PMSM prediction control method and system based on adaptive superhelix algorithm

Abstract

The invention discloses a PMSM prediction control method and system based on an adaptive superhelix algorithm, and the method comprises the steps: building a mathematical model based on a permanent magnet synchronous motor based on an FOC control frame, and obtaining a motor motion equation and an electromagnetic torque equation based on a dq axis; based on a sliding mode control theory, designing a rotating speed ring controller, selecting a linear sliding mode surface, carrying out sliding mode surface design on rotating speed, adopting a rotating speed error as a sliding mode surface, and designing a super-spiral sliding mode speed controller with an adaptive rate; designing a dynamic boundary layer function, and replacing a sign function in an original controller; stability proving of the controller is completed to obtain feasible stability conditions of the controller; the method comprises the following steps: acquiring a discretization equation of motor current as a prediction model, performing Clark-Park transformation on current collected by a sensor to a dq coordinate system to obtain a prediction equation, performing vector synthesis on the obtained dq current value in a prediction module through the prediction equation, performing optimization through a cost function to obtain an accurate prediction current vector, and acting the prediction current vector on a motor execution mechanism. And the motor is further controlled. According to the method, the robustness of the permanent magnet synchronous motor system under unknown disturbance is enhanced, and buffeting is reduced.

Description

Technical Field

[0001] The invention relates to the field of motor control, and in particular to a PMSM predictive control method and system based on an adaptive super-helical algorithm. Background Art

[0002] Permanent magnet synchronous motor (PMSM) is widely used in home appliances, medical, transportation, aerospace and other fields due to its high power density, simple structure and small size. However, due to its nonlinear and dynamic characteristics, the control stability of PMSM faces technical challenges under different loads and operating conditions, especially in the pursuit of efficient, stable and robust control methods. The existing control structure mostly adopts dual closed-loop control (speed loop and current loop), in which the speed loop mainly focuses on robustness, while the current loop pursues accuracy and response speed.

[0003] Traditional sliding mode control can effectively resist external interference due to its strong robustness, but it will produce high-frequency chattering, especially in high-speed dynamic scenarios. For this reason, the super spiral algorithm (STA) in the second-order sliding mode control was proposed to reduce the chattering problem. However, the performance of STA depends on the reasonable adjustment of the gain parameters, and usually requires a known disturbance gradient boundary. If the gain is too large, the chattering increases and the energy consumption is high. If the gain is too small, the anti-interference ability is insufficient. In addition, the discontinuous function in STA cannot completely eliminate the chattering, resulting in a decrease in controller efficiency.

[0004] In current loop control, the predictive control strategy of traditional PI controllers is mostly single-step or finite set control variables, which makes it difficult to accurately track the desired current. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to enhance the robustness of a permanent magnet synchronous motor system under unknown disturbances and reduce jitter.

[0006] In view of the above problems, the present invention provides a PMSM predictive control method based on an adaptive super-helical algorithm, comprising the following steps:

[0007] Step 1: Based on the FOC control framework, a mathematical model based on the permanent magnet synchronous motor is established, and the motor motion equation and electromagnetic torque equation based on the dq axis are obtained;

[0008] Step 2: Based on the sliding mode control theory, design the speed loop controller, select the linear sliding mode surface, design the sliding mode surface for the speed, use the speed error as the sliding mode surface, and design the super helical sliding mode speed controller with adaptive rate;

[0009] Step 3: Design a dynamic boundary layer function and replace the symbol function in the original controller;

[0010] Step 4: Complete the stability proof of the controller to obtain its feasible stability conditions;

[0011] Step 5: Obtain the discretized equation of the motor current as the prediction model. The current collected by the sensor is transformed into the dq coordinate system through Clark-Park to obtain the prediction equation. The obtained dq current value is vector synthesized in the prediction module through the prediction equation, and the cost function is optimized to obtain an accurate predicted current vector, which acts on the motor actuator (switch bridge arm) to control the motor.

