Senseless control method and system based on fast and slow time scale characteristics

Abstract

The invention discloses a sensorless control method and system based on fast and slow time scale characteristics, and belongs to the technical field of permanent magnet synchronous motor control. Firstly, a basic dynamic equation of the surface-mounted permanent magnet synchronous motor on a two-phase synchronous rotation orthogonal coordinate system is deduced, and a simplified mathematical model based on fast and slow time scale characteristics is obtained. Then, a novel sliding-mode observer is constructed and used for estimating the position and speed information of the servo system in real time, and therefore non-sensing control is achieved. And finally, based on a singular perturbation theory, respectively carrying out Lyapunov stability analysis in a fast time scale and a slow time scale so as to obtain a gain determination method of the sliding-mode observer. Based on the fast and slow time scale characteristics of the permanent magnet synchronous motor, a novel modeling method and a sensorless control technology are provided, and estimated values of the position and the speed are used in a servo driving system.

Description

Technical Field

[0001] The present application relates to the field of permanent magnet synchronous motor control technology, and in particular to a sensorless control method and system based on fast and slow time scale characteristics. Background Art

[0002] In recent years, with the rapid development of power electronics, automatic control and computer technologies, AC servo control systems have gradually replaced DC drive control systems in the field of high-performance speed regulation. Permanent magnet synchronous motors have a dominant position in AC speed regulation systems due to their high power density and fast dynamic response speed. However, the operating characteristics and dynamic performance of permanent magnet synchronous motors depend on the acquisition accuracy of position and speed. In some places where space is limited or mechanical sensors cannot be installed, sensorless control technology is applied and has become a research hotspot in the field of motor control.

[0003] Sensorless control technology is usually implemented based on an observer, which estimates the position and speed of the servo system online based on the current and voltage dynamics of the permanent magnet synchronous motor. Traditional methods implement sensorless control technology based on the back electromotive force model on a two-phase stationary orthogonal coordinate system, based on inverse tangent operation or phase-locked loop technology. The observer gain parameters of the prior art are usually selected by trial and error, and their criteria lack strict theoretical proof, and the existing methods do not consider the fast and slow time scale characteristics of current and speed. The mathematical model of the permanent magnet synchronous motor usually consists of electrical dynamics and mechanical systems, and the time constants of the two are quite different, which is a typical dual time scale system.

[0004] Therefore, it is very important to design a sensorless control method and system based on the fast and slow time scale characteristics. Summary of the invention

[0005] The present application provides a sensorless control method and system based on fast and slow time scale characteristics, which can be used to solve the technical problem that the prior art does not consider the fast and slow time scale characteristics of current and speed.

[0006] The present application provides a sensorless control system based on fast and slow time scale characteristics, the system includes a nominal voltage module, a sliding mode observer module, a position estimation module, a sliding mode surface module, and a sliding mode control law module, wherein:

[0007] The nominal voltage module is based on the q-axis voltage u q , d-axis current signal i d and velocity estimates Get the q-axis nominal voltage u qo , and sent to the sliding mode observer module;

[0008] The sliding mode observer module estimates the velocity at the previous moment. and the estimated q-axis current And the fast-changing sliding mode control law V q and the slowly varying sliding mode control law V m , get the estimated speed at the current moment and current estimation And simultaneously sent to the sliding mode observer module for iterative calculation of the estimated value at the next moment, the position estimation module and the sliding surface module;

[0009] The position estimation module multiplies the velocity estimate by the number of magnetic pole pairs p n , get the estimated value of electrical angular velocity, integrate to get the estimated value of position And it is used for vector transformation of permanent magnet synchronous motor servo control;

[0010] The sliding surface module estimates the value of the q-axis current and the q-axis current signal i q , calculate the difference to get the q-axis current tracking error Δi q , and is designed as the sliding surface function S q , and sent to the sliding mode control law module;

[0011] The sliding mode control law module is used to calculate the sliding surface function S q Perform the sign function sgn(·) operation and multiply it by the observer gain to obtain the fast-changing sliding mode control law V q and the slowly varying sliding mode control law V m , and sent to the sliding mode observer module.

[0012] On the other hand, the present application provides a sensorless control method based on fast and slow time scale characteristics, which is performed by a sensorless control method and system based on fast and slow time scale characteristics provided by the present application, and the method includes:

[0013] Step 1: Establish a fast and slow time scale mathematical model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system;

[0014] Step 2: Construction of a new sliding mode observer;

[0015] Step 3: Dynamic analysis of fast estimation error;

[0016] Step 4: Dynamic analysis of slow estimation error.

