Novel sliding mode control method for fractional order of rotating speed of permanent magnet synchronous motor
阅读说明：本技术 一种新型永磁同步电机转速分数阶滑模控制方法 (Novel sliding mode control method for fractional order of rotating speed of permanent magnet synchronous motor ) 是由 张广明 高鹏 梅磊 欧阳慧珉 潘慧慧 高丽华 于 2019-09-24 设计创作，主要内容包括：本发明公开了一种新型永磁同步电机转速分数阶滑模控制方法,其包括,S1：在分数阶PID滑模面的基础上,结合非线性函数构建一种非线性分数阶PID滑模面；S2：利用自适应超螺旋算法设计自适应超螺旋趋近律；S3：设计扩展状态观测器观测电机负载；S4：以非线性分数阶PID滑模面和自适应超螺旋趋近律为基础建立永磁同步电机滑模转速控制器方程,用于控制永磁同步电机转速。本发明在分数阶PID滑模面的基础上,结合非线性函数构建一种新型非线性分数阶PID滑模面,解决在进入滑动状态下传统分数阶PID滑模面控制精度不高,响应速度不快等问题。(The invention discloses a novel permanent magnet synchronous motor rotating speed fractional order sliding mode control method, which comprises the following steps of S1: on the basis of the fractional order PID sliding mode surface, a nonlinear fractional order PID sliding mode surface is constructed by combining a nonlinear function; s2: designing a self-adaptive supercoiled approximation law by using a self-adaptive supercoiled algorithm; s3: designing an extended state observer to observe the load of the motor; s4: and establishing a permanent magnet synchronous motor sliding mode rotating speed controller equation based on the nonlinear fractional order PID sliding mode surface and the self-adaptive supercoiled approach law for controlling the rotating speed of the permanent magnet synchronous motor. The invention constructs a novel nonlinear fractional order PID sliding mode surface by combining a nonlinear function on the basis of the fractional order PID sliding mode surface, and solves the problems of low control precision, low response speed and the like of the traditional fractional order PID sliding mode surface in a sliding state.)
1. A novel sliding mode control method for fractional order of rotating speed of a permanent magnet synchronous motor is characterized by comprising the following steps: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
constructing a nonlinear fractional order PID sliding mode surface by combining nonlinear functions fal (x, alpha and delta) on the basis of the fractional order PID sliding mode surface;
designing a self-adaptive supercoiled approximation law by using a self-adaptive supercoiled algorithm;
designing an extended state observer to observe the load of the motor;
and establishing a sliding mode rotating speed controller equation of the permanent magnet synchronous motor based on the nonlinear fractional order PID sliding mode surface and the self-adaptive supercoiled approach law, wherein the sliding mode rotating speed controller equation is used for controlling the rotating speed of the permanent magnet synchronous motor.
2. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to claim 1 is characterized in that: the expression of the fractional order PID sliding mode surface is as follows:
wherein e (t) is the error between the actual rotating speed and the set rotating speed of the motor, and u and epsilon are respectively the integral fraction order and the differential fraction order of the fraction order.
3. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to claim 2 is characterized in that: substituting e (t) into a nonlinear function fal (x, alpha, delta) to obtain fal (e (t), alpha, delta), and applying fal (e (t), alpha, delta) to a proportional term, an integral term and a differential term of the fractional PID sliding mode surface to obtain an expression of the nonlinear fractional PID sliding mode surface as follows:
Kp＞0,Ki＞0,Kd＞0，u＝-ε (4)
wherein e (t) is the error between the actual rotating speed and the set rotating speed of the motor, and u and epsilon are respectively the integral fraction order and the differential fraction order of the fraction order; α, δ are the filter factor and the non-linear factor, respectively, of the non-linear function.
4. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to any one of claims 1 to 3 is characterized in that: the nonlinear function is:
5. the novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to claim 4 is characterized in that: δ, α satisfy the following selection rule:
0＜δ＜1
0＜α＜1。
6. the novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to claim 5 is characterized in that: and obtaining the self-adaptive supercoiled approximation law by taking first order differential of the expression of the nonlinear fractional order PID sliding mode surface as follows:
wherein, γ1,κ1V, θ are both positive coefficients.
7. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to any one of claims 3, 5 or 6, is characterized in that: the expression of the design extended state observer is as follows:
where ω is the actual mechanical rotor angular velocity of the motor,
8. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to claim 7 is characterized in that: the sliding mode rotating speed controller equation is as follows:
wherein p isnIs the number of pole pairs of the motor,
9. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to any one of claims 1 to 3, 5, 6 or 8 is characterized in that: the permanent magnet synchronous motor is a surface-mounted permanent magnet synchronous motor.
10. The novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor according to claim 5 is characterized in that: the value of the nonlinear factor alpha is related to the nonlinearity of the nonlinear function, and when the value is more than 0 and less than 1 and more than 0 and less than 1, the nonlinear function fal (x, alpha and delta) can reduce the steady-state error; the nonlinear function fal (x, alpha, delta) has the characteristics that large error (| x | > delta) corresponds to low gain (| fal (x, alpha, delta) | < | x |), and small error (| x | ≦ delta) corresponds to high gain (| fal (x, alpha, delta) | > | x |).
Technical Field
The invention relates to the technical field of permanent magnet synchronous motors, in particular to a novel rotating speed fractional order sliding mode control method of a permanent magnet synchronous motor.
Background
Permanent magnet synchronous motors are becoming one of the most competitive motion control products due to their inherent advantages of low rotor inertia, high efficiency, high power density, etc., and are widely used in industrial applications. In such applications, speed control of permanent magnet synchronous machines becomes a critical task. The traditional PID (proportional integral derivative) controller has the advantages of simple structure, easy realization and the like, so the traditional PID controller is widely applied to the rotating speed control of the permanent magnet synchronous motor. However, because the permanent magnet synchronous motor has the characteristics of nonlinearity, time variation, strong coupling and the like, the traditional PID control algorithm is difficult to obtain satisfactory motor speed regulation performance.
The sliding mode control has the advantages of robustness to parameter change and external interference, simplicity in implementation and the like, and becomes one of the most common nonlinear control methods of the permanent magnet synchronous motor at present. In recent years, fractional calculus has been widely used in sliding mode control improvement. Compared with a traditional integer order controller, the additional degree of freedom of the fractional order integrator and the differentiator is used, so that the performance can be further improved, and the shaking phenomenon of the sliding mode can be effectively reduced. However, the existing fractional order sliding mode has the defects of low control precision, low response speed and the like, and the requirement of the permanent magnet synchronous motor in a high-quality control system is difficult to meet.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the problems existing in the existing fractional order sliding modes.
Therefore, the invention aims to provide a novel fractional order sliding mode control method for the rotating speed of a permanent magnet synchronous motor, which is used for constructing a novel nonlinear fractional order PID sliding mode surface by combining a nonlinear function on the basis of the fractional order PID sliding mode surface and solving the problems of low control precision, low response speed and the like of the traditional fractional order PID sliding mode surface in a sliding state.
In order to solve the technical problems, the invention provides the following technical scheme: a novel sliding mode control method for fractional order of rotating speed of a permanent magnet synchronous motor comprises the following steps: constructing a nonlinear fractional order PID sliding mode surface by combining nonlinear functions fal (x, alpha and delta) on the basis of the fractional order PID sliding mode surface; designing a self-adaptive supercoiled approximation law by using a self-adaptive supercoiled algorithm; designing an extended state observer to observe the load of the motor; and establishing a sliding mode rotating speed controller equation of the permanent magnet synchronous motor based on the nonlinear fractional order PID sliding mode surface and the self-adaptive supercoiled approach law, wherein the sliding mode rotating speed controller equation is used for controlling the rotating speed of the permanent magnet synchronous motor.
