Non-singular fast terminal sliding mode observer based on neural network phase-locked loop

Abstract

The invention discloses a non-singular fast terminal sliding mode observer based on a neural network phase-locked loop. A Sigmoid function is adopted to design a non-singular fast terminal sliding mode surface in the observer; a stator current error system is defined, an equivalent item of a sliding mode control law is obtained according to an equivalent sliding mode control principle, a switching control law is designed for control of the stator current error system state on a sliding mode surface, and the sliding mode control law in the observer is obtained according to the equivalent item and the switching control law; introducing a rapid tracking differentiator comprising a terminal attractor, wherein the rapid tracking differentiator is used for accurately tracking and filtering the back electromotive force; and a phase-locked loop in the observer is controlled through the BP neural network, and the phase-locked loop is used for extracting an electrical angle and an electrical angular velocity signal from the back electromotive force to obtain a final sliding-mode observer. According to the method, the convergence speed is effectively increased, high-frequency buffeting is reduced, phase delay is compensated, and the dynamic performance is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a non-singular fast terminal sliding mode observer based on a neural network phase-locked loop. Background Art

[0002] Permanent magnet synchronous motors have the advantages of low moment of inertia, wide speed regulation range, high working efficiency, high efficiency and energy saving, and are widely used in aerospace, new energy vehicles, intelligent robots and other fields. According to the installation position of the rotor permanent magnet, permanent magnet synchronous motors can be divided into two categories: built-in permanent magnet synchronous motors and surface mounted permanent magnet synchronous motors. In order to obtain accurate SPMSM rotor position and speed information, mechanical sensors such as photoelectric encoders and rotary encoders are usually used, but the reliability of the encoder will be limited by the application site, so sensorless control has become a hot topic of research today.

[0003] Permanent magnet synchronous motor position sensorless technology can be divided into two categories according to different position estimation principles: one is based on the salient pole characteristics of the motor, and realizes the identification of the rotor position through high-frequency signal injection method and open-loop starting method; the other is to estimate the rotor position by detecting back electromotive force.

[0004] As a fundamental model estimation method with strong robustness, sliding mode observer is widely used in sensorless control because of its simple design, low requirements on system model accuracy, and strong anti-interference ability to parameter changes and external interference. However, due to the discontinuity of the switching sliding mode function, the traditional sliding mode observer is prone to high-frequency jitter in the system, which seriously affects the position estimation accuracy.

[0005] In the prior art, many solutions for eliminating the jitter of sliding mode observers have been proposed to solve the above problems. Most of the time, a low-pass filter is introduced. If the filter cutoff frequency is too high, the filtering effect will be too poor. If the filter cutoff frequency is too low, the system phase lag will be caused, resulting in an increase in the position estimation error, making it difficult to balance the phase and filtering effect. The introduction of a phase-locked loop (PLL) can solve the frequency and phase problems between the input signal and the internal oscillator signal, but it will also lead to an increase in the error in the motor rotor position estimation. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a non-singular fast terminal sliding mode observer based on a neural network phase-locked loop, which can effectively increase the convergence speed, reduce high-frequency jitter, compensate for phase delay and improve dynamic performance.

[0007] In order to solve the above technical problems, the present invention provides a non-singular fast terminal sliding mode observer based on a neural network phase-locked loop, and the design method includes the following steps:

[0008] Step 1) Design a nonsingular fast terminal sliding mode surface in the observer using the Sigmoid function;

[0009] Step 2) Define the stator current error system, obtain the equivalent term of the sliding mode control law according to the principle of equivalent sliding mode control, design the switching control law through the state of the stator current error system on the sliding mode surface, and obtain the sliding mode control law in the observer according to the equivalent term and the switching control law;

[0010] Step 3) Introduce a fast tracking differentiator with a terminal attractor, which is used for accurate tracking and filtering of the back electromotive force;

[0011] Step 4) Control the phase-locked loop in the observer through a BP neural network. The phase-locked loop is used to extract the electrical angle and electrical angular velocity signals from the back electromotive force to obtain the final sliding mode observer.

[0012] Furthermore, the nonsingular fast terminal sliding mode surface is:

[0013] is the current observation error, where a, b > 0; 0 < λ < 1; is the Sigmoid(s) function with smooth and continuous characteristics, and its expression is d is an adjustable parameter.

