Permanent magnet synchronous motor discrete finite time adaptive backstepping control method and system

Abstract

The invention belongs to the technical field of permanent magnet synchronous motor tracking control, and particularly discloses a permanent magnet synchronous motor discrete finite time self-adaptive backstepping control method and a permanent magnet synchronous motor discrete finite time self-adaptive backstepping control system. The method comprises the following steps: firstly, establishing a discrete time system model of the permanent magnet synchronous motor, and designing a discrete finite time adaptive backstepping controller of the permanent magnet synchronous motor based on a minimum operator according to a backstepping method principle and in combination with an uncertain nonlinear function of an adaptive neural network technology processing system; then proving the finite time stability from the last subsystem to the first subsystem by using a Lyapunov stability theory, and estimating the stability time; and finally, enabling the permanent magnet synchronous motor to quickly track an expected signal by utilizing a discrete finite time self-adaptive backstepping controller of the permanent magnet synchronous motor based on a minimum operator. The feasibility of the method is verified through simulation and experimental results, and the designed controller has good tracking effect and robustness.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet synchronous motor tracking control, and in particular relates to a discrete finite time adaptive backstepping control method and system for a permanent magnet synchronous motor. Background Art

[0002] Permanent Magnet Synchronous motor (PMSM) has the advantages of high efficiency and high reliability, and has been widely used in modern industries such as transportation and industrial production. However, since the permanent magnet synchronous motor is a typical nonlinear, multivariable, strongly coupled system and is easily affected by uncertain factors such as parameter changes and load disturbances, how to control the permanent magnet synchronous motor to obtain ideal dynamic and static characteristics is a challenging problem. At present, there are many good design methods for the controller of the PMSM system, such as backstepping control, sliding mode control, adaptive control, robust control, etc.

[0003] With the continuous development of modern technology, high-performance computers have been widely used in the field of control. Compared with continuous-time control, discrete-time control has more advantages in stability and feasibility, and is more suitable for computer control. There have been some feasibility studies on the application of discrete-time control on PMSM. In recent years, finite-time control has the advantages of high control accuracy and fast convergence speed, and its research has gradually attracted the interest of many scholars. Finite-time control of continuous-time systems has been widely used, and finite-time control methods for discrete nonlinear systems have only been further developed in recent years. However, there are no results on discrete finite-time stability for PMSM systems under widely used computer discrete control.

[0004] Using the traditional backstepping method to design a discrete finite-time controller for PMSM will result in the introduction of future state information into the virtual control signal, making it difficult to design the controller. At the same time, since PMSM is a complex high-order nonlinear system, its stator resistance, load torque, etc. will change during operation and are difficult to measure. External interference and model uncertainty will affect system performance. Summary of the invention

[0005] The object of the present invention is to propose a discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor, so as to enable the permanent magnet synchronous motor system to quickly track a preset desired signal within a finite time.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme:

[0007] A discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor comprises the following steps:

[0008] Step 1. Establish a discrete mathematical model of the permanent magnet synchronous motor;

[0009] Step 2. Based on the discrete mathematical model of the permanent magnet synchronous motor constructed in step 1, according to the neural network technology and the principle of backstepping, a discrete finite time adaptive backstepping controller of the permanent magnet synchronous motor based on the minimum operator is designed;

[0010] Step 3. Utilize the permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on minimum operator to make the permanent magnet synchronous motor quickly track the desired signal.

[0011] In addition, based on the discrete finite time adaptive backstepping control method of the permanent magnet synchronous motor, the present invention also proposes a discrete finite time adaptive backstepping control system of the permanent magnet synchronous motor adapted thereto, which adopts the following technical solutions:

[0012] The discrete finite time adaptive backstepping control system of permanent magnet synchronous motor includes:

[0013] A model building module is used to build a discrete mathematical model of a permanent magnet synchronous motor;

[0014] The controller design module is based on the discrete mathematical model of the permanent magnet synchronous motor, and according to the neural network technology and the backstepping principle, a discrete finite time adaptive backstepping controller for the permanent magnet synchronous motor based on the minimum operator is designed;

[0015] And a tracking control module, which utilizes a permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on a minimum operator to enable the permanent magnet synchronous motor to quickly track a desired signal.