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: the expression of the fractional order PID sliding mode surface is as follows:
wherein e (t) is the error between the actual rotating speed and the set rotating speed of the motor, and u and epsilon are respectively the integral fraction order and the differential fraction order of the fraction order.
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: substituting e (t) into a nonlinear function fal (x, alpha, delta) to obtain fal (e (t), alpha, delta), and applying fal (e (t), alpha, delta) to a proportional term, an integral term and a differential term of the fractional PID sliding mode surface to obtain an expression of the nonlinear fractional PID sliding mode surface as follows:
Kp＞0,Ki＞0,Kd＞0，u＝-ε (4)
wherein e (t) is the error between the actual rotating speed and the set rotating speed of the motor, and u and epsilon are respectively the integral fraction order and the differential fraction order of the fraction order; α, δ are the filter factor and the non-linear factor, respectively, of the non-linear function.
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: the nonlinear function is:
as a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: δ, α satisfy the following selection rule: delta is more than 0 and less than 1; alpha is more than 0 and less than 1.
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: and obtaining the self-adaptive supercoiled approximation law by taking first order differential of the expression of the nonlinear fractional order PID sliding mode surface as follows:
wherein, γ1,κ1V, θ are both positive coefficients.
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: the expression of the design extended state observer is as follows:
where ω is the actual mechanical rotor angular velocity of the motor,
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: the sliding mode rotating speed controller equation is as follows:
wherein p isnIs the number of pole pairs of the motor,
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: the permanent magnet synchronous motor is a surface-mounted permanent magnet synchronous motor.
As a preferred scheme of the novel sliding mode control method for the fractional order of the rotating speed of the permanent magnet synchronous motor, the method comprises the following steps: the value of the nonlinear factor alpha is related to the nonlinearity of the nonlinear function, and when the value is more than 0 and less than 1 and more than 0 and less than 1, the nonlinear function fal (x, alpha and delta) can reduce the steady-state error; the nonlinear function fal (x, alpha, delta) has the characteristics that large error (| x | > delta) corresponds to low gain (| fal (x, alpha, delta) | < | x |), and small error (| x | ≦ delta) corresponds to high gain (| fal (x, alpha, delta) | > | x |).
The invention has the beneficial effects that:
1. on the basis of a fractional order PID sliding mode surface, a novel nonlinear fractional order PID sliding mode surface is constructed by combining a nonlinear function, and the problems that the traditional fractional order PID sliding mode surface is low in control precision, low in response speed and the like when entering a sliding state are solved;
2. designing an adaptive supercoiled sliding mode approach law by using an adaptive supercoiled algorithm so as to improve the control effect under the approach state of the sliding mode;
3. and designing an extended state observer to estimate the load disturbance of the motor.
Compared with the prior art, the rotating speed control algorithm of the permanent magnet synchronous motor provided by the invention has good static characteristic, dynamic characteristic and strong robustness to external interference.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
fig. 1 is a diagram of a speed control system of a permanent magnet synchronous motor according to the present invention.
Fig. 2 is a frame diagram of a fractional order sliding mode control method for the rotating speed of the novel permanent magnet synchronous motor provided by the invention.
Fig. 3 is a response curve for two sliding surfaces.
FIG. 4 is a speed output response curve for two controllers.
FIG. 5 is a detail amplification response curve of the rotational speed of the two controllers.
FIG. 6 is a graph of the tamper resistant output response of two controllers.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Referring to fig. 1 to 6, a first embodiment of the present invention provides a novel sliding mode control method for fractional order of rotation speed of a permanent magnet synchronous motor, which is used in a control loop of the permanent magnet synchronous motor, and specifically, the speed loop adopts the novel sliding mode control method for fractional order of rotation speed of the permanent magnet synchronous motor. The schematic diagram of the speed control system of the permanent magnet synchronous motor is shown in the attached figure 2.