[0017] Furthermore, the fast and slow time scale mathematical model of the two-phase synchronous rotation orthogonal coordinate system in step 1 is:

[0018]

[0019] Among them, d / dt is the differential operator; ω m is the mechanical angular velocity; F is the viscous friction coefficient; J is the moment of inertia; KT =3p n ψ f / 2 is the electromagnetic torque coefficient, p n is the number of magnetic pole pairs, ψ f is the permanent magnet flux; T m is the load torque disturbance; ε=L s / R s is the singular perturbation parameter, L s and R s are the inductance and resistance of the stator winding respectively; i q is the current of the q-axis stator winding; the nominal voltage u qo =u q -ω e L s i d ,u q is the voltage of the q-axis stator winding, i d is the current of the d-axis stator winding, ω e is the electrical angular velocity, and satisfies ω e =p n ω m .

[0020] Furthermore, the mechanical angular velocity ω of the permanent magnet synchronous motor in step 1 is m is the slow mode; and the current i d and i q , compared with the mechanical angular velocity ω m It is a fast dynamic system, a typical fast and slow time scale system; the current i d and i q With ω e Multiply L s i q , L s i d and ψ f The cross-coupled back electromotive force of the d-axis and q-axis are formed respectively;

[0021] To decouple ω e For current i q The influence of , defines the q-axis nominal voltage equation as shown below:

[0022]

[0023] Furthermore, the new sliding mode observer constructed in step 2 is as follows:

[0024]

[0025] Among them, the logo represents the estimated value of the corresponding variable; the sliding mode control law satisfies:

[0026]

[0027] Among them, V m and V q are the slow-changing and fast-changing sliding mode control laws respectively; g m >0 and g q >0 are the slow-varying and fast-varying sliding mode observer gains respectively; “sgn(·)” represents the sign function; the sliding surface is constructed as:

[0028]

[0029] Among them, S q is the sliding surface function; Δi q is the q-axis current estimation error.

[0030] Furthermore, in step 2, the fast and slow time scale systems and the constructed new sliding mode observer are combined to obtain the following observer estimation error dynamic equation:

[0031]

[0032] in, is the speed estimation error;

[0033] The sliding mode observer uses the information of the q-axis. When the estimated error dynamic system meets the convergence conditions, the real-time estimated values ​​of position and velocity can be obtained and used in the sensorless control system of the servo drive.

[0034] Furthermore, the reduced-order fast estimation error dynamic equation obtained in step 3 is:

[0035]

[0036] Where τ is the fast time scale; the symbol “·(τ)” represents the fast time component of the corresponding variable;

[0037] In order to make the fast estimation error dynamics satisfy the Lyapunov stability theory, the fast-varying sliding mode observer gain g q The following constraints must be met:

[0038] g q >p n ψ f |Δω m (τ)|

[0039] Here, the symbol “|·|” represents the absolute value function.

[0040] Furthermore, the reduced-order slow estimation error dynamic equation obtained in step 4 is:

[0041]

[0042] In order to make the slow estimation error dynamics satisfy the Lyapunov stability theory, the slowly varying sliding mode observer gain g m The following constraints must be met:

[0043]

[0044] Where H>0 is the load torque disturbance T m The upper bound value of |T m |≤H.

[0045] Furthermore, in order to make the estimated error dynamic system obtained in step 3 and step 4 converge, Lyapunov stability analysis is performed in fast and slow time scales respectively, thereby obtaining a gain determination method of a sliding mode observer;

[0046] The quasi-steady-state solution of the estimated error dynamic system in step 2 is:

[0047]

[0048] It can be seen from steps three and four that the sliding mode observer constructed in the present invention meets the convergence condition and can obtain the real-time estimated values ​​of the position and speed of the servo system, thereby ensuring the realization and effectiveness of the sensorless control algorithm.

[0049] 1. The present invention takes the surface-mounted permanent magnet synchronous motor as the research object, and based on the two-phase synchronous rotating orthogonal coordinate system, establishes a simplified mathematical model with fast and slow time scale characteristics by introducing the q-axis nominal voltage equation and singular perturbation theory.

[0050] 2. The constructed sliding mode observer makes full use of the information of the q-axis. When the estimated error dynamic system meets the convergence conditions, the real-time estimated values ​​of position and velocity can be obtained and used in the sensorless control system of servo drive.

[0051] 3. Lyapunov stability analysis was performed in both fast and slow time scales to obtain the gain determination method of the sliding mode observer. It can be seen that the constructed sliding mode observer meets the convergence conditions and can obtain the real-time estimated values ​​of the position and speed of the servo system, ensuring the realization and effectiveness of the sensorless control algorithm.

