Sliding mode control method of permanent magnet synchronous motor based on adaptive reaching law

Abstract

The present invention provides a sliding mode control method for a permanent magnet synchronous motor based on an adaptive reaching law, comprising the following steps: S1, constructing a mathematical model of the permanent magnet synchronous motor in a d-q synchronous rotating coordinate system; S2, designing an adaptive reaching law for sliding mode control; S3, designing a sliding mode surface; S4, deriving a sliding mode control law based on the adaptive reaching law; S5, performing sliding mode control on the permanent magnet synchronous motor according to the sliding mode control law. The adaptive reaching law sliding mode control proposed in the present invention can converge to the sliding mode surface more quickly and has less jitter than the traditional exponential reaching law sliding mode control.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law. Background Art

[0002] Permanent magnet synchronous motors are increasingly widely used in a variety of modern AC servo systems such as robots, electric vehicles, CNC machine tools, aerospace, etc. due to their advantages such as high performance, high power density, simple structure, and light weight. The most classic control strategy is proportional integral control (PI), which is widely used in linear steady-state systems due to its simple structure and good stability. However, the permanent magnet synchronous motor is a multivariable strongly coupled nonlinear system. In addition, in practical applications, the permanent magnet synchronous motor is affected by various disturbances, such as external load disturbances, internal friction, parameter mismatch disturbances, etc. These factors make it difficult for the PI control strategy to meet higher control performance requirements.

[0003] In order to overcome the influence of the above-mentioned interferences and improve the performance of control strategies, more and more high-performance and high-precision control strategies have been proposed in recent years. Among these control strategies, sliding mode control has received great attention in the control field due to its simple structure, low requirements on model accuracy, and insensitivity to disturbances. At present, sliding mode control has been successfully applied to motor speed regulation systems. However, sliding mode control is not perfect, because the discontinuity of the system and the switching terms in the traditional exponential sliding mode approaching law cause the sliding mode control to have a jitter phenomenon. In order to ensure the arrival time of the moving point to the sliding surface, the gain of the exponential approaching law must be increased. The gain of the approaching law becomes larger, that is, the approaching law becomes larger, and the speed of the moving point when it reaches the sliding surface becomes larger, which will cause a larger jitter phenomenon. In summary, in order to improve the performance of sliding mode control, the contradiction between the approaching speed and the sliding mode jitter is an important problem that needs to be solved in sliding mode control. The reaching law of sliding mode control directly affects the motion trajectory of the system state reaching the sliding surface. Therefore, starting from the reaching law, proposing a reaching law with better performance is one of the effective ways to resolve the contradiction between the sliding mode reaching speed and the sliding mode chattering. Summary of the invention

[0004] In order to solve the contradiction between arrival speed and vibration in sliding mode control and improve the performance of sliding mode control, the present invention proposes a sliding mode control method for a permanent magnet synchronous motor based on an adaptive reaching law. The implementation steps of the method are as follows:

[0005] S1. Construct a mathematical model of a permanent magnet synchronous motor in a dq synchronous rotating coordinate system;

[0006] The mathematical model includes the stator voltage equation, the electromagnetic torque equation and the mechanical motion equation; among them,

[0007] The stator voltage equation is as follows:

[0008]

[0009] Among them, U q , U d 、i q 、i d are the stator voltage and current in the dq synchronous rotating coordinate system, ω e is the electrical angular velocity, R is the stator resistance, ψ d and ψ q are the stator flux in the dq synchronous rotating coordinate system, ψ d =L d i d +ψ f , ψ q =L q i q , L d and L q are the inductance in the dq synchronous rotating coordinate system, ψ f is the permanent magnet flux amplitude;

[0010] The electromagnetic torque equation is as follows:

[0011]

[0012] Among them, T e is the electromagnetic torque, n p is the pole pair number;

[0013] The mechanical equation of motion is as follows:

[0014]

[0015] Where J is the moment of inertia, ω m is the mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, B is the viscous friction coefficient;

[0016] According to equations (1) to (3), the speed control object of the permanent magnet synchronous motor is derived as a first-order system in the following form:

[0017]

[0018] in, ω m The derivative of = Formula (4)i q The previous corresponding coefficient, =T L The previous corresponding coefficient, =ω m The former corresponding coefficient;

[0019] When considering the case of parameter perturbation, equation (4) can be rewritten as:

[0020]