[0014] Furthermore, the control law is as follows:

[0015] v = v eq + v sw ,

[0016]

[0017] where |s| δ = [|s α | δ |s β | δ T ; k, η, r, μ > 0; 0 < δ < 1; 0 < Q < 1;

[0018] v eq is obtained from and without considering the back electromotive force. v sw consists of two parts. k|s| δ sign(s) / (Q + re -μ|s| ) makes the observer gain adaptively change according to the magnitude of the stator current error through setting a scaling function, which is used for; ηs is used to ensure the approaching rate when the state of the stator current error system is far from the sliding mode surface.

[0019] ​Further, the differentiator is:

[0020]

[0021] where R, t, h > 0; m > 1; R is the time scale, representing the overall tracking speed; t represents the linear factor, h is the weight of the non-linear factor, z1, z2 are the state variables of the tracking differentiator, v x , x = α, β are the input variables, for accurately tracking v x and can also be used as a filter for v x .

[0022] Further, the BP neural network has an M:N:P topology, with M nodes in the input layer, P nodes in the output layer, and N hidden nodes in the hidden layer.

[0023] Further, the transfer function of the hidden layer is selected as the sigmoid function; the transfer function of the output layer is a linear function.

[0024] Further, the BP neural network adopts the quantized conjugate gradient algorithm.

[0025] Further, in step 4), initially, the PI controller outputs parameters to the BP neural network for training, and the trained BP neural network is used to replace the PI controller to control the phase-locked loop in the observer.

[0026] Advantages of the present invention:

[0027] Compared with the traditional non-singular terminal sliding mode observer, the designed new observer can obtain a smaller phase lag, has better static and dynamic responses of the system, faster convergence speed, and higher tracking accuracy. When there are load disturbances in the system, it can still accurately estimate the position and speed of the motor rotor, and has strong robustness. Description of the Drawings

[0028] Figure 1 is the flowchart of the design method of the present invention;

[0029] Figure 2 is the structural diagram of the improved observer of the present invention;

[0030] Figure 3 is the structural diagram of the three-layer BP neural network used in the present invention;

[0031] Figure 4 is the structural block diagram of the improved neural network type PLL of the present invention;

[0032] Figure 5 is the simulation diagram of the rotational speed estimation under variable load of the present invention;

[0033] Figure 6 is the estimated curve graph of the α-axis back electromotive force of the present invention;

[0034] Figure 7 is the estimated curve graph of the β-axis back electromotive force of the present invention;

[0035] Figure 8 is the α-axis back electromotive force curve graph before filtering of the present invention;

[0036] Figure 9 is the simulation comparison graph of the rotational speed between the present invention and the existing observer;

[0037] Figure 10 is the speed estimation graph under variable load of the present invention;

[0038] Figure 11 is the enlarged graph of the rotational speed comparison of the present invention;

[0039] Figure 12 is the rotational speed estimation error graph of the present invention. Detailed Embodiment

[0040] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited do not limit the present invention.

[0041] Refer to Figure 1 As shown, in an embodiment of the nonsingular fast terminal sliding mode observer based on a neural network phase-locked loop of the present invention, first, a new nonsingular fast terminal sliding mode surface is designed so that the observer can avoid the nonsingular problem during operation and can make the current observation error converge to zero in a short time; then, by combining and improving the fractional reaching law, the control law of the new sliding mode observer is designed, and the inherent chattering of the sliding mode can be suppressed by adapting the dynamic switching function; next, in order to avoid the phase lag caused by the low-pass filter in the traditional observer, a low-chattering fast tracking differentiator with a terminal attractor is added; finally, the PI controller in the traditional phase-locked loop is replaced with a neural network control, so that the system obtains better dynamic performance.

[0042] For the sake of simplifying the analysis, a model of the surface-mounted permanent magnet synchronous motor system is established. Usually, the following assumptions are made: the rotor has no damping winding; the spatial magnetic field is sinusoidally distributed, and the induced electromotive force in the stator armature winding is also a sine wave; the core eddy current and hysteresis losses are not considered; the saturation of the stator core is ignored, and the magnetic circuit is defaulted to be linear with unchanged inductance parameters.

[0043] Based on the above assumptions, the mathematical model of the permanent magnet synchronous motor in the α-β coordinate system is established as:

[0044]

[0045] In the formula: iα , i β are the α and β axis currents in the stationary two-phase coordinate system; u α , u β are the α and β axis voltages in the stationary two-phase coordinate system; R s is the stator resistance; L is the equivalent inductance of the α and β axes of the stator winding; e α , e β are the back electromotive forces of the α and β phases; ψ f is the permanent magnet flux linkage; ω r is the rotational angular velocity of the dq coordinate system; θ e is the rotor position.