The dynamic equation of the electromagnetic torque of the permanent magnet synchronous motor can be expressed as follows:
wherein, TeIs an electromagnetic torque; p is a radical ofnIs the number of pole pairs;
For the surface-mounted permanent magnet synchronous motor, L is the characteristic of the surface-mounted permanent magnet synchronous motord＝LqL, the dynamics of the electromagnetic torque of the permanent magnet synchronous machineEquation (1) can be re-expressed as:
wherein J is moment of inertia; b is viscous friction; t isLIs the external load torque; ω is the actual mechanical rotational speed of the permanent magnet synchronous motor.
Then, adopt idThe state equation of the permanent magnet synchronous motor can be obtained according to the formula (2) as shown in the following formula (3), and the state equation (3) is used as a basis and foundation for constructing a sliding-mode rotating speed controller equation:
the invention relates to a novel permanent magnet synchronous motor rotating speed fractional order sliding mode control method, which comprises the following steps:
s1: on the basis of the existing fractional order PID (proportional integral derivative) sliding mode surface, a novel nonlinear fractional order PID sliding mode surface is constructed by combining a nonlinear function;
s2: designing a self-adaptive supercoiled approximation law by using a self-adaptive supercoiled algorithm;
s3: designing an extended state observer to observe the load of the motor;
s4: and establishing a permanent magnet synchronous motor sliding mode rotating speed controller equation based on a nonlinear fractional order PID sliding mode surface and a self-adaptive super-spiral approximation law.
Specifically, in step S1, the expression of the existing fractional PID sliding mode surface is:
the nonlinear function fal (x, alpha, delta) described in the present invention is a summary of empirical knowledge of control engineering. The nonlinear function fal (x, α, δ) has the following characteristics: the value of the nonlinear factor alpha is related to the nonlinearity of the nonlinear function, and when the value is more than 0 and less than 1 and more than 0 and less than 1, the nonlinear function fal (x, alpha and delta) can obviously reduce the steady-state error; the nonlinear function fal (x, alpha, delta) also has the characteristics that large error (| x | > delta) corresponds to low gain (| fal (x, alpha, delta) | < | x |), small error (| x | ≦ delta) and high gain (| fal (x, alpha, delta) | > | x |), so that the nonlinear function has the characteristic of rapid convergence.
The invention designs a novel nonlinear fractional order PID sliding mode surface, an error signal e (t) obtains a nonlinear error signal fal (e (t), alpha and delta) through a nonlinear function fal (x, alpha and delta), and the nonlinear error signal fal (e (t), alpha and delta) is applied to a proportional term, an integral term and a differential term of the fractional order PID.
In the invention, on the basis of a fractional order PID sliding mode surface, a novel nonlinear fractional order PID sliding mode surface established by combining a nonlinear function fal (x, alpha, delta) is as follows:
Kp＞0,Ki＞0,Kd＞0，u＝-ε (5)
wherein e (t) is the difference between the actual rotating speed and the set rotating speed of the motor, and u and epsilon are respectively an integral fraction order and a differential fraction order.
The nonlinear function in the above is:
where α, δ are the filter factor and the non-linear factor, respectively.
In the novel fractional order sliding mode control method for the rotating speed of the permanent magnet synchronous motor, the design process of designing the self-adaptive supercoiled approach law by utilizing the self-adaptive supercoiled algorithm is as follows:
according to the state equation (3) of the medium permanent magnet synchronous motor, the (3) can be replaced by a unified single-input equation (7);
wherein x is a state variable, u1Is a control function, and f (x) is a differentiable, partially known vector function. Now, first order differential is taken for the nonlinear fractional order PID sliding mode surface (4), and the following can be obtained:
wherein the content of the first and second substances,a (x, t) can in turn be written as follows:
wherein, delta1,δ2Are all positive numbers, but the specific values are unknown. The supercoiled approach law can now be designed according to equation (9) as:
eta in the formula (10)1Beta is a time-varying gain and is a function of the parameter eta in the supercoiled approach law by the following adaptation rate1β performing real-time updates:
wherein, γ1,κ1V, θ are both positive coefficients.
