Permanent magnet synchronous motor control method based on dynamic surface active disturbance rejection

Abstract

The invention discloses a permanent magnet synchronous motor control method based on dynamic surface active disturbance rejection. Comprising the steps that a tracking differentiator tracks an expected position signal of the permanent magnet synchronous motor, and a tracking signal and a differential signal of the expected position signal are obtained and output; the dynamic surface expansion state observer is used for obtaining a state estimation value, giving an estimation value by taking a known factor and an uncertain factor as sum disturbance, and compensating the estimation value of the sum disturbance; according to the dynamic surface nonlinear state error feedback control law, the output value of a controller is obtained through the output of a tracking differentiator and the feedback value of the actual position, the total disturbance estimated value of the nonlinear expansion state observer is added into the system control law in a feedforward compensation mode, and the total control law of the system is obtained; the second-order dynamic surface active-disturbance-rejection permanent magnet synchronous motor speed controller is designed on the basis of a nonlinear active-disturbance-rejection controller by introducing a dynamic surface control thought into an extended state observer and transforming a nonlinear state error feedback control law, and engineering implementation is facilitated.

Description

Technical Field

[0001] The invention relates to a motor control method, in particular to a permanent magnet synchronous motor control method based on dynamic surface self-disturbance rejection. Background Art

[0002] AC permanent magnet synchronous motor has many advantages, such as high efficiency and high power density, and is widely used in industrial control. At the same time, the control system of AC permanent magnet synchronous motor has typical nonlinear and strong coupling characteristics, which leads to the lack of accurate mathematical model. Therefore, in traditional servo control, PID control is widely used and has achieved certain control effects. However, when the PID system is affected by inaccurate motor parameters and load disturbances, its own accuracy is difficult to meet the higher requirements of servo control occasions. In order to improve the performance of servo system and solve the problems of conventional PID control strategy, many researchers have done a lot of research. Among them, the principle of self-disturbance rejection control is applied to the speed control system of permanent magnet synchronous motor, and a relatively significant effect is achieved. However, the classic second-order nonlinear self-disturbance rejection controller has problems such as insufficient disturbance estimation ability, low control efficiency and stability, resulting in poor engineering practicality. Summary of the invention

[0003] In order to overcome the above-mentioned defects, the purpose of the present invention is to propose a permanent magnet synchronous motor control method based on dynamic surface self-disturbance rejection, introduce the dynamic surface self-disturbance rejection controller into the field of permanent magnet synchronous motor speed control, overcome the problems existing in the prior art, and while solving the coupling problem of permanent magnet synchronous motor control, further improve the disturbance estimation capability of the controller and improve the stability and control efficiency of the system.

[0004] To achieve the above object, the permanent magnet synchronous motor control method based on dynamic surface self-disturbance rejection of the present invention comprises: a tracking differentiator, a dynamic surface extended state observer and a dynamic surface nonlinear state error feedback control law;

[0005] The tracking differentiator tracks the desired position signal of the permanent magnet synchronous motor, obtains a tracking signal of the desired position signal and a differential signal thereof, and outputs them;

[0006] The dynamic surface expansion state observer is used to obtain a state estimation value, and to give an estimation value of the known factors and the uncertainty factors as a sum disturbance, and to compensate the estimation value of the sum disturbance;

[0007] The dynamic surface nonlinear state error feedback control law obtains the controller output value by tracking the output of the differentiator and the feedback value of the actual position, and adds the total disturbance estimation value of the nonlinear extended state observer into the system control law in the form of feedforward compensation to obtain the overall control law of the system;

[0008] The design method of the dynamic surface expansion state observer includes:

[0009] According to the state equation of the second-order controlled system of permanent magnet synchronous motor:

[0010]

[0011] Where: y is the output, f(x1,x2,t) is the known disturbance, ω(t) is the unknown disturbance, f(x1,x2,t)+ω(t) is the total disturbance, b is the control gain, and u is the control amount;

[0012] The discrete form of the active disturbance rejection controller applicable to the second-order system (8) is obtained as follows:

[0013] (2) Tracking Differentiator:

[0014]

[0015] (2) Extended State Observer:

[0016]

[0017] (3) Nonlinear state error feedback control law:

[0018]

[0019] Among them, v is the input, v1 tracks v, v2 is the differential of v1, z1, z2, z3 are the estimates of x1, x2, f(x1,x2,t)+ω(t), T, r, h, β 01 , β 02 , β 03 , b0, a1, a2, δ, k1, k2, α1, α2 are all adjustable parameters;

[0020] In order to completely eliminate the influence of nonlinear functions, the equation (10) is transformed equivalently, that is,

[0021]

[0022] Where f3 = β 03 fal(e,a2,δ),f2=β 02 fal(e,a1,δ),f1=β 01 e; Introduce dynamic surface control law u to replace Right now