[0012] Furthermore, in step 1, the mathematical model based on the permanent magnet synchronous motor is:

[0013]

[0014] The equation of motion is:

[0015]

[0016] Due to the use of surface-mount motors, L d =L q , so the electromagnetic torque equation is:

[0017]

[0018] In the formula, u d 、u q are the direct-axis and quadrature-axis components of the stator voltage respectively; i d ,i q are the direct-axis and quadrature-axis components of the stator current respectively; L d , L q are the inductance of dq axis respectively; R s is the stator resistance; ω e is the electrical angular velocity of the motor; ω m is the mechanical angular velocity; n p is the pole pair number; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; B is the friction coefficient; ψ f is the magnetic flux of the rotor permanent magnet.

[0019] Furthermore, in step 2, the speed error is selected as the linear sliding surface s, that is,

[0020] s=ω ref -ω (4)

[0021] Among them, ω ref is the reference speed, ω is the actual speed, the sliding surface s in (4) is differentiated, and (2) is substituted into it to obtain

[0022]

[0023] in, Assume that h(t, ω) and g(t, ω) are

[0024]

[0025] The second-order differential of the sliding surface s is expressed as

[0026]

[0027] Among them, i q Assume that are all bounded, that is

[0028]

[0029] is the control input i q The designed supercoil control rate is

[0030]

[0031] The adaptive rate of the designed super-helical sliding mode controller is as follows:

[0032]

[0033] Where k1, k2, γ1, γ2, and μ are all positive constants.

[0034] Furthermore, in step 3, a dynamic boundary layer function is designed to replace the symbol function in the original controller. The dynamic boundary layer function makes the boundary layer thickness φ change with the movement of the state trajectory. When the system trajectory is far away from the equilibrium point, φ decreases rapidly, accelerating the convergence speed; when the system trajectory approaches the equilibrium point, φ gradually decreases to 0 at a gentler speed; the specific form is as follows:

[0035]

[0036] Among them, φ(s) is the dynamic boundary layer function, and its specific form is:

[0037]

[0038] In the formula, φ max is the maximum value of the boundary layer thickness, and n is the coefficient for adjusting the adaptive change rate of the boundary layer. So far, the improved adaptive super-helical sliding mode control is:

[0039]

[0040] Furthermore, in step 4, the Lyapunov function is taken as

[0041]

[0042] Among them, ε α =α-α * , ε β =β-β * ,, V0 represents the superhelical part without the adaptive rate parameter, and the following two items represent the adaptive parameter part. For V0, let

[0043]

[0044] have

[0045]

[0046] It is easy to see that v0 is positive definite. Since tanh(s) and sign(s) have the same sign characteristics when s>0 and s<0, that is, when s>0, both are greater than 0, and when s<0, both are less than 0. Based on The expression of can be obtained inside and outside the boundary layer, which is negative definite, and the superhelix is ​​stable;

[0047] Next, we prove the stability of the adaptive rate.

[0048]

[0049] Since 0<γ1,γ2<1, k1,k2 are both positive constants, according to the commonly used inequality relationship have to

[0050]

[0051] When |s|>μ and α>α m hour, because If you take Then φ=0, V is negative definite. When |s|<μ, φ is negative definite according to the value of α. In summary, the overall Lyapunov function Negative definite, stability is proved.

[0052] Furthermore, the step 5 specifically includes:

[0053] The motor model (1) is discretized using the first-order Euler method to obtain:

[0054]

[0055] Where: i d (k+1), i q (k+1) are the predicted current values ​​of the d and q axes at the next moment; i d (k),,i q(k) is the current sampling value of the d and q axes at the current moment; u d (k),u q (k) is the voltage value of d and q axes at the current moment; T s is the sampling period of the system, through the cost function

[0056]

[0057] Calculate the minimum value and find the best two vectors within a period Ts. The synthesized new vector can track the desired current vector without error.