As shown in step S3, the present invention further uses an extended state observer to observe the load disturbance of the motor to improve the disturbance resistance of the system, wherein the extended state observer is designed as follows:
where ω is the actual mechanical rotor angular velocity of the motor, z21Is an observed value of the rotational speed of the motor,
Combining the sliding mode surfaces and the formulas of equations (4) to (5), the approach laws of equations (10) to (11), the extended state observer of equation (12), and the state equation of the permanent magnet synchronous motor of equation (3), a sliding mode rotational speed controller equation for outputting a control signal to control the rotational speed of the permanent magnet synchronous motor can be established:
wherein p isnIs the number of pole pairs of the motor,
In order to verify the effectiveness of the method provided by the invention, simulation comparison research is carried out on the control effects of the traditional fractional order PID sliding mode control method and the novel permanent magnet synchronous motor rotating speed fractional order sliding mode control method under the software Matlab/Simulink environment.
The parameters of the permanent magnet synchronous motor are set as follows:
U＝400V；
Ld＝Lq＝L＝5.25mH；
J＝0.009kg·m2；
B＝0.008(Nm·s)/rad；
pn＝4。
firstly, the method 1: the rotation speed fractional order sliding mode control of the novel permanent magnet synchronous motor.
The key parameter setting of the control method is as follows:
Kp＝0.1；Ki＝0.3；Kd＝0.3；ε＝0.01；u＝-0.01；ν＝0.05；θ＝15；γ1＝10；κ1＝25
the parameters of the extended state observer are set as follows:
secondly, a method 2: and (3) traditional fractional order PID sliding mode surface sliding mode control.
The traditional fractional order PID sliding mode surface design is as follows:
wherein the content of the first and second substances,
The traditional fractional order sliding mode control adopts an exponential approach law:
wherein k ∈ R+,η∈R+Respectively is the switch gain and the exponential coefficient of the exponential approximation law; sign(s) is a switching function.
The parameters of the traditional fractional order PID sliding mode surface sliding mode control method are set as follows:
based on the above, the control effects of the two control methods are shown in fig. 3 to 6. Fig. 3 is a comparison graph of response of two sliding mode surfaces, fig. 4 is a comparison graph of actual rotating speed of a motor, fig. 5 is an enlarged comparison graph of details of the actual rotating speed of the motor, and fig. 6 is a comparison graph of disturbance resistance of the rotating speed of the motor. It can be seen from fig. 3 that the new slip-form surface proposed by the present invention approaches zero more quickly than the conventional slip-form surface. Fig. 4 shows that the method of the present invention has faster dynamic response than the conventional control method. As can be seen from FIG. 5, the method provided by the invention has higher stability precision and smaller steady-state error than the conventional control method. Fig. 6 shows that the method provided by the present invention has stronger interference resistance, i.e., better robustness, than the conventional control method.
Compared with the traditional fractional order PID sliding mode surface sliding mode control method, the control method designed by the invention has better dynamic performance, static performance and external interference resistance.
It is important to note that the construction and arrangement of the present application as shown in the various exemplary embodiments is illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters (e.g., temperatures, pressures, etc.), mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter recited in this application. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of this invention. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. In the claims, any means-plus-function clause is intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present inventions. Therefore, the present invention is not limited to a particular embodiment, but extends to various modifications that nevertheless fall within the scope of the appended claims.
Moreover, in an effort to provide a concise description of the exemplary embodiments, all features of an actual implementation may not be described (i.e., those unrelated to the presently contemplated best mode of carrying out the invention, or those unrelated to enabling the invention).
It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure, without undue experimentation.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
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