[0016] In addition, based on the above-mentioned discrete finite time adaptive backstepping control method for a permanent magnet synchronous motor, the present invention further proposes a computer device, which includes a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement the steps of the above-mentioned discrete finite time adaptive backstepping control method for a permanent magnet synchronous motor.

[0017] In addition, based on the above-mentioned discrete finite time adaptive backstepping control method for a permanent magnet synchronous motor, the present invention also proposes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the above-mentioned discrete finite time adaptive backstepping control method for a permanent magnet synchronous motor.

[0018] The present invention has the following advantages:

[0019] The present invention provides a discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor based on a discrete time model, and the method realizes the finite-time control of a discrete system of a permanent magnet synchronous motor. The discrete finite-time backstepping control method based on the minimum operator proposed in the present invention obtains future state information through a new backstepping recursive method to overcome the causal contradiction problem, and uses neural network technology and combines an adaptive neural network algorithm to process the uncertain nonlinear function of the discrete system of the permanent magnet synchronous motor. In addition, in the process of system stability analysis, the present invention gradually performs finite-time stability analysis from the last subsystem to the first subsystem according to the new design method, and provides a calculation formula for the stabilization time. The present invention well realizes that the permanent magnet synchronous motor tracks the preset reference signal in a finite time, and the designed discrete finite-time adaptive backstepping controller for the permanent magnet synchronous motor based on the minimum operator has good tracking effect and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Flow chart of a discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor according to an embodiment of the present invention;

[0021] Figure 2 A system block diagram of a discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor in the present invention;

[0022] Figure 3 It is a simulation diagram of the position response curve of the permanent magnet synchronous motor using the control method of the present invention;

[0023] Figure 4 This is a simulation diagram of the position response curve of a permanent magnet synchronous motor using a comparison method;

[0024] Figure 5 It is a simulation diagram of position tracking error curve of a permanent magnet synchronous motor using the control method of the present invention;

[0025] Figure 6 This is a simulation diagram of the position tracking error curve of a permanent magnet synchronous motor using a comparison method;

[0026] Figure 7 It is a simulation diagram of the q-axis voltage of a permanent magnet synchronous motor using the control method of the present invention;

[0027] Figure 8 This is the simulation diagram of the q-axis voltage of the permanent magnet synchronous motor using the comparison method;

[0028] Fig. 9 This is a simulation diagram of the d-axis voltage of a permanent magnet synchronous motor using the control method of the present invention;

[0029] Fig.10 This is a simulation diagram of the d-axis voltage of a permanent magnet synchronous motor using a comparison method;

[0030] Fig.11 This is an experimental diagram of the speed response curve of a permanent magnet synchronous motor using the control method of the present invention;

[0031] Fig.12 This is a diagram showing the q-axis voltage experiment of a permanent magnet synchronous motor using the control method of the present invention;

[0032] Fig.13 This is a diagram showing the d-axis voltage experiment of a permanent magnet synchronous motor using the control method of the present invention;

[0033] Fig.14 This is an experimental diagram of the q-axis current of a permanent magnet synchronous motor using the control method of the present invention;

[0034] Fig.15 This is an experimental diagram of the d-axis current of a permanent magnet synchronous motor using the control method of the present invention. DETAILED DESCRIPTION

[0035] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0036] Example 1

[0037] This embodiment 1 provides a discrete finite-time adaptive backstepping control method based on the discrete-time mathematical model of the permanent magnet synchronous motor. This method designs a discrete finite-time adaptive backstepping controller for the permanent magnet synchronous motor based on the minimum operator in view of the control accuracy requirements and the existing nonlinear problems of the permanent magnet synchronous motor, so as to achieve the stability of the permanent magnet synchronous motor system in a finite time and make the tracking error converge within a bounded range, thus solving the "cause-effect contradiction" problem inherent in the traditional backstepping method. At the same time, combined with the adaptive neural network technology, the unknown nonlinear functions of the permanent magnet synchronous motor system are processed to reduce the impact on the system performance.

[0038] like Figure 1 As shown, the discrete finite time adaptive backstepping control method for a permanent magnet synchronous motor comprises the following steps:

[0039] Step 1. Establish a discrete mathematical model of the permanent magnet synchronous motor.