[0058] The present invention also provides a PMSM predictive control system based on an adaptive super-helical algorithm, comprising the following modules:

[0059] The mathematical model building module is used to build a mathematical model based on the permanent magnet synchronous motor based on the FOC control framework, and obtain the motor motion equation and electromagnetic torque equation based on the dq axis;

[0060] The sliding film speed controller design module is used to design the speed loop controller based on the sliding mode control theory, select the linear sliding mode surface, design the sliding mode surface for the speed, use the speed error as the sliding mode surface, and design the super spiral sliding mode speed controller with adaptive rate;

[0061] Dynamic boundary layer function design module, used to design dynamic boundary layer function and replace the symbol function in the original controller;

[0062] A stability proof module, used to complete the stability proof of the controller to obtain its feasible stability conditions;

[0063] The prediction control module is used to obtain the discretized equation of the motor current as a prediction model. The current collected by the sensor is transformed into the dq coordinate system by Clark-Park to obtain the prediction equation. The obtained dq current value is vector synthesized in the prediction module through the prediction equation, and the cost function is optimized to obtain an accurate predicted current vector, which acts on the motor actuator to control the motor.

[0064] Furthermore, in the mathematical model building module, the mathematical model based on the permanent magnet synchronous motor is:

[0065]

[0066] The equation of motion is:

[0067]

[0068] Due to the use of surface-mount motors, L d =L q, so the electromagnetic torque equation is:

[0069]

[0070] In the formula, u d 、u q are the direct-axis and quadrature-axis components of the stator voltage respectively; i d ,i q are the direct-axis and quadrature-axis components of the stator current respectively; L d , L q are the inductance of dq axis respectively; R s is the stator resistance; ω e is the electrical angular velocity of the motor; ω m is the mechanical angular velocity; n p is the pole pair number; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; B is the friction coefficient; ψ f is the magnetic flux of the rotor permanent magnet.

[0071] Furthermore, in the sliding film speed controller design module, the speed error is selected as the linear sliding surface s, that is,

[0072] s=ω ref -ω (4)

[0073] Among them, ω ref is the reference speed, ω is the actual speed, the sliding surface s in (4) is differentiated, and (2) is substituted into it to obtain

[0074]

[0075] in, Assume that h(t, ω) and g(t, ω) are

[0076]

[0077] The second-order differential of the sliding surface s is expressed as

[0078]

[0079] Among them, i q Assume that are all bounded, that is

[0080]

[0081] is the control input i q The designed supercoil control rate is

[0082]

[0083] The adaptive rate of the designed super-helical sliding mode controller is as follows:

[0084]

[0085] Where k1, k2, γ1, γ2, and μ are all positive constants.

[0086] Furthermore, in the dynamic boundary layer function design module, the dynamic boundary layer function makes the boundary layer thickness φ change with the movement of the state trajectory. When the system trajectory is far away from the equilibrium point, φ decreases rapidly, accelerating the convergence speed; when the system trajectory approaches the equilibrium point, φ gradually decreases to 0 at a gentler speed; the specific form is as follows:

[0087]

[0088] Among them, φ(s) is the dynamic boundary layer function, and its specific form is:

[0089]

[0090] In the formula, φ max is the maximum value of the boundary layer thickness, and n is the coefficient for adjusting the adaptive change rate of the boundary layer. So far, the improved adaptive super-helical sliding mode control is:

[0091]

[0092] In the predictive control module:

[0093] The motor model (1) is discretized using the first-order Euler method to obtain:

[0094]

[0095] Where: id(k+1) and iq(k+1) are the predicted current values ​​of the d and q axes at the next moment respectively; id(k) and iiq(k) are the current sampling values ​​of the d and q axes at the current moment; ud(k) and uq(k) are the voltage values ​​of the d and q axes at the current moment; Ts is the sampling period of the system.

[0096]

[0097] Calculate the minimum value and find the best two vectors within a period Ts. The synthesized new vector can track the desired current vector without error.