[0052] 4. Based on the fast and slow time scale characteristics of permanent magnet synchronous motors, the present invention proposes a new modeling method and sensorless control technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is the block diagram of the sensorless control algorithm based on sliding mode observer in this application. DETAILED DESCRIPTION

[0054] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0055] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0056] Based on the fast and slow time scale characteristics of permanent magnet synchronous motors, the present invention proposes a new modeling method and sensorless control technology. Based on singular perturbation theory and Lyapunov stability analysis method, the present invention obtains the gain determination criterion of the designed sliding mode observer. The system and method provided by the present application can perform online real-time estimation of the position and speed of permanent magnet synchronous motors, and provide a parameter setting method for the sliding mode observer.

[0057] A sensorless control method and system based on fast and slow time scale characteristics, such as Figure 1 As shown, the system of the present invention includes a nominal voltage module, a sliding mode observer module, a position estimation module, a sliding mode surface module, and a sliding mode control law module, wherein:

[0058] The nominal voltage module is based on the q-axis voltage u q , d-axis current signal i d and velocity estimates Get the q-axis nominal voltage u qo , and send it to the sliding mode observer module;

[0059] The sliding mode observer module estimates the velocity at the previous moment. and the estimated q-axis current And the fast-changing sliding mode control law V q and the slowly varying sliding mode control law V m , get the estimated speed at the current moment and current estimation And send it to the sliding mode observer module (for iterative calculation of the estimated value at the next moment), the position estimation module and the sliding surface module at the same time;

[0060] The position estimation module multiplies the velocity estimate by the number of magnetic pole pairs p n , we get the estimated value of electrical angular velocity, and integrating it gives us the estimated value of position And it will be used for vector transformation of permanent magnet synchronous motor servo control;

[0061] The sliding surface module estimates the value of the q-axis current and the q-axis current signal i q , and the difference is obtained to obtain the q-axis current tracking error Δi q , which is designed as the sliding surface function S q , and send it to the sliding mode control law module;

[0062] The sliding mode control law module is used to calculate the sliding surface function S q Perform the sign function sgn(·) operation and multiply it by the observer gain to obtain the fast-changing sliding mode control law V q and the slowly varying sliding mode control law V m , and sends it to the sliding mode observer module.

[0063] A sensorless control method based on fast and slow time scale characteristics, which is executed by the above system, specifically comprises the following steps:

[0064] Step 1: Establish a fast and slow time scale mathematical model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system.

[0065] First, based on the mathematical model of the permanent magnet synchronous motor in the three-phase stationary ABC coordinate system, the dynamic equations of the permanent magnet synchronous motor in the two synchronous rotating orthogonal dq coordinate systems are obtained through vector transformation as shown below:

[0066]

[0067] Among them, u d and u q are the voltages of the d-axis and q-axis stator windings respectively; R s is the resistance of the stator winding; i d and i q are the currents of the d-axis and q-axis stator windings respectively; L d and L q are the inductances of the d-axis and q-axis stator windings respectively; d / dt is the differential operator; ψ f is the permanent magnet flux; T e is the electromagnetic torque; p n is the number of magnetic pole pairs; J is the moment of inertia; F is the viscous friction coefficient; T m is the load torque disturbance; ω e and ω m are the electrical angular velocity and the mechanical angular velocity respectively, and satisfy ω e =p n ω m .

[0068] Secondly, the present invention takes the surface-mounted permanent magnet synchronous motor as the research object, which satisfies the constraint relationship L d =L q =L s (L s is the inductance of the stator winding). Therefore, the mathematical model of the permanent magnet synchronous motor can be simplified to the following electrical dynamic equation: (due to)

[0069]

[0070] And the corresponding mechanical dynamic equation, namely

[0071]

[0072] Among them, K T =3p n ψ f / 2 is the electromagnetic torque coefficient.

[0073] Then, according to equations (5) to (7), the current i of the permanent magnet synchronous motor is d and i q , compared with the mechanical angular velocity ω m (Slow mode) is a fast dynamic, which is a typical fast and slow time scale system. In addition, from equations (5) and (6), it can be obtained that e Multiply L s i q , L s i d and ψ f The cross-coupled back electromotive force of the d-axis and q-axis is formed respectively. e For current i q Influenced by this, the present invention defines the q-axis nominal voltage equation as shown below:

[0074]

[0075] Among them, the nominal voltage u qo =u q -ω e L s i d .