[0046] Next, the design of the non-singular fast terminal sliding mode observer is carried out:

[0047] The design of the non-singular fast terminal sliding mode observer is mainly divided into three stages: First is the design of the sliding mode surface; then is the design of the reaching law; finally is the design of the phase-locked loop. A new type of non-singular terminal sliding mode surface is designed. On the basis of this sliding mode surface, the enhanced fractional reaching law and the exponential reaching law are combined. Through the tracking differentiator and finally using neural network control, the system chattering can be reduced, the phase delay can be compensated, and the dynamic performance can be improved.

[0048] The above-mentioned sliding mode surface is also called the switching function, which determines the stability and dynamic performance of the sliding mode. Common sliding mode surfaces include linear sliding mode surfaces, integral sliding mode surfaces, terminal sliding mode surfaces, and high-order sliding mode surfaces, etc. This application adopts a non-singular fast terminal sliding mode surface. Compared with the traditional sliding mode surface, the non-singular fast terminal sliding mode has the advantages of fast convergence speed and high robustness. Its basic form is:

[0049]

[0050] where a, b > 0; 0 < λ < 1; is a Sigmoid(s) function with smooth and continuous characteristics, and its expression is

[0051]

[0052] where d is an adjustable parameter. t is time.

[0053] When the state variables of the sliding mode observer enter the sliding mode, it satisfies S is the sliding mode surface, that is:

[0054] where is the current observation error, is the differential of the current observation error, is the observed value of the stator current. is consistent.

[0055] As can be seen from Equation (4), when the error state is far from the equilibrium point, the linear term dominates the state convergence rate, while when the error state approaches the equilibrium point, the non-linear term dominates the state convergence rate. Therefore, in the sliding phase, the non-singular fast terminal sliding mode surface (2) can achieve global fast convergence, and its convergence speed is comparable to that of the traditional non-singular fast terminal sliding mode surface. It does not contain negative exponential states, preventing singularity, and compared with the traditional non-singular terminal sliding mode surface, it does not require differential states.

[0056] To obtain the back electromotive force, according to the equivalent sliding mode control principle, the equivalent term v eq of the sliding mode control law is obtained. Then, by controlling the system state on the sliding mode surface, the switching control law v sw is designed to achieve the switching of the system near the sliding mode surface and realize the robust control of uncertainties and disturbances. The control law is as follows:

[0057] v = v eq + v sw (5)

[0058]

[0059] where |s| δ = [|s α | δ |s β | δ T ; k, η, r, μ > 0; 0 < δ < 1; 0 < Q < 1, all of which are adjustable parameters.

[0060] The v eq in the control law (6) is obtained by and without considering the back electromotive force, and is obtained by transforming the sliding mode surface used in this application according to the equivalent sliding mode control principle. v sw consists of two parts. k|s| δ sign(s) / (Q + re -μ|s| ) designs a scaling function to make the observer gain adaptively change according to the magnitude of the stator current error, which is used to ensure the approaching rate when the system state of the stator current error is close to the sliding mode surface. When the trajectory reaches the sliding surface, the value of k / (Q + re -μ|s| ) decreases, so that the control deflection value becomes smaller, which can reduce the frequency of over-driving near the sliding mode surface, adaptively change the sliding mode observer gain and prevent over-driving, and is the main factor to eliminate the occurrence of chattering. ηs is used to ensure the approaching rate when the system state of the stator current error is far from the sliding mode surface. ​

[0061] To verify the effectiveness of the novel nonsingular terminal sliding mode observer proposed in this application, it is necessary to conduct a stability analysis. Based on the Lyapunov stability criterion, the Lyapunov function is defined as

[0062]

[0063] Derive formula (7) and make it satisfy the stability condition, that is Then there is

[0064]

[0065] Outside {|s x | ≤ min((2|e x | / k) 1 / δ , |e x | / η), x = α, β}, is negative definite. For it then starts within {V ≤ c} because it is negative on the boundary V = c. Therefore, the solution is uniformly bounded. By selecting appropriate parameters k, η, δ, the system chattering can be weakened, high-precision current observation values can be obtained, and the stability of the system can be ensured.