[0098] The beneficial effects of the present invention are as follows:

[0099] (1) The present invention aims to solve the energy consumption and loss problems caused by the overestimation of the controller gain due to the unknown upper bound of the disturbance. The adaptive rate is used to automatically adjust the controller gain, which can reduce the gain overestimation phenomenon and effectively improve the response and accuracy of the speed loop.

[0100] (2) Based on the concept of dynamic boundary layer, the present invention designs a dynamic boundary layer function combining tanh and sign. According to the sliding mode state of the system at the current moment, within the set boundary layer range, the boundary layer thickness can be adaptively modified according to the current situation, and the switching speed of the sliding mode can be dynamically adjusted, thereby reducing chattering and improving the accuracy and robustness of control without artificially modifying the boundary layer thickness.

[0101] (3) The present invention uses a dual-vector model predictive current control method, which has better current response speed and accuracy, smaller current pulsation and torque pulsation than the traditional PI current loop controller. Compared with the traditional single-step finite set model predictive current control method, it can achieve error-free tracking of the current reference value. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 It is a structural block diagram of the control system of the present invention;

[0103] Figure 2 is the dynamic boundary function image of the present invention;

[0104] Figure 3 It is a schematic diagram of the dynamic boundary layer of the present invention;

[0105] Figure 4 Schematic diagram of current control vector synthesis for dual vector model prediction;

[0106] Figure 5 It is a comparison diagram of the speed curve of adaptive super-helical sliding mode control without dynamic boundary layer function and PI control and ordinary super-helical sliding mode control;

[0107] Figure 6 A comparison diagram of the speed curve of the dynamic boundary layer adaptive super-helical sliding mode control proposed by the present invention and the speed response chattering of the common adaptive super-helical sliding mode control;

[0108] Figure 7 It is a comparison diagram of the speed curve of the dynamic boundary layer adaptive super-helical sliding mode control proposed by the present invention and the speed curve of the adaptive super-helical sliding mode control using the tanh function as a replacement, wherein Figure (a) is a speed response comparison diagram;

[0109] Figure 8 is a comparison diagram of the q-axis current response curve of the dual-vector model predictive current control proposed in the present invention and the q-axis current of traditional PI control and single-step finite set predictive control, where Figure (a) is PI control, Figure (b) is single-step finite set predictive control, and Figure (c) is the dual-vector control proposed in the present invention. DETAILED DESCRIPTION

[0110] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0111] The present invention provides a composite control scheme of a permanent magnet synchronous motor speed loop controller and a current loop controller, aiming to improve the rapid response and control accuracy of the system as a whole. The overall block diagram of the system is as follows: Figure 1 As shown. Among them, DBL+ASTSMC is the speed controller proposed by the present invention. The speed and angle of the motor are acquired by the encoder instead of the sensorless algorithm, and then the acquired signal value is sent to the processor for software calculation. Below, the steps of a PMSM predictive control method based on an adaptive superhelical algorithm are described in detail:

[0112] Step 1, the present invention adopts a vector control (FOC) scheme, firstly based on the FOC theory, a dq axis mathematical model of the permanent magnet synchronous motor is established:

[0113]

[0114] The equation of motion is:

[0115]

[0116] Due to the use of surface-mount motors, L d =L q , so the electromagnetic torque equation is:

[0117]

[0118] In the formula, u d 、u q are the direct-axis and quadrature-axis components of the stator voltage respectively; i d ,i q are the direct-axis and quadrature-axis components of the stator current respectively; L d , L q are the inductance of dq axis respectively; R s is the stator resistance; ω e is the electrical angular velocity of the motor; ω m is the mechanical angular velocity; n p is the pole pair number; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; B is the friction coefficient; ψ fis the magnetic flux of the rotor permanent magnet.