[0023] Step 1, define the first subsystem of system (8) The dynamic surface equation is

[0024] S1=z1-x1 (13)

[0025] Then taking the derivative of S1, we get

[0026]

[0027] Then there is a virtual control law

[0028]

[0029] make Passing through a first-order low-pass filter to avoid multiple differentiation, we can get x 1d , that is, the following formula

[0030]

[0031] Step 2, Second Subsystem The dynamic surface equation is

[0032] S2=z2-x 1d (17)

[0033] Taking the derivative of S2, we get

[0034]

[0035] Virtual Control Law

[0036]

[0037] Likewise, Through a first-order low-pass filter to avoid multiple differentiation, we can get x 2d , that is,

[0038]

[0039] Step 3, the third subsystem The dynamic surface equation is

[0040] S3=z3-x 2d (twenty one)

[0041] Taking the derivative of S3, we get

[0042]

[0043] The final actual control law is

[0044]

[0045] Among them, k1, k2, k3, τ1, τ2 are adjustable parameters, and τ1>0, τ2>0;

[0046] The stability is demonstrated as follows:

[0047] definition i=1,2, then from equations (13) and (17) we get

[0048]

[0049] According to formula (15) and (16), we can get

[0050]

[0051] Similarly

[0052]

[0053] From equations (14), (15), (16) and (18), (19), (20), we get

[0054]

[0055] in, is a continuous smooth function;

[0056] definition

[0057]

[0058] According to equations (26), (27), and (28), we can get

[0059] Defining the Lyapunov function

[0060]

[0061] From system (8), we know that x1, All are continuous, assuming p is any positive number, g i The maximum value is set to g imax , let k i =2+a0, and set τ i satisfy Then there is

[0062]

[0063] When V=p, α0>ε / p, we have That is, as long as the parameters k1, k2, k3, τ1, τ2 are selected appropriately, the system converges.

[0064] Furthermore, the formula of the dynamic surface nonlinear state error feedback control law is as follows:

[0065]

[0066] Among them, S4 and S5 are dynamic surface equations, is a virtual control law, τ3, k4, k5 are adjustable parameters and τ3>0.

[0067] Furthermore, the method also includes the step of replacing the speed controller with a second-order dynamic surface anti-disturbance control.

[0068] Furthermore, the method also includes the step of replacing the q-axis current controller with a second-order dynamic surface anti-disturbance rejection controller.

[0069] The present invention introduces dynamic surface anti-disturbance control technology into the field of permanent magnet synchronous motor speed control for the first time. Based on the nonlinear anti-disturbance control controller, a second-order dynamic surface anti-disturbance permanent magnet synchronous motor speed controller is designed by introducing the dynamic surface control idea into the extended state observer and the transformation of the nonlinear state error feedback control law, which is convenient for engineering implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is the structure diagram of the second-order dynamic surface active disturbance rejection controller. DETAILED DESCRIPTION

[0071] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0072] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0073] The terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "plurality" means two or more.

[0074] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0075] (1) The control method of the present invention establishes the following mathematical formula.

[0076] In the traditional ABC coordinate system, the voltage and flux equations of the permanent magnet synchronous motor have the characteristics of multivariable, strong coupling and nonlinearity. Therefore, it is necessary to transform its coordinates into the dq coordinate system to reduce variables and eliminate nonlinearity. The voltage and flux equations in the dq coordinate system can be expressed as:

[0077] u d =(R s +L d p)i d -ω e L q i q (1)

[0078] u q =ω e L d i d +(R s +L q p)i q +ω e ψ f (2)

[0079] ψ d =L d i d +ψ f (3)

[0080] ψ q =L q i q (4)

[0081] In the formula, u d 、u q 、i d 、i q , d , q Respectively represent the d-axis and q-axis voltage, current and flux in the synchronous rotating coordinate system; ω e In addition, in the subsequent study of the second-order dynamic surface anti-disturbance controller, the motion equation and current equation under the d and q axes need to be given, which are in the following form:

[0082]

[0083] In the formula, ω m Represents the mechanical angular velocity, T L represents load, B represents friction coefficient, K t represents the thrust coefficient, for ω mDerivative again, and substitute the current state equation into it, make some transformations, and get the following equation:

[0084]

[0085] (2) Principle of Active Disturbance Rejection Control

[0086] The tracking differentiator, extended state observer and nonlinear state error feedback control law constitute the three main parts of the active disturbance rejection controller.

[0087] It can be seen from formula (7) that the permanent magnet synchronous motor speed system is a second-order controlled system, so this paper adopts a second-order active disturbance rejection controller. The state equation of the second-order controlled system is expressed as follows:

[0088]

[0089] Where: y is the output, f(x1,x2,t) is the known disturbance, ω(t) is the unknown disturbance, f(x1,x2,t)+ω(t) is the total disturbance, b is the control gain, and u is the control amount.