[0021] in, = Formula (5)i q The parameter perturbation term corresponding to the previous coefficient is =T L The parameter perturbation term corresponding to the previous coefficient is =ω m The parameter perturbation term corresponding to the previous coefficient, ΔB is the perturbation of parameter B, ΔJ is the perturbation of parameter J, Δψ f is the parameter ψ f The perturbation amount;

[0022] Define the total disturbance of the system as d(t), which is composed of internal parameter disturbance and external load disturbance. The expression of the total disturbance of the system d(t) is as follows:

[0023] d(t)=Δαi q -(β+Δβ)T L -Δγω m (6);

[0024] Assume that the total disturbance d(t) of the system satisfies:

[0025] |d(t)|≤d0 (7);

[0026] Among them, d0 is the upper bound of the total disturbance of the system;

[0027] Then the expression (4) of the speed control object of the permanent magnet synchronous motor is rewritten as:

[0028]

[0029] S2, design the adaptive reaching law s of sliding mode control;

[0030] Adaptive reaching law The expression is as follows:

[0031]

[0032] Among them, x is the system state, λ, a, b, ε, k, α1, α2 are all unknown parameters, and ε>0, k>0, 1>a>0, 1>b>0, α1>α2>0; tanh(λs) is the hyperbolic tangent function, and its expression is as follows:

[0033]

[0034] S3, designed sliding surface s(t);

[0035] The expression of sliding surface s(t) is as follows:

[0036]

[0037] Where c is a positive constant, e(t) is the velocity error, e(t) = ω ref (t)-ω m (t),ω ref is the speed reference value, ω m is the actual speed feedback value;

[0038] S4. Derivation of sliding mode control law u(t) according to equations (8), (9) and (11);

[0039] The expression of sliding mode control law u(t) is as follows:

[0040]

[0041] in, ω ref The derivative of

[0042] S5. Perform sliding mode control on the permanent magnet synchronous motor according to the sliding mode control law u(t).

[0043] Preferably, the following steps are further included between step S4 and step S5:

[0044] A sliding mode disturbance observer is designed, and the total disturbance of the system is estimated by using the sliding mode disturbance observer to obtain the estimated value of the total disturbance of the system, and the estimated value of the total disturbance of the system is supplemented into the sliding mode control law u(t) to obtain the supplemented sliding mode control law u(t).

[0045] Preferably, the total disturbance d(t) of the system is expanded into a system state variable, and equation (8) is expanded into a system of the following form:

[0046]

[0047] According to formula (14), the following sliding mode disturbance observer is designed:

[0048]

[0049] Among them, y(e ω ) is the sliding mode rate of the sliding mode disturbance observer error, ω m The estimated value of is, l is the observer gain, is the estimated value of the total disturbance of the system.

[0050] Preferably, the observation error equation of the sliding mode disturbance observer is derived by subtracting (14) and (15), and the observation error equation is as follows:

[0051]

[0052] Among them, e ω and e d are velocity observation error and disturbance observation error respectively;

[0053] The sliding mode surface of the sliding mode disturbance observer is as follows:

[0054]

[0055] Among them, the derivative of the sliding mode surface of the sliding mode disturbance observer is:

[0056]

[0057] The reaching law of the sliding mode disturbance observer is selected as follows:

[0058]

[0059] Among them, ε ω is the switching gain of the reaching law;

[0060] Will Considered as a disturbance term, the sliding mode rate of the sliding mode disturbance observer error is derived according to formulas (16)-(19):

[0061]

[0062] Preferably, the expression of the supplemented sliding mode control law u(t) is as follows:

[0063]

[0064] Substituting equation (20) into equation (15) we can obtain the total disturbance estimate of the system: The total disturbance estimate of the system Substitute into equation (21) to obtain the compensated sliding mode control law.

[0065] The present invention can achieve the following technical effects:

[0066] The adaptive reaching law sliding mode control proposed by the present invention can converge to the sliding mode surface more quickly and has less jitter than the traditional exponential reaching law sliding mode control. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flow chart of a sliding mode control method for a permanent magnet synchronous motor based on an adaptive reaching law provided in an embodiment of the present invention;

[0068] Figure 2 It is an application block diagram of the sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law provided in an embodiment of the present invention in speed control of a permanent magnet synchronous motor;

[0069] Figure 3 It is a schematic diagram of control law waveforms respectively applying the exponential sliding mode control strategy and the adaptive reaching law sliding mode control strategy in the motor simulation model;

[0070] Figure 4a-4c This is a comparison diagram of the effects of the present invention and the traditional technical solution in the motor starting experiment;

[0071] Figure 5a-5c It is a comparison diagram of the effects of the present invention and the traditional technical solution in an experiment of applying a step torque of 0.8 N·m. DETAILED DESCRIPTION

[0072] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0073] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0074] Figure 1 The flowchart of the sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law provided in accordance with an embodiment of the present invention is shown.