[0119] Step 2, design the super-helical sliding mode speed controller. For the convenience of analysis and practicality, the speed error is selected as the linear sliding mode surface s, that is:

[0120] s=ω ref -ω (4)

[0121] Among them, ω ref is the reference speed, and ω is the actual speed. In order to obtain the control rate of the controller, the sliding surface s in (4) is differentiated and substituted into (2), and we can get:

[0122]

[0123] in, is regarded as a load disturbance. Assume h(t, ω) and g(t, ω) are:

[0124]

[0125] The second-order differential of the sliding surface s can be expressed as:

[0126]

[0127] Among them, i q Assume that are all bounded, that is:

[0128]

[0129] Can be control input i q The designed supercoil control rate is:

[0130]

[0131] Among them, α and β are the super-helical sliding mode control gains. In order to cope with the situation where the upper bound of the disturbance is unknown, an adaptive rate is designed. The design idea is to dynamically increase the control gains α and β until the system trajectory reaches the set second-order sliding surface. At this time, in order to maintain the system on the sliding surface, the control gain begins to decrease. Once the system trajectory deviates from the sliding surface, the control gain will increase again until the system reaches the sliding surface again. The designed adaptive rate is as follows:

[0132]

[0133] Where k1, k2, γ1, γ2, and μ are all positive constants.

[0134] Step 3: In order to weaken the chattering caused by the sliding mode control sign function sign, the present invention proposes a piecewise function based on the dynamic boundary layer concept for replacement. Figure 3 The graph of the boundary layer function under different boundary layer thicknesses is shown. The idea of ​​conventional saturation function replacement or tanh replacement is that when the sliding surface s is within the boundary layer, linear or smooth nonlinear control is used instead of jumping at the origin like the sign function, so as to make the control signal smoother. However, the thickness of the boundary layer is often fixed, and the system trajectory can only remain stable within the boundary layer and cannot converge to the switching plane. Therefore, the present invention designs a dynamic boundary layer function so that the boundary layer thickness φ changes with the movement of the state trajectory. When the system trajectory is far away from the equilibrium point, φ decreases rapidly, accelerating the convergence speed; when the system trajectory approaches the equilibrium point, φ gradually decreases to 0 at a slower speed; this enables the system to improve the steady-state accuracy while weakening the jitter. The specific form is as follows:

[0135]

[0136] Among them, φ(s) is the dynamic boundary layer function, and its specific form is:

[0137]

[0138] In the formula, φ max is the maximum value of the boundary layer thickness, n is the coefficient for adjusting the adaptive change rate of the boundary layer, and its function graph is shown in Figure 2 As shown. So far, the improved adaptive super-helical sliding mode control is:

[0139]

[0140] Step 4, prove the stability of the adaptive super-helical sliding mode control system. Assume that the Lyapunov function is

[0141]

[0142] Among them, ε α =α-α * , ε β =β-β * , V0 represents the superhelical part without the adaptive rate parameter, and the following two items represent the adaptive parameter part. For V0, let

[0143]

[0144] have

[0145]

[0146] It is easy to see that V0 is positive definite. Since tanh(s) and sign(s) have the same sign characteristics when s>0 and s<0, that is, when s>0, both are greater than 0, and when s<0, both are less than 0. Based on The expression of can be obtained that it is negative definite both inside and outside the boundary layer, and the superhelix body is stable.

[0147] Next, we prove the stability of the adaptive rate.

[0148]

[0149] Since 0<γ1,γ2<1, k1,k2 are both positive constants, according to the commonly used inequality relationship Available

[0150]

[0151] When |s|>μ and α>α m hour, because If you take Then φ=0, V is negative definite. When |s|<μ, it can be divided into two cases according to the different values ​​of α

[0152]

[0153] Accordingly, there are

[0154]

[0155] At the beginning, the adaptive coefficient α is still very small, φ is the second term of formula (20), α increases linearly with time and reaches α in a finite time. m During this period, φ<0, so Negative definite. When α exceeds α m When φ is the first term of formula (20), φ>0, and it is impossible to judge The sign of the adaptive rate α m is reduced. When the system is unstable, s gradually deviates from the sliding surface s=0, |s| will increase, and when |s|>μ, it will return to situation 1. At this time, the system is stable and will return to |s|<μ in a finite time. In summary, within a large range, the system is still stable. So far, the stability of the adaptive second-order super-helical sliding mode speed controller has been proved.