[0090] By comparing with formula (7), we can know that x1 = ω, u=u q ,

[0091] The discrete form of the active disturbance rejection controller for the second-order system (8) is as follows:

[0092] (1) Tracking differentiator:

[0093]

[0094] (2) Extended State Observer:

[0095]

[0096] (3) Nonlinear state error feedback control law:

[0097]

[0098] Among them, v is the input, v1 tracks v, v2 is the differential of v1, z1, z2, z3 are the estimates of x1, x2, f(x1,x2,t)+ω(t), T, r, h, β 01 , β 02 , β 03 , b0, a1, a2, δ, k1, k2, α1, α2 are all adjustable parameters. The specific function expressions of fhan(x1, x2, r, h) and fal(e, a, δ) can be found in relevant literature.

[0099] (3) Dynamic surface anti-disturbance control design

[0100] The disturbance estimation capability of the extended state observer in the conventional ADRC is insufficient, and the control efficiency and stability of the nonlinear state error feedback control rate are low. Therefore, this paper mainly improves the traditional extended state observer and nonlinear state error feedback control rate.

[0101] 3.1 Design of dynamic surface expansion state observer

[0102] The reason why the conventional extended state observer has insufficient disturbance estimation capability is that it adopts a continuous piecewise function fal(e,a,δ) that is not smooth and differentiable at the piecewise point ±δ, which makes the system output prone to oscillation. To address this problem, the existing improvement methods mainly focus on constructing a continuous smooth function to replace fal(e,a,δ). This paper will be different from the existing methods and will no longer adopt the conventional idea of ​​replacing nonlinear functions. Instead, it will consider introducing the idea of ​​dynamic surface control into the extended state observer.

[0103] In order to completely eliminate the influence of nonlinear functions, it is necessary to perform an equivalent transformation on equation (10), namely:

[0104]

[0105] Where f3 = β 03 fal(e,a2,δ),f2=β 02 fal(e,a1,δ),f1=β 01 e. Introducing dynamic surface control law to replace Right now

[0106] Step 1, define the first subsystem of system (8) The dynamic surface equation is

[0107] S1=z1-x1 (13)

[0108] Then taking the derivative of S1 we get

[0109]

[0110] Then there is a virtual control law

[0111]

[0112] make Passing through a first-order low-pass filter to avoid multiple differentiation, we can get x 1d , that is, the following formula

[0113]

[0114] Step 2, Second Subsystem The dynamic surface equation is

[0115] S2=z2-x 1d (17)

[0116] Taking the derivative of S2, we get

[0117]

[0118] Virtual Control Law

[0119]

[0120] Likewise, Through a first-order low-pass filter to avoid multiple differentiation, we can get x 2d , that is,

[0121]

[0122] Step 3, the third subsystem The dynamic surface equation is

[0123] S3=z3-x 2d (twenty one)

[0124] Taking the derivative of S3, we get

[0125]

[0126] The final actual control law is

[0127]

[0128] Among them, k1, k2, k3, τ1, τ2 are adjustable parameters, and τ1>0, τ2>0.

[0129] The stability is demonstrated as follows:

[0130] definition i=1,2, then from equations (13) and (17) we get

[0131]

[0132] According to formula (15) and (16), we can get

[0133]

[0134] Similarly

[0135]

[0136] From equations (14), (15), (16) and (18), (19), (20), we get

[0137]

[0138] in, is a continuous smooth function.

[0139] definition

[0140]

[0141] According to formula (26), (27), (28), we can get

[0142] Defining the Lyapunov function

[0143]

[0144] From system (8), we know that x1, All are continuous, assuming p is any positive number, g i The maximum value is set to g imax , let k i =2+a0, and set τ i satisfy Then there is

[0145]

[0146] When V=p, α0>ε / p, we have That is, as long as the parameters k1, k2, k3, τ1, τ2 are selected appropriately, the system converges.

[0147] 3.2 Design of nonlinear state error feedback control law for dynamic surface

[0148] For the second-order system in equation (8), combined with the outputs v1 and v2 of the tracking differentiator, the dynamic surface nonlinear state error feedback control law can be obtained as follows:

[0149]

[0150] Among them, S4 and S5 are dynamic surface equations, is a virtual control law, τ3, k4, k5 are adjustable parameters and τ3>0. The giving process and stability proof of the above formula are similar to those in Section 2.1.

[0151] From the above analysis, we can see that the structure diagram of the second-order dynamic surface active disturbance rejection controller is as follows: Figure 1 shown.

[0152] Similarly, the speed controller and the q-axis current controller can be replaced by a second-order dynamic surface anti-disturbance control controller, and the q-axis current loop in the system is open-loop processed. This solution has been studied and will not be described here.