[0075] like Figure 1 As shown, the sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law provided by an embodiment of the present invention comprises the following steps:

[0076] S1. Construct a mathematical model of the permanent magnet synchronous motor in the dq synchronous rotating coordinate system.

[0077] The mathematical model includes the stator voltage equation, the electromagnetic torque equation and the mechanical motion equation; among them,

[0078] The stator voltage equation is as follows:

[0079]

[0080] Among them, U q , U d 、i q 、i d are the stator voltage and current in the dq synchronous rotating coordinate system, ω eis the electrical angular velocity, R is the stator resistance, ψ d and ψ q are the stator flux in the dq synchronous rotating coordinate system, ψ d =L d i d +ψ f , ψ q =L q i q , L d and L q are the inductance in the dq synchronous rotating coordinate system, ψ f is the permanent magnet flux amplitude;

[0081] The electromagnetic torque equation is as follows:

[0082]

[0083] Among them, T e is the electromagnetic torque, n p is the pole pair number;

[0084] The mechanical equation of motion is as follows:

[0085]

[0086] Where J is the moment of inertia, ω m is the mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, B is the viscous friction coefficient;

[0087] According to equations (1) to (3), the speed control object of the permanent magnet synchronous motor is derived as a first-order system in the following form:

[0088]

[0089] in, ω m The derivative of = Formula (4)i q The previous corresponding coefficient, =T L The previous corresponding coefficient, =ω m The former corresponding coefficient;

[0090] When considering the case of parameter perturbation, equation (4) can be rewritten as:

[0091]

[0092] in, = Formula (5)i q The parameter perturbation term corresponding to the previous coefficient is =T L The parameter perturbation term corresponding to the previous coefficient is =ω m The parameter perturbation term corresponding to the previous coefficient, ΔB is the perturbation of parameter B, ΔJ is the perturbation of parameter J, Δψ f is the parameter ψ f The perturbation amount;

[0093] Define the total disturbance of the system as d(t), which is composed of internal parameter disturbance and external load disturbance. The expression of the total disturbance of the system d(t) is as follows:

[0094] d(t)=Δαi q -(β+Δβ)T L -Δγω m (6);

[0095] Assume that the total disturbance d(t) of the system satisfies:

[0096] |d(t)|≤d0 (7);

[0097] Among them, d0 is the upper bound of the total disturbance of the system;

[0098] Then the expression (4) of the speed control object of the permanent magnet synchronous motor is rewritten as:

[0099]

[0100] S2. Design of Adaptive Reaching Law for Sliding Mode Control

[0101] Adaptive reaching law The expression is as follows:

[0102]

[0103] Among them, x is the system state, λ, a, b, ε, k, α1, α2 are all unknown parameters, and ε>0, k>0, 1>a>0, 1>b>0, α1>α2>0; tanh(λs) is the hyperbolic tangent function, and its expression is as follows:

[0104]

[0105] S3, designed sliding surface s(t);

[0106] The expression of sliding surface s(t) is as follows:

[0107]

[0108] Where c is a positive constant, e(t) is the velocity error, e(t) = ω ref (t)-ω m (t),ω ref is the speed reference value, ω m It is the actual speed feedback value.

[0109] S4. Derive the sliding mode control law u(t) according to equations (8), (9) and (11).

[0110] According to formula (11), the derivative of the sliding surface e(t) is:

[0111]

[0112] Using equation (9), combined with equation (8), equation (11) and equation (12), the current reference value i can be derived: qref , that is, the sliding mode control law u(t) is as follows:

[0113]

[0114] in, ω ref The derivative of .

[0115] S5. Perform sliding mode control on the permanent magnet synchronous motor according to the sliding mode control law u(t).

[0116] If the total disturbance d(t) of the system in equation (13) is considered, the following steps are also included between step S4 and step S5:

[0117] A sliding mode disturbance observer is designed, and the total disturbance of the system is estimated by using the sliding mode disturbance observer to obtain the estimated value of the total disturbance of the system, and the estimated value of the total disturbance of the system is supplemented into the sliding mode control law u(t) to obtain the supplemented sliding mode control law u(t).