[0156] Step 5, in order to reduce the pulsation caused by the traditional PI current loop controller and the current error caused by the single-step model prediction, the present invention adopts a dual-vector current prediction method to improve the current loop controller of the traditional permanent magnet synchronous motor control system, and discretizes the motor model (1) using the first-order Euler method to obtain:

[0157]

[0158] Where: i d (k+1), i q(k+1) are the predicted current values ​​of the d and q axes at the next moment; i d (k),,i q (k) is the current sampling value of the d and q axes at the current moment; u d (k) and u q (k) is the voltage value of d and q axes at the current moment; T s is the sampling period of the system. Through the cost function

[0159]

[0160] Calculate the minimum value and find the best two vectors within a period Ts. The new vector synthesized by different duty cycles within a period can track the desired current vector without error. Satisfies the following relationship:

[0161]

[0162] Among them, s opt1，2 is the rate of change of the current of the optimal vector over time, and t1 is the action time of the first vector.

[0163] For the first vector, after the optimal choice is obtained through cost function iteration among the 7 finite set vectors, the action time is

[0164]

[0165] The expression of current slope is

[0166]

[0167] Where s0 is the current slope of the zero voltage vector.

[0168] The method of the present invention is simulated and verified in Matlab / Simulink environment. The motor speed is 1000rpm, the number of pole pairs is 4, the three-phase bridge arm is 220V, and the IGBT is used. Figure 5 The operating characteristics of the adaptive superhelical sliding mode control proposed in the present invention are compared with those of the ordinary superhelical and PI control at this speed. It can be seen that the method proposed in the present invention has a smaller overshoot and a shorter adjustment time than the ordinary superhelical algorithm, and due to the existence of the gain adaptation rate and the speed error as the sliding mode surface, this method will make the system approach the sliding mode surface over time, and the image shows that the speed jitter amplitude will gradually converge to 1000rpm over time. In contrast, PI control has a larger steady-state error, a slower convergence speed and poorer accuracy. Figure 6 It is a comparison between the adaptive super-helical control combined with the dynamic boundary layer function and the ordinary adaptive super-helical control. It can be seen that the chattering phenomenon of the former is significantly smaller than that of the latter. Figure 7It is a comparison between the dynamic boundary layer adaptive superhelical control and the adaptive superhelical jitter with the tanh function replacing the sign function. In comparison, the former has a more stable fluctuation during the entire operating condition. Figure 8 (a), (b), and (c) are the q-axis current waveforms using PI control, single-step finite set predictive control, and dual-vector model predictive control, respectively. It can be seen that the dual-vector method has the smallest and most accurate current fluctuation, which can better suppress the motor current high-order harmonics, reduce torque pulsation, and improve operating performance and sector selection accuracy.

[0169] The above is an implementation of the present invention. Based on this implementation, the speed estimation of the permanent magnet synchronous motor system can be simulated in MATLAB / Simulink. Based on this implementation, the simulation of the permanent magnet synchronous motor running under different working conditions can also be performed in a real-time simulator such as dSPACE or RT-LAB. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A PMSM predictive control method based on an adaptive superhelical algorithm, characterized in that: The following steps are involved: Step 1: Based on the FOC control framework, a mathematical model based on the permanent magnet synchronous motor is established, and the motor motion equation and electromagnetic torque equation based on the dq axis are obtained; Step 2: Based on the sliding mode control theory, design the speed loop controller, select the linear sliding mode surface, design the sliding mode surface for the speed, use the speed error as the sliding mode surface, and design the super helical sliding mode speed controller with adaptive rate; Step 3: Design a dynamic boundary layer function and replace the symbol function in the original controller; Step 4: Complete the stability proof of the controller to obtain its feasible stability conditions; Step 5: Obtain the discretized equation of the motor current as the prediction model. The current collected by the sensor is transformed into the dq coordinate system through Clark-Park to obtain the prediction equation. The obtained dq current value is vector synthesized in the prediction module through the prediction equation, and the cost function is optimized to obtain an accurate predicted current vector, which acts on the motor actuator to control the motor.

