorless control method of permanent magnet synchronous motor based on self-adaptive high-order terminal sliding mode observer according to claim 7, wherein in S6, the rotation speed loop adopts PI controller, and the PI controller is designed as follows:
iq＝Kpωeq+∫Kiωeqdt
In the above formula, K p and K i are the proportional gain and the integral gain of the PI controller, ω eq is the error between the rotation speed given value and the actual value, and ω eq can be expressed as:
ωeq＝ωref-ωe
Where ω ref is the given rotational speed and ω e is the estimated rotational speed.
9. The sensorless control method of permanent magnet synchronous motor based on self-adaptive high-order terminal sliding-mode observer according to claim 8, wherein in S7, the whole control strategy adopts vector control strategy, the motor output torque is controlled by torque current component i q only, the outer loop and inner loop of rotating speed are both tracked and controlled by PI controller, the self-adaptive high-order sliding-mode observer and phase-locked loop technology are utilized to replace the use of sensors in traditional vector control, and the rotor position and rotating speed are obtained by designed algorithm.
10. An adaptive high-order terminal sliding mode observer, characterized in that the observer is obtained by steps S1-S5 according to any one of claims 1-9.
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| CN118367830B (en) * | 2024-05-13 | 2025-04-25 | 中南大学 | Adaptive back-EMF observer method for permanent magnet synchronous motor based on coordinate transformation |
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