[0076] Finally, considering that the mechanical dynamic equation (7) contains the q-axis current signal i q , based on the classical singular perturbation theory, the dynamic equations (7) and (8) are modeled as a singular perturbation system as shown below:

[0077]

[0078] Where ε = L s / R s is the singular perturbation parameter.

[0079] Step 2: Construction of a new sliding mode observer.

[0080] First, based on the sliding mode control theory and the singular perturbation system (9), the observer is designed as follows:

[0081]

[0082] Among them, the logo Represents the estimated value of the corresponding variable.

[0083] Secondly, the sliding mode control law satisfies

[0084]

[0085] Among them, V m and V q are the slow-changing and fast-changing sliding mode control laws respectively; g m >0 and g q >0 are the slow-varying and fast-varying sliding mode observer gains, respectively; “sgn(·)” represents the sign function.

[0086] Then, the sliding surface is constructed as

[0087]

[0088] Among them, S q is the sliding surface function; Δi q is the q-axis current estimation error.

[0089] Finally, combining equations (9) and (10), the estimated error dynamics of the observer is

[0090]

[0091] in, is the speed estimation error.

[0092] Step 3: Quick estimation error dynamic analysis.

[0093] First, a fast time scale is introduced as follows:

[0094]

[0095] Where τ is the fast time scale; t o is the initial moment.

[0096] Secondly, according to the classical singular perturbation theory, the differential of the slow-varying state in the fast time scale τ is zero. Therefore, the reduced-order fast estimation error dynamic equation is obtained as follows:

[0097]

[0098] Here, the symbol “·(τ)” represents the fast time component of the corresponding variable.

[0099] Then, define the positive definite Lyapunov candidate function as follows:

[0100]

[0101] Where, "T" means transpose; V f (τ) is the candidate Lyapunov function in the fast time scale.

[0102] Finally, find V f Differentiating (τ) with respect to (15) yields the following inequality:

[0103]

[0104] It can be seen from this that if the fast-varying sliding mode observer gain g q The following constraints are met:

[0105] g q >p n ψ f |Δω m (τ)|(18)

[0106] Here, the symbol “|·|” represents the absolute value function. Then, inequality (17) can be simplified to

[0107]

[0108] Step 4: Dynamic analysis of slow estimation error.

[0109] According to the famous singular perturbation and sliding mode control technology, when the system state trajectory reaches the sliding mode surface, the estimated error dynamic system (13) enters the sliding mode period and will be equivalent to a reduced-order subsystem.

[0110] First, let ε = 0 to obtain the reduced-order slow estimation error dynamic equation as shown below:

[0111]

[0112] Next, define the positive definite Lyapunov candidate function as follows:

[0113]

[0114] Then, find V s (t) Differentiating (20) gives the following inequality:

[0115]

[0116] From the second equation of (20), we can get the quasi-steady-state solution of the estimated error dynamic system (13) as

[0117]

[0118] Finally, combining (22) and (23), we can obtain the following inequality:

[0119]

[0120] It can be seen from this that if the slow-varying sliding mode observer gain g m The following constraints are met:

[0121]

[0122] Where H>0 is the load torque disturbance T m The upper bound value of |T m |≤H. Then, inequality (24) is simplified to

[0123]

[0124] From (18) and (25), we can see that the present invention performs Lyapunov stability analysis in the fast and slow time scales, thereby obtaining a method for determining the gain of the sliding mode observer. It can be seen that the constructed sliding mode observer meets the convergence conditions and can obtain the real-time estimated values ​​of the position and speed of the servo system, ensuring the realization and effectiveness of the sensorless control algorithm.

[0125] In this implementation, in order to verify the effectiveness and advantages of the designed system, the interrupt execution cycle T s =0.1ms, the inverter switching frequency is 10kHz.

[0126] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0127] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

[0128] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A sensorless control system based on fast and slow time scale characteristics, characterized in that: The system includes a nominal voltage module, a sliding mode observer module, a position estimation module, a sliding mode surface module, and a sliding mode control law module, wherein: The nominal voltage module is based on the q-axis voltage u q , d-axis current signal i d and velocity estimates Get the q-axis nominal voltage u qo , and sent to the sliding mode observer module; The sliding mode observer module estimates the velocity at the previous moment. and the estimated q-axis current And the fast-changing sliding mode control law V q and the slowly varying sliding mode control law V m , get the estimated speed at the current moment and current estimation And simultaneously sent to the sliding mode observer module for iterative calculation of the estimated value at the next moment, the position estimation module and the sliding surface module; The position estimation module multiplies the velocity estimate by the number of magnetic pole pairs p n , get the estimated value of electrical angular velocity, integrate to get the estimated value of position And it is used for vector transformation of permanent magnet synchronous motor servo control; The sliding surface module estimates the value of the q-axis current and the q-axis current signal i q , calculate the difference to get the q-axis current tracking error Δi q , and is designed as the sliding surface function S q , and sent to the sliding mode control law module; The sliding mode control law module is used to calculate the sliding surface function S q Perform the sign function sgn(·) operation and multiply it by the observer gain to obtain the fast-changing sliding mode control law V q and the slowly varying sliding mode control law V m , and sent to the sliding mode observer module.