2. The PMSM predictive control method based on the adaptive superhelical algorithm according to claim 1, characterized in that: In step 1, the mathematical model based on the permanent magnet synchronous motor is: The equation of motion is: Due to the use of surface-mount motors, L d =L q , so the electromagnetic torque equation is: In the formula, u d 、u q are the direct-axis and quadrature-axis components of the stator voltage respectively; i d ,i q are the direct-axis and quadrature-axis components of the stator current respectively; L d , L q are the inductance of dq axis respectively; R s is the stator resistance; ω e is the motor electrical angular velocity; ω m is the mechanical angular velocity; n p is the pole pair number; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; B is the friction coefficient; ψ f is the rotor permanent magnet flux.

3. The PMSM predictive control method based on the adaptive superhelical algorithm according to claim 2 is characterized in that: In step 2, the speed error is selected as the linear sliding surface s, that is, s = ω ref -oh (4) Among them, ω ref is the reference speed, ω is the actual speed, the sliding surface s in (4) is differentiated, and (2) is substituted into it to obtain in, Assume that h(t, ω) and g(t, ω) are The second-order differential of the sliding surface s is expressed as Among them, i q Assume that are all bounded, that is is the control input i q The designed supercoil control rate is The adaptive rate of the designed super-helical sliding mode controller is as follows: Where k1, k2, γ1, γ2, and μ are all positive constants.

4. The PMSM predictive control method based on the adaptive superhelical algorithm according to claim 3 is characterized in that: The step 3 designs a dynamic boundary layer function, which replaces the symbol function in the original controller. The dynamic boundary layer function makes the boundary layer thickness φ change with the movement of the state trajectory. When the system trajectory is far away from the equilibrium point, φ decreases rapidly, accelerating the convergence speed; when the system trajectory approaches the equilibrium point, φ gradually decreases to 0 at a gentler speed; the specific form is as follows: Among them, φ(s) is the dynamic boundary layer function, and its specific form is: In the formula, φ max is the maximum value of the boundary layer thickness, and n is the coefficient for adjusting the adaptive change rate of the boundary layer. So far, the improved adaptive super-helical sliding mode control is:

5. The PMSM predictive control method based on the adaptive superhelical algorithm according to claim 4, characterized in that: In step 4, the Lyapunov function is taken as Among them, ε α =α-α * , ε β =β-β * , V0 represents the superhelical part without the adaptive rate parameter, and the following two items represent the adaptive parameter part. For V0, let have It is easy to see that V0 is positive definite. Since tanh(s) and sign(s) have the same sign characteristics when s>0 and s<0, that is, when s>0, both are greater than 0, and when s<0, both are less than 0. Based on The expression of can be obtained inside and outside the boundary layer, which is negative definite, and the superhelix is ​​stable; Next, we prove the stability of the adaptive rate. Since 0<γ1,γ2<1, k1,k2 are both positive constants, according to the commonly used inequality relationship have to When |s|>μ and α>α m hour, because If you take Then φ=0, is negative definite. When |s|<μ, φ is negative definite according to the value of α. In summary, the overall Lyapunov function Negative definite, stability is proved.

6. The PMSM predictive control method based on the adaptive superhelical algorithm according to claim 4 is characterized in that: The step 5 specifically includes: The motor model (1) is discretized using the first-order Euler method to obtain: Where: id(k+1) and iq(k+1) are the predicted current values ​​of the d and q axes at the next moment respectively; id(k) and iq(k) are the current sampling values ​​of the d and q axes at the current moment; ud(k) and uq(k) are the voltage values ​​of the d and q axes at the current moment; Ts is the sampling period of the system. Calculate the minimum value and find the best two vectors within a period Ts. The synthesized new vector can track the desired current vector without error.