[0118] More specifically, the total disturbance d(t) of the system is expanded into a system state variable, and equation (8) is expanded into the following system:

[0119]

[0120] According to formula (14), the following sliding mode disturbance observer is designed:

[0121]

[0122] Among them, y(e ω ) is the sliding mode rate of the sliding mode disturbance observer error, ω m The estimated value of is, l is the observer gain, is the estimated value of the total disturbance of the system.

[0123] The observation error equation of the sliding mode disturbance observer is derived by subtracting (14) from (15). The observation error equation is as follows:

[0124]

[0125] Among them, e ω and e d are velocity observation error and disturbance observation error respectively;

[0126] The sliding mode surface of the sliding mode disturbance observer is as follows:

[0127]

[0128] Among them, the derivative of the sliding mode surface of the sliding mode disturbance observer is:

[0129]

[0130] The reaching law of the sliding mode disturbance observer is selected as follows:

[0131]

[0132] Among them, ε ω is the switching gain of the reaching law;

[0133] Will Considered as a disturbance term, the sliding mode rate of the sliding mode disturbance observer error is derived according to formulas (16)-(19):

[0134]

[0135] Substituting equation (20) into equation (15) we can obtain the total disturbance estimate of the system: The total disturbance estimate of the system Compensate to the sliding mode control law u(t) to obtain the supplemented sliding mode control law u(t), that is, Substituting d(t) in equation (13), we can obtain the compensated sliding mode control law. The expression of the supplemented sliding mode control law u(t) is as follows:

[0136]

[0137] Figure 2 The application of the sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law provided in an embodiment of the present invention in the speed control of a permanent magnet synchronous motor is shown.

[0138] like Figure 2 As shown, this method is applied to the speed control of a permanent magnet synchronous motor to realize sliding mode control of the permanent magnet synchronous motor based on an adaptive reaching law.

[0139] The effect of the sliding mode control method of the permanent magnet synchronous motor based on the adaptive reaching law proposed in the present invention is verified through simulation and experiments.

[0140] Figure 3 The control law waveforms of the exponential sliding mode control strategy and the adaptive reaching law sliding mode control strategy in the motor simulation model are shown. Figure 3 It can be seen that the exponential reaching law sliding mode control has obvious chattering phenomenon, while the adaptive reaching law sliding mode control has significantly weaker chattering phenomenon compared with it.

[0141] Figure 4a-4c The figure shows the comparison of motor starting experimental results conducted on the permanent magnet synchronous motor experimental platform. Figure 4a It is the traditional exponential reaching law sliding mode control. Figure 4b is an adaptive reaching law sliding mode control, Figure 4c It is a traditional exponential reaching law sliding mode control + sliding mode disturbance observer. Figure 4a-4c The σ marked in the figure is the speed overshoot, t s is the response time. From the experimental results, it can be seen that the adaptive reaching law sliding mode control has less response time and no overshoot than the exponential reaching law sliding mode control. The response time becomes faster after the adaptive reaching law sliding mode control is added with the sliding mode disturbance observer.

[0142] Figure 5a-5c The figure shows the comparison of experimental results after adding 0.8 load torque on the permanent magnet synchronous motor experimental platform. Figure 5a It is the traditional exponential reaching law sliding mode control. Figure 5b For the adaptive reaching law sliding mode control, Figure 5c It is an adaptive reaching law sliding mode control + sliding mode disturbance observer. Figure 5a-5c The σ marked in the figure is the maximum speed fluctuation value, t s is the adjustment time. From the experimental results, it can be seen that the maximum speed fluctuation values ​​are arranged in descending order: adaptive reaching law sliding mode control plus sliding mode disturbance observer, adaptive reaching law sliding mode control, exponential reaching law sliding mode control. And the adjustment time increases in turn. In other words, the anti-disturbance performance of adaptive reaching law sliding mode control plus sliding mode disturbance observer, adaptive reaching law sliding mode control, and exponential reaching law sliding mode control is weakened in turn.

[0143] In summary, the adaptive sliding mode control proposed in the present invention has more excellent performance than the traditional exponential reaching law sliding mode control.