[0066] To further reduce high-frequency noise and avoid the phase delay caused by the low-pass filter, a low-chattering fast tracking differentiator with a terminal attractor is added. Through the differentiator, the accurate tracking and filtering of the back electromotive force are realized, and at the same time, the influence of the sliding mode chattering on the system is further reduced. The differentiator is

[0067]

[0068] where R, t, h > 0; m > 1; R is the time scale, representing the overall tracking speed. The larger the value of R, the faster the tracking speed. t and h represent the weights of the linear factor and the nonlinear factor respectively, and these variables also represent the tracking speed when the equilibrium point is closer or farther away. As the value of m increases, the tracking speed when farther away from the equilibrium point also increases. However, this may cause unnecessary noise in the system. z1 and z2 are the state variables of the tracking differentiator, and v x , x = α, β are the input variables. To achieve accurate tracking of v x , it can also be used as a filter for v x because it is obtained through two integrations. Compared with the low-pass filter, the tracking differentiator reduces the phase lag by adjusting the tracking rate without causing attenuation of the magnitude of the back electromotive force. The improved NFTSMO control structure is as Figure 2 shown.

[0069] The back electromotive forces of the α and β axes are obtained through a new type of nonsingular terminal sliding mode observer, and the electrical angle and electrical angular velocity signals are extracted from the back electromotive force by using the phase-locked loop principle. The closed-loop transfer function of the phase-locked loop is

[0070]

[0071] where is the estimated rotor position angle; k p , k i are the parameters of the PI controller, which cannot be changed during the operation of the system. However, in actual operation, the motor is vulnerable to various factors such as environmental temperature and load disturbance, making it difficult for the PI controller to achieve the ideal control effect. Therefore, the PI controller is changed to a BP neural network to control the PLL.

[0072] The BP neural network is a nonlinear model that uses error backpropagation based on a multi-layer perceptron. Figure 3 This is a three-layer BP neural network used in this application. The input layer has M nodes, the output layer has P nodes, and there is also a hidden layer with N nodes, forming an M:N:P topology. The transfer function of the hidden layer is selected as the sigmoid function; the transfer function of the output layer is a linear function. In order to avoid phenomena such as local extrema in the learning process of the traditional BP algorithm, the quantization conjugate gradient algorithm is used.

[0073] Bring the trained weight thresholds into the network to obtain the output O of the hidden layer neurons j is

[0074]

[0075] where f(·) is the transfer function of the hidden layer; ω is the weight coefficient of each node.

[0076] The output z of the output layer neurons k is

[0077]

[0078] where p(·) is the transfer function of the output layer.

[0079] Combining neural network predictive control (NNPC) with PLL technology, the block diagram of the improved neural network-based PLL is as shown in Figure 4 shown. Figure 4 In

[0080] Based on the above-established observer, the preset motor speed is 500 r / min, the starting torque is 3 N·m, and the load becomes 7 N·m at 0.2 s. The performance of this observer is simulated and analyzed in the MATLAB / Simulink environment, as Figure 5 shown, it can achieve accurate estimation of the required rotor position and speed in the permanent magnet synchronous motor vector control system without position.

[0081] To verify the performance of the novel sliding mode observer method designed in this paper in the PMSM speed regulation system, a simulation study is carried out in the MATLAB / Simulink environment. At the same time, a non-singular terminal sliding mode observer simulation is constructed in this section for comparison. The comparative experiment uses the same motor parameters and the same disturbance observer. The initial given speed of the system is 200 r / min, the starting torque is 3 N·m, the load becomes 7 N·m at 0.2 s, and the simulation time is 0.5 s. The simulation results of the novel non-singular terminal fast sliding mode observer are as Figures 6 - 12 shown. Finally, the comparison effect is based on the speed fluctuation image. The original operating parameters of the PMSM are shown in Table 1.

[0082] Table 1 Operating parameters of permanent magnet synchronous motor:

[0083]

[0084]

[0085] Figure 6 is the estimation of the back electromotive force on the α-axis; Figure 7 is the estimation of the back electromotive force on the β-axis; Figure 8 is the back electromotive force on the α-axis before filtering.

[0086] Through Figure 6 and Figure 7 it can be seen that adding a low-chattering fast tracking differentiator to the sliding mode observer can accurately and quickly track the back electromotive force. Then, by comparing Figure 6 and Figure 8 it can be obtained that the low-chattering fast tracking differentiator reduces the phase lag problem caused by using a low-pass filter in the traditional non-singular sliding mode observer, and it will not cause the attenuation of the back electromotive force magnitude. The sliding mode observer with the low-chattering fast tracking differentiator can obtain a smooth back electromotive force estimation value, and the static and dynamic responses of the system are good.