[0040] First, the dq coordinate axis mathematical model of the permanent magnet synchronous motor is established, as shown in formula (1):

[0041]

[0042] in, represents the derivative of a variable with respect to time t, θ represents the rotor angle of the permanent magnet synchronous motor, ω represents the rotor angular velocity, J represents the moment of inertia of the permanent magnet synchronous motor, and n pIndicates the number of pole pairs of the permanent magnet synchronous motor, L d and L q is the stator inductance in the dq coordinate system; i d and i q are the excitation currents on the d and q axes respectively; φ f represents the flux generated by the permanent magnet of the permanent magnet synchronous motor, B represents the friction coefficient of the permanent magnet synchronous motor, T L Represents the load torque of the permanent magnet synchronous motor, R s Indicates the stator resistance of the permanent magnet synchronous motor; u d and u q Represents the voltage on the d and q axes, u d and u q is the input signal of the system.

[0043] The discrete mathematical model of the permanent magnet synchronous motor is described by the Euler method as follows:

[0044]

[0045] Among them, Δ T represents the sampling time, θ(k) and θ(k+1) represent the rotor angle of the permanent magnet synchronous motor at time k and time k+1 respectively, ω(k) and ω(k+1) represent the rotor angular velocity at time k and time k+1 respectively; i d (k) and i d (k+1) are the excitation currents on the d-axis at time k and time k+1, i q (k) and i q (k+1) are the excitation currents on the q axis at time k and time k+1 respectively; u d (k) and u q (k) represents the voltage on the d and q axes at time k respectively.

[0046] Define the following variables:

[0047] x1(k)=θ(k), x2(k)=ωk), x3(k)=i q (k), x4(k)=i d (k);

[0048]

[0049] The simplified discrete mathematical model of the permanent magnet synchronous motor dq coordinate axis is as follows:

[0050]

[0051] Step 2. Based on the discrete mathematical model of the permanent magnet synchronous motor constructed in step 1, a discrete finite-time adaptive backstepping controller for the permanent magnet synchronous motor based on the minimum operator is designed according to the neural network technology and the backstepping principle.

[0052] It should be noted that the use of traditional backstepping method to design discrete finite time controller for PMSM will lead to the introduction of future state information into virtual control signals, making it difficult to implement controller design. The present invention adopts a new backstepping recursive method to solve the "cause and effect contradiction" problem. At the same time, since PMSM is a complex high-order nonlinear system, its stator resistance, load torque, etc. will change during operation and are difficult to measure. External interference and model uncertainty will affect system performance. The present invention uses neural network technology to identify uncertain nonlinear functions online to reduce the impact on system performance.

[0053] Step 2.1. Define the system errors e1(k), e2(k), e3(k), and e4(k) as shown in formula (4):

[0054]

[0055] Among them, x d (k) is the preset tracking position signal, and α1(k) and α2(k) are virtual control functions.

[0056] Step 2.2. According to formula (3), the first and second equations in the system error defined by formula (4) are obtained:

[0057]

[0058] The virtual control function α1(k) based on the minimum operator is constructed by the backstepping method as follows:

[0059]

[0060] Where f1(k)=x1(k)-x d (k+1), κ1 represents the control gain, κ1>0, 0<γ<1 is a positive constant.

[0061] Substituting formula (6) into formula (5) yields:

[0062]

[0063] In step 2.2, substitute the second equation of the system error defined by formula (4) into e1(k+1), and recursively obtain formula (7) by designing a virtual control function α1(k) based on the minimum operator. Similarly, steps 2.3 to 2.5 are also similar back-stepping recursive methods.

[0064] Step 2.3. According to formula (3), the second and third equations in the system error defined by formula (4) are obtained:

[0065]

[0066] Where f2(k)=(1+a2Δ T )x2(k)+a3Δ T x3(k)x4(k)+a4Δ T T L -α1(k+1).

[0067] The virtual control function α2(k) based on the minimum operator is constructed by backstepping method as follows:

[0068]

[0069] Where, κ2 represents the control gain, κ2>0;

[0070] Substituting formula (9) into formula (8) yields:

[0071]

[0072] Step 2.4. According to formula (3), the third equation in the system error defined by formula (4) is obtained:

[0073]

[0074] Where, f3(k)=(1+b1Δ T )x3(k)+b2Δ T x2(k)+b3Δ T x2(k)x4(k)-α2(k+1).