7. A PMSM predictive control system based on an adaptive superhelical algorithm, characterized in that: Includes the following modules: The mathematical model building module is used to build a mathematical model based on the permanent magnet synchronous motor based on the FOC control framework, and obtain the motor motion equation and electromagnetic torque equation based on the dq axis; The sliding film speed controller design module is used to design the speed loop controller based on the sliding mode control theory, select the linear sliding mode surface, design the sliding mode surface for the speed, use the speed error as the sliding mode surface, and design the super spiral sliding mode speed controller with adaptive rate; Dynamic boundary layer function design module, used to design dynamic boundary layer function and replace the symbol function in the original controller; A stability proof module, used to complete the stability proof of the controller to obtain its feasible stability conditions; The prediction control module is used to obtain the discretized equation of the motor current as a prediction model. The current collected by the sensor is transformed into the dq coordinate system by Clark-Park to obtain the prediction equation. The obtained dq current value is vector synthesized in the prediction module through the prediction equation, and the cost function is optimized to obtain an accurate predicted current vector, which acts on the motor actuator to control the motor.

8. The PMSM predictive control system based on the adaptive superhelical algorithm according to claim 7, characterized in that: In the mathematical model building module, the mathematical model based on the permanent magnet synchronous motor is: The equation of motion is: Due to the use of surface-mount motors, L d =L q , so the electromagnetic torque equation is: In the formula, u d 、u q are the direct-axis and quadrature-axis components of the stator voltage respectively; i d ,i q are the direct-axis and quadrature-axis components of the stator current respectively; L d , L q are the inductance of dq axis respectively; R s is the stator resistance; ω e is the motor electrical angular velocity; ω m is the mechanical angular velocity; n p is the pole pair number; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; B is the friction coefficient; ψ f is the rotor permanent magnet flux.

9. The PMSM predictive control system based on the adaptive superhelical algorithm according to claim 8, characterized in that: In the sliding film speed controller design module, the speed error is selected as the linear sliding surface s, that is, s = ω ref -oh (4) Among them, ω ref is the reference speed, ω is the actual speed, the sliding surface s in (4) is differentiated, and (2) is substituted into it to obtain in, Assume that h(t, ω) and g(t, ω) are The second-order differential of the sliding surface s is expressed as Among them, i q Assume that are all bounded, that is is the control input i q The designed supercoil control rate is The adaptive rate of the designed super-helical sliding mode controller is as follows: In the formula, k1, k2, γ1, γ2, and μ are all positive constants.

10. The PMSM predictive control system based on the adaptive superhelical algorithm according to claim 9, characterized in that: In the dynamic boundary layer function design module, the dynamic boundary layer function makes the boundary layer thickness φ change with the movement of the state trajectory. When the system trajectory is far away from the equilibrium point, φ decreases rapidly, accelerating the convergence speed; when the system trajectory approaches the equilibrium point, φ gradually decreases to 0 at a gentler speed; the specific form is as follows: Among them, φ(s) is the dynamic boundary layer function, and its specific form is: In the formula, φ max is the maximum value of the boundary layer thickness, and n is the coefficient for adjusting the adaptive change rate of the boundary layer. So far, the improved adaptive super-helical sliding mode control is: In the predictive control module: The motor model (1) is discretized using the first-order Euler method to obtain: Where: id(k+1) and iq(k+1) are the predicted current values ​​of the d and q axes at the next moment respectively; id(k) and iq(k) are the current sampling values ​​of the d and q axes at the current moment; ud(k) and uq(k) are the voltage values ​​of the d and q axes at the current moment; Ts is the sampling period of the system. Calculate the minimum value and find the best two vectors within a period Ts. The synthesized new vector can track the desired current vector without error.

Images