[0153] The present invention introduces dynamic surface anti-disturbance control technology into the field of permanent magnet synchronous motor speed control for the first time. Based on the nonlinear anti-disturbance control controller, a second-order dynamic surface anti-disturbance permanent magnet synchronous motor speed controller is designed by introducing the dynamic surface control idea into the extended state observer and the transformation of the nonlinear state error feedback control law, which is convenient for engineering implementation.

[0154] The present invention is described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of ordinary technicians in the field without departing from the purpose of the present invention. Many other changes and modifications that do not depart from the concept and scope of the present invention should be regarded as the protection scope of the present invention.

[0155] In the description of this specification, specific features, structures, materials or characteristics may be combined in an appropriate manner in any one or more embodiments or examples.

[0156] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A permanent magnet synchronous motor control method based on dynamic surface anti-disturbance control, characterized in that: include: Tracking differentiator, dynamic surface expansion state observer and dynamic surface nonlinear state error feedback control law; The tracking differentiator tracks the desired position signal of the permanent magnet synchronous motor, obtains a tracking signal of the desired position signal and a differential signal thereof, and outputs them; The dynamic surface expansion state observer is used to obtain a state estimation value, and to give an estimation value of the known factors and the uncertainty factors as a sum disturbance, and to compensate the estimation value of the sum disturbance; The dynamic surface nonlinear state error feedback control law obtains the controller output value by tracking the output of the differentiator and the feedback value of the actual position, and adds the total disturbance estimation value of the nonlinear extended state observer into the system control law in the form of feedforward compensation to obtain the overall control law of the system; The design method of the dynamic surface expansion state observer includes: According to the state equation of the second-order controlled system of permanent magnet synchronous motor: Where: y is the output, f(x1,x2,t) is the known disturbance, ω(t) is the unknown disturbance, f(x1,x2,t)+ω(t) is the total disturbance, b is the control gain, and u is the control amount; The discrete form of the active disturbance rejection controller applicable to the second-order system (8) is obtained as follows: (1) Tracking differentiator: (2) Extended State Observer: (3) Nonlinear state error feedback control law: Among them, v is the input, v1 tracks v, v2 is the differential of v1, z1, z2, z3 are the estimates of x1, x2, f(x1,x2,t)+ω(t), T, r, h, β 01 , β 02 , β 03 , b0, a1, a2, δ, k1, k2, α1, α2 are all adjustable parameters; In order to completely eliminate the influence of nonlinear functions, the equation (10) is transformed equivalently, that is, Where f3 = β 03 fal(e,a2,δ),f2=β 02 fal(e,a1,δ),f1=β 01 e; Introduce dynamic surface control law to replace Right now Step 1, define the first subsystem of system (8) The dynamic surface equation is S1=z1-x1 (13) Then taking the derivative of S1, we get Then there is a virtual control law make Passing through a first-order low-pass filter to avoid multiple differentiation, we can get x 1d , that is, the following formula Step 2, Second Subsystem The dynamic surface equation is S2=z2-x 1d (17) Taking the derivative of S2, we get Virtual Control Law Likewise, Through a first-order low-pass filter to avoid multiple differentiation, we can get x 2d , that is, Step 3, the third subsystem The dynamic surface equation is S3=z3-x 2d (21) Taking the derivative of S3, we get The final actual control law is Among them, k1, k2, k3, τ1, τ2 are adjustable parameters, and τ1>0, τ2>0; The stability is demonstrated as follows: definition i=1,2, then from equations (13) and (17) we get According to formula (15) and (16), we can get Similarly From equations (14), (15), (16) and (18), (19), (20), we get in, is a continuous smooth function; definition According to equations (26), (27), and (28), we can get Defining the Lyapunov function From system (8), we know that x1, All are continuous, assuming p is any positive number, g i The maximum value is set to g imax , let k i =2+a0, and set τ i satisfy Then there is When V=p, α0>ε / p, we have That is, as long as the parameters k1, k2, k3, τ1, τ2 are selected appropriately, the system converges.

2. The permanent magnet synchronous motor control method based on dynamic surface anti-disturbance control according to claim 1, characterized in that: The formula of the dynamic surface nonlinear state error feedback control law is as follows: Among them, S4 and S5 are dynamic surface equations, is a virtual control law, τ3, k4, k5 are adjustable parameters and τ3>

0.

3. The permanent magnet synchronous motor control method based on dynamic surface anti-disturbance control according to claim 1, characterized in that: The method also includes the step of replacing the speed controller with a second-order dynamic surface active disturbance rejection controller.

4. The permanent magnet synchronous motor control method based on dynamic surface anti-disturbance control according to claim 1, characterized in that: The method also includes the step of replacing the q-axis current controller with a second-order dynamic surface anti-disturbance control controller.

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