[0075] Considering the RBF (Radial Basis Function) neural network approximation theorem, there is an RBF neural network So that:

[0076]

[0077] Where W3 is the ideal weight column vector of the RBF neural network, S3[Z3(k)] represents the basis function vector of the RBF neural network, and Z3(k) = [x1(k), x2(k), x3(k), x4(k), x d (k),x d (k+1),x d (k+2),x d (k+3)] T , τ3 is the approximation error, and satisfies |τ3|≤ε3, where ε3 is a constant and ε3>0.

[0078] According to the backstepping method, the control law based on the minimum operator as shown in formula (13) and the adaptive law as shown in formula (14) are selected respectively:

[0079]

[0080] Where, κ3 represents the control gain, κ3>0, is the estimated network weight of W3, is the weight approximation error, δ3 is a bounded positive constant.

[0081] Substituting formula (13) into formula (11), we obtain:

[0082]

[0083] Step 2.5. According to formula (3), the fourth equation in the system error defined by formula (4) is obtained:

[0084]

[0085] Where, f4(k)=(1+c1Δ T )x4(k)+c2Δ T x2(k)x3(k).

[0086] Considering the RBF neural network approximation theorem, there exists an RBF neural network So that:

[0087]

[0088] Where W4 is the weight column vector of the RBF neural network, S4[Z4(k)] represents the RBF neural network basis function vector, Z4(k)=[x2(k),x3(k),x4(k)] T , τ4 is the approximation error, and satisfies |τ4|≤ε4, where ε4 is a constant and ε4>0.

[0089] According to the backstepping method, the control law based on the minimum operator as shown in formula (18) and the adaptive law as shown in formula (19) are selected respectively:

[0090]

[0091] Where, κ4 represents the control gain, κ4>0, is the estimated network weight of W4, is the weight approximation error, δ4 is a bounded positive constant.

[0092] Substituting formula (18) into formula (16) yields:

[0093]

[0094] The discrete finite-time adaptive backstepping controller for permanent magnet synchronous motor based on the minimum operator is designed as follows:

[0095]

[0096] Step 2.6. After completing the design of the discrete finite-time adaptive backstepping controller for the permanent magnet synchronous motor based on the minimum operator, perform stability analysis on the permanent magnet synchronous motor system controlled by the controller.

[0097] According to the design of discrete finite-time adaptive backstepping controller for permanent magnet synchronous motor, the finite-time stability analysis of the fourth subsystem shown in formula (20), the third subsystem shown in formula (15), the second subsystem shown in formula (10) and the first subsystem shown in formula (7) are given in sequence, that is, the finite-time stability analysis from the last subsystem to the first subsystem is given. In this embodiment, the fourth subsystem is the last subsystem.

[0098] Step 2.6.1. Select the Lyapunov function V of the third and fourth subsystems i (k):

[0099] V i (k)=|e i (k)| (21)

[0100] Where i = 3, 4, then V i The first-order difference ΔV of (k) i (k) is:

[0101]

[0102] when When , we get:

[0103]

[0104] when When , we get:

[0105]

[0106] The RBF neural network basis function vector S i [Z i (k)] satisfies ||S i [Z i (k)]||≤ι i The conditions, ιi represents a positive constant, and defines η i =||W i ||, select the Lyapunov function V i,η (k):

[0107]

[0108] get:

[0109]

[0110] when When , we get:

[0111]

[0112] Among them, ε i represents a positive constant;

[0113] when When , we get:

[0114]

[0115] in, for The modulus of , so we get:

[0116]

[0117] From formula (29), we can see that choosing appropriate parameters δ i Make (|(1-δ i )|-1+ι i )<0, we get:

[0118]

[0119] in ψ i =ε i +ι i |η i |.

[0120] When the error Established, further obtained is bounded, so u q (k),u d (k) and are all bounded. Therefore χ i is a bounded positive constant. Therefore, we get:

[0121]

[0122] when When i satisfy:

[0123]

[0124] Among them, e i (0) indicates the initial value of the error.

[0125] When k ≥ K i When |e i (k)|≤χ i The maximum stabilization time of the third and fourth subsystems is K M =max{K3,K4}.

[0126] Step 2.6.2. Select the Lyapunov function V2(k) of the second subsystem:

[0127] V2(k)=|e2(k)| (32)

[0128] Then the first-order difference ΔV2(k) of V2(k) is:

[0129]

[0130] Where ζ2=|a1Δ T χ3|. When When , we get:

[0131]

[0132] when When , we get:

[0133] ΔV2(k)≤-|e2(k)|+ζ2 (35)

[0134] So we get:

[0135]

[0136] when When , there is a stable time K2 that satisfies:

[0137]

[0138] Among them, e2(0) represents the initial value of error;

[0139] Similarly, when k≥K2, |e2(k)|≤ζ2.