2. A sensorless control method based on fast and slow time scale characteristics, the method is executed by the sensorless control method and system based on fast and slow time scale characteristics according to claim 1, characterized in that: The method comprises: Step 1: Establish a fast and slow time scale mathematical model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system; Step 2: Construction of a new sliding mode observer; Step 3: Dynamic analysis of fast estimation error; Step 4: Dynamic analysis of slow estimation error.

3. The sensorless control method based on fast and slow time scale characteristics according to claim 2 is characterized in that: The mathematical model of the fast and slow time scales on the orthogonal coordinate system of the two-phase synchronous rotation in step 1 is: Among them, d / dt is the differential operator; ω m is the mechanical angular velocity; F is the viscous friction coefficient; J is the moment of inertia; K T =3p n ψ f / 2 is the electromagnetic torque coefficient, p n is the number of magnetic pole pairs, ψ f is the permanent magnet flux; T m is the load torque disturbance; ε=L s / R s is the singular perturbation parameter, L s and R s are the inductance and resistance of the stator winding respectively; i q is the current of the q-axis stator winding; the nominal voltage u qo =u q -ω e L s i d ,u q is the voltage of the q-axis stator winding, i d is the current of the d-axis stator winding, ω e is the electrical angular velocity, and satisfies ω e =p n ω m .

4. The sensorless control method based on fast and slow time scale characteristics according to claim 3 is characterized in that: The mechanical angular velocity ω of the permanent magnet synchronous motor in step 1 m is the slow mode; and the current i d and i q , compared with the mechanical angular velocity ω m is fast dynamic; current i d and i q With ω e Multiply L s i q , L s i d and ψ f The cross-coupled back electromotive force of the d-axis and q-axis are formed respectively; To decouple ω e For current i q The influence of , defines the q-axis nominal voltage equation as shown below:

5. The sensorless control method based on fast and slow time scale characteristics according to claim 2 is characterized in that: The new sliding mode observer constructed in step 2 is as follows: Among them, the logo represents the estimated value of the corresponding variable; the sliding mode control law satisfies: Among them, V m and V q are the slow-changing and fast-changing sliding mode control laws respectively; g m >0 and g q >0 are the slow-varying and fast-varying sliding mode observer gains respectively; "sgn(·)" represents the sign function; the sliding surface is constructed as: Among them, S q is the sliding surface function; Δi q is the q-axis current estimation error.

6. The sensorless control method based on fast and slow time scale characteristics according to claim 5 is characterized in that: In step 2, the fast and slow time scale systems and the constructed new sliding mode observer are combined to obtain the following observer estimation error dynamic equation: in, is the speed estimation error; The sliding mode observer uses the information of the q-axis. When the estimated error dynamic system meets the convergence conditions, the real-time estimated values ​​of position and velocity can be obtained and used in the sensorless control system of the servo drive.

7. The sensorless control method based on fast and slow time scale characteristics according to claim 2 is characterized in that: The reduced-order fast estimation error dynamic equation obtained in step 3 is: Where τ is the fast time scale; the symbol "·(τ)" represents the fast time component of the corresponding variable; In order to make the fast estimation error dynamics satisfy the Lyapunov stability theory, the fast-varying sliding mode observer gain g q The following constraints must be met: g q >p n ψ f |Here m (t)| Here, the symbol "|·|" represents the absolute value function.

8. The sensorless control method based on fast and slow time scale characteristics according to claim 2 is characterized in that: The reduced-order slow estimation error dynamic equation obtained in step 4 is: In order to make the slow estimation error dynamically satisfy the Lyapunov stability theory, the slowly varying sliding mode observer gain g m The following constraints must be met: Where H>0 is the load torque disturbance T m The upper bound value of |T m |≤H.

9. A sensorless control method based on fast and slow time scale characteristics according to claim 7 and claim 8, characterized in that: In order to make the estimated error dynamic system obtained in step 3 and step 4 converge, Lyapunov stability analysis is performed in fast and slow time scales respectively, thereby obtaining a gain determination method of a sliding mode observer; The quasi-steady-state solution of the estimated error dynamic system in step 2 is:

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