[0087] To verify the superiority of NFTSMO compared with the traditional nonsingular terminal sliding mode observer, this application compares the traditional nonsingular terminal sliding mode observer (NTSMO), the nonsingular terminal sliding mode observer plus the neural network phase locked loop structure (NTSMO+NNPLL), and the novel nonsingular fast sliding mode observer, as Figure 9 shown. When there is a load disturbance in the system, the maximum speed error of NTSMO+NNPC is between ±1.5 r / min. Compared with the NTSMO with a maximum speed error of between ±3 r / min, the error is reduced by 50% after improvement. This simulation shows that the improved NNPLL has a significant and obvious improvement on the system. On this basis, NFTSMO combines the advantages of the traditional NTSMO and combines the neural network and the novel control law. After improvement, NFTSMO has a higher speed estimation accuracy when the load torque changes, and the maximum speed error is between ±0.5 r / min.

[0088] Figure 10 is the speed estimation under variable load; Figure 11 is the enlarged diagram of speed comparison, Figure 12 is the speed estimation error, which can be obtained through Figures 10 - 12 It can be seen that when there is a load disturbance in the system, NTFSMO can still accurately estimate the position and speed of the motor rotor. When there is a starting torque, the maximum speed estimation error is between ±0.8 r / min. When the load changes suddenly, the speed estimation error stabilizes between ±1.5 r / min.

[0089] From the simulation results under the above different conditions, it can be seen that when the external load changes, the motor can still operate normally, and the proposed control algorithm can still accurately estimate and track, which shows that the novel nonsingular fast terminal sliding mode observer designed by the present invention has strong robustness.

[0090] The above-described embodiments are only preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention.

Claims

1. A nonsingular fast terminal sliding mode observer based on a neural network phase-locked loop, characterized in that, The design method includes the following steps: Step 1) Design a nonsingular fast terminal sliding mode surface in the observer by using the Sigmoid function; Step 2) Define the stator current error system, obtain the equivalent term of the sliding mode control law according to the equivalent sliding mode control principle, design the switching control law through the state of the stator current error system on the sliding mode surface, and obtain the sliding mode control law in the observer according to the equivalent term and the switching control law; Step 3) Introduce a fast tracking differentiator with a terminal attractor, which is used for accurate tracking and filtering of the back electromotive force, and at the same time further reduces the influence of the sliding mode chattering on the system; Step 4) Control the phase-locked loop in the observer through a BP neural network. The phase-locked loop is used to extract the electrical angle and electrical angular velocity signals from the back electromotive force to obtain the final sliding mode observer.

2. The nonsingular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 1, wherein The nonsingular fast terminal sliding mode surface is: is the current observation error, where a, b > 0; 0 < λ < 1; is the Sigmoid(s) function with smooth and continuous characteristics, and its expression is d is an adjustable parameter.

3. The nonsingular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 1, characterized in that, The control law is as follows: v = v eq + v sw , where |s| δ = [|s α | δ |s β | δ T ; k, η, r, μ > 0; 0 < δ < 1; 0 < Q < 1;​ v eq is obtained by and without considering the back electromotive force, v sw consists of two parts, k|s| δ sign(s) / (Q + re -μ|s| ) By setting the scaling function, the observer gain adaptively changes according to the magnitude of the stator current error, which is used to ensure the approaching rate when the system state of the stator current error is close to the sliding mode surface; ηs is used to ensure the approaching rate when the system state of the stator current error is far from the sliding mode surface.

4. The nonsingular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 1, wherein The differentiator is: Among them, R, t, h > 0; m > 1; R is the time scale, representing the overall tracking speed; t represents the linear factor, h is the weight of the non-linear factor, z1, z2 are the state variables of the tracking differentiator, v x , x = α, β are the input variables, for accurately tracking v x , and can also be used as a filter for v x .

5. The non-singular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 1, characterized in that, The BP neural network has an M:N:P topology, with M nodes in the input layer, P nodes in the output layer, and N hidden nodes in the hidden layer.

6. The non-singular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 5, wherein The transfer function of the hidden layer selects the sigmoid function; the transfer function of the output layer is a linear function.

7. The non-singular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 1, wherein The BP neural network adopts the quantization conjugate gradient algorithm.

8. The non-singular fast terminal sliding mode observer based on a neural network phase-locked loop according to claim 1, wherein In step 4), initially, the input and output signals of the PI controller are first used to train the BP neural network, and the trained BP neural network is used to replace the original PI controller in the phase-locked loop.

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