[0140] Step 2.6.3. Select the Lyapunov function V1(k) of the first subsystem:

[0141] V1(k)=|e1(k)| (37)

[0142] Then the first-order difference ΔV1(k) of V1(k) is:

[0143]

[0144] where ζ1=|Δ T ζ2|. When When , we get:

[0145]

[0146] when When , we get:

[0147] ΔV1(k)≤-|e1(k)|+ζ1 (40)

[0148] So we get:

[0149]

[0150] when When , there is a stable time K1 that satisfies:

[0151]

[0152] Among them, e1(0) represents the initial value of the error.

[0153] Therefore, it can be seen that when When |e1(k)|≤ζ1, the position tracking error e1(k) of the permanent magnet synchronous motor system is ultimately bounded and the system state x1(k) can track the preset expected position signal x in a finite time. d (k).

[0154] Step 3. Utilize a permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on minimum operator to make the permanent magnet synchronous motor quickly track the desired signal.

[0155] Figure 2 It is a schematic diagram of a composite controlled object composed of a discrete finite time adaptive backstepping controller based on a minimum operator, a coordinate transformation, and an SVPWM (space vector pulse width modulation) inverter in the present invention.

[0156] where θ * represents the desired rotor angle, α and β represent the axes of the two-phase stationary coordinate system, represents the voltage of the α-axis of the two-phase stationary coordinate system, represents the voltage of the β-axis in the two-phase stationary coordinate system, and a, b, and c represent the axes in the three-phase coordinate system.

[0157] The controller of the present invention obtains future state information through the backstepping recursion method based on the minimum operator to overcome the causal contradiction problem, and uses neural network technology to process the unknown nonlinear function of the system. The u output by the controller d and u q After the inverter conversion, the actual output is i A 、i B 、i C , thereby achieving finite-time stability of the permanent magnet synchronous motor system.

[0158] In a virtual environment, the discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor proposed in the present invention is simulated to verify the feasibility of the control method proposed in the present invention.

[0159] The parameters of permanent magnet synchronous motor are selected as follows:

[0160] J=0.002795Kg·m 2 , R s =0.68Ω,B=0.001158N·m / (rad / s),φ f =0.1245Wb, L d =0.00215H,L q =0.00258H,n p =3.

[0161] The reference signal selected is x d (k) = 4cos(Δ T kπ / 2), sampling time Δ T =0.0025s, the initial conditions are all 0, and the load torque is:

[0162]

[0163] During the simulation process, the RBF neural network is designed and

[0164] and Contains 11 nodes with centers evenly distributed in the interval [-10, 10] and a width of 2.

[0165] Select the adaptive law parameters: δ3 = 0.2994, δ4=0.2,

[0166] The control method of the present invention is simulated and compared with the discrete adaptive neural network control method using command filtering technology, and the same adaptive law parameters are selected during the simulation process. The simulation results are shown in Figure 2. Figures 3 to 10 shown.

[0167] Figure 3 , Figure 5 , Figure 7 and Fig. 9 The simulation results of the permanent magnet synchronous motor considering discrete finite time control using the control method of the present invention are as follows: Figure 4 , Figure 6 , Figure 8 and Fig.10 The simulation results of the permanent magnet synchronous motor controlled by discrete adaptive neural network using the contrast method, i.e. command filtering technology. Figures 3 to 6 It can be seen that both methods can effectively track the position curve of the permanent magnet synchronous motor, but the discrete finite time adaptive backstepping control method of the permanent magnet synchronous motor based on the minimum operator designed by the present invention can better track the position reference signal, with a relatively smaller tracking error and a faster convergence speed. When the load torque changes, the tracking curve fluctuation is smaller when the discrete finite time control method of the present invention is used. Figure 7 and Figure 8 The q-axis voltage curves of the permanent magnet synchronous motor of the control method of the present invention and the comparative method are respectively represented, Fig. 9 and Fig.10 The voltage simulation diagrams of the d-axis of the permanent magnet synchronous motor respectively represent the control method of the present invention and the comparative method. It can be seen that the voltage of the permanent magnet synchronous motor using the control method of the present invention fluctuates in a very small range and can be limited to a reasonable range. Therefore, the superiority of the discrete finite time adaptive backstepping method of the permanent magnet synchronous motor of the present invention can be seen through simulation.