[0144] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" 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 representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0145] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

[0146] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A sliding mode control method for a permanent magnet synchronous motor based on an adaptive reaching law, characterized in that: The steps include: S1. Construct a mathematical model of a permanent magnet synchronous motor in a dq synchronous rotating coordinate system; The mathematical model includes a stator voltage equation, an electromagnetic torque equation and a mechanical motion equation; wherein, The stator voltage equation is as follows: Among them, U q , U d 、i q 、i d are the stator voltage and current in the dq synchronous rotating coordinate system, ω e is the electrical angular velocity, R is the stator resistance, ψ d and ψ q are the stator flux in the dq synchronous rotating coordinate system, ψ d =L d i d +ψ f , ψ q =L q i q , L d and L q are the inductance in the dq synchronous rotating coordinate system, ψ f is the permanent magnet flux amplitude; The electromagnetic torque equation is as follows: Among them, T e is the electromagnetic torque, n p is the pole pair number; The mechanical motion equation is as follows: Where J is the moment of inertia, ω m is the mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, B is the viscous friction coefficient; According to equations (1) to (3), the speed control object of the permanent magnet synchronous motor is derived as a first-order system in the following form: in, ω m The derivative of = Formula (4)i q The previous corresponding coefficient, =T L The previous corresponding coefficient, =ω m The former corresponding coefficient; When considering the case of parameter perturbation, equation (4) can be rewritten as: in, = Formula (5)i q The parameter perturbation term corresponding to the previous coefficient is =T L The parameter perturbation term corresponding to the previous coefficient is =ω m The parameter perturbation term corresponding to the previous coefficient, ΔB is the perturbation of parameter B, ΔJ is the perturbation of parameter J, Δψ f is the parameter ψ f The perturbation amount; Define the total disturbance of the system as d(t), which is composed of internal parameter disturbance and external load disturbance. The expression of the total disturbance of the system d(t) is as follows: d(t)=Dai q -(β+Δβ)T L -Dgo m (6); Assume that the total disturbance d(t) of the system satisfies: |d(t)|≤d0 (7); Among them, d0 is the upper bound of the total disturbance of the system; Then the expression (4) of the speed control object of the permanent magnet synchronous motor is rewritten as: S2. Design of Adaptive Reaching Law for Sliding Mode Control Adaptive reaching law The expression is as follows: Among them, x is the system state, λ, a, b, ε, k, α1, α2 are all unknown parameters, and ε>0, k>0, 1>a>0, 1>b>0, α1>α2>0; tanh(λs) is the hyperbolic tangent function, and its expression is as follows: S3, designed sliding surface s(t); The expression of the sliding surface s(t) is as follows: Where c is a positive constant, e(t) is the velocity error, e(t) = ω ref (t)-ω m (t),ω ref is the speed reference value, ω m is the actual speed feedback value; S4. Derivation of sliding mode control law u(t) according to equations (8), (9) and (11); The expression of the sliding mode control law u(t) is as follows: in, ω ref The derivative of S5. Perform sliding mode control on the permanent magnet synchronous motor according to the sliding mode control law u(t).

2. The sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law according to claim 1, characterized in that: The following steps are also included between step S4 and step S5: A sliding mode disturbance observer is designed, and the total disturbance of the system is estimated by using the sliding mode disturbance observer to obtain a total disturbance estimation value of the system, and the total disturbance estimation value of the system is supplemented into the sliding mode control law u(t) to obtain a supplemented sliding mode control law u(t).

3. The sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law as claimed in claim 2, characterized in that: The total disturbance d(t) of the system is expanded into a system state variable, and equation (8) is expanded into a system of the following form: According to formula (14), the following sliding mode disturbance observer is designed: Among them, y(e ω ) is the sliding mode rate of the sliding mode disturbance observer error, ω m The estimated value of is, l is the observer gain, is the estimated value of the total disturbance of the system.

4. The sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law as claimed in claim 3, characterized in that: The observation error equation of the sliding mode disturbance observer is derived by subtracting equation (14) from equation (15), and the observation error equation is as follows: Among them, e ω and e d are velocity observation error and disturbance observation error respectively; The sliding mode surface of the sliding mode disturbance observer is as follows: Among them, the derivative of the sliding mode surface of the sliding mode disturbance observer is: The reaching law of the sliding mode disturbance observer is selected as follows: Among them, ε ω is the switching gain of the reaching law; Will Considered as a disturbance term, the sliding mode rate of the sliding mode disturbance observer error is derived according to formulas (16)-(19):

5. The sliding mode control method of a permanent magnet synchronous motor based on an adaptive reaching law as claimed in claim 4, characterized in that: The expression of the supplemented sliding mode control law u(t) is as follows: Substituting equation (20) into equation (15) we can obtain the total disturbance estimate of the system: The total disturbance estimate of the system Substitute into equation (21) to obtain the compensated sliding mode control law.

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