[0168] Experiments were carried out on the LINKS-PMSM1.0 AC servo experimental platform to further verify the effectiveness of the discrete finite-time adaptive backstepping control method for permanent magnet synchronous motor based on the minimum operator designed in the present invention and to conduct analysis.

[0169] The platform consists of a permanent magnet synchronous motor, a simulation host and a servo drive. The rated speed of the permanent magnet synchronous motor is 1000r / min, the rated power is 3kW, the rated torque is 15N·m and the rated current is 7.3A.

[0170] The control algorithm is written in MATLAB / Simulink of the simulation host, and Link-RT software provides a real-time operating environment for the Simulink model.

[0171] The expected speed of the experiment is preset to 200r / min, the load torque is preset to 1.0N·m, and the sampling time is 0.0002s. The adaptive law parameter δ2=0.00006 is selected. δ3=0.00006, The experimental results are as follows Figures 11 to 15 shown.

[0172] Fig.11 is the speed response curve of the permanent magnet synchronous motor using the control method of the present invention, Fig.12 is the q-axis voltage curve of the permanent magnet synchronous motor using the control method of the present invention, Fig.13 is the d-axis voltage curve of the permanent magnet synchronous motor using the control method of the present invention, Fig.14 is the q-axis current curve of the permanent magnet synchronous motor using the control method of the present invention, Fig.15 The d-axis current curve of the permanent magnet synchronous motor using the control method of the present invention. Figures 11 to 15 It can be seen that the speed response rising curve of the permanent magnet synchronous motor using the control method of the present invention is smooth and has no overshoot phenomenon. The permanent magnet synchronous motor can reach the desired speed within a limited time and has good control performance.

[0173] The above simulation and experimental results show that the discrete finite-time adaptive backstepping control method for the permanent magnet synchronous motor proposed in the present invention can quickly track the reference signal and has good tracking effect and robustness. Therefore, it has practical implementation significance.

[0174] Example 2

[0175] Embodiment 2 describes a discrete finite-time adaptive backstepping control system for a permanent magnet synchronous motor. The system and the discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor in the above-mentioned embodiment 1 are based on the same inventive concept.

[0176] Specifically, the permanent magnet synchronous motor discrete finite time adaptive backstepping control system includes:

[0177] A model building module is used to build a discrete mathematical model of a permanent magnet synchronous motor;

[0178] The controller design module is based on the discrete mathematical model of the permanent magnet synchronous motor, and according to the neural network technology and the principle of backstepping, a discrete finite time adaptive backstepping controller of the permanent magnet synchronous motor based on the minimum operator is designed;

[0179] And a tracking control module, which utilizes a permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on a minimum operator to enable the permanent magnet synchronous motor to quickly track a desired signal.

[0180] It should be noted that, in the discrete finite-time adaptive backstepping control system of the permanent magnet synchronous motor, the implementation process of the functions and effects of each functional module is specifically described in the implementation process of the corresponding steps in the method in Example 1, and will not be repeated here.

[0181] Example 3

[0182] This embodiment 3 describes a computer device, which is used to implement the steps of the permanent magnet synchronous motor discrete finite time adaptive backstepping control method described in the above embodiment 1.

[0183] The computer device includes a memory and one or more processors. The memory stores executable codes, and when the processor executes the executable codes, the steps of the discrete finite time adaptive backstepping control method of the permanent magnet synchronous motor are implemented.

[0184] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0185] Example 4

[0186] This embodiment 4 describes a computer-readable storage medium, which is used to implement the steps of the permanent magnet synchronous motor discrete finite time adaptive backstepping control method described in the above embodiment 1.

[0187] The computer-readable storage medium in this embodiment 4 stores a program thereon, and when the program is executed by a processor, it is used to implement the steps of the discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor.

[0188] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card, etc. equipped on the device.

[0189] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A discrete finite-time adaptive backstepping control method for a permanent magnet synchronous motor, characterized in that: The steps include: Step 1. Establish a discrete mathematical model of the permanent magnet synchronous motor; Step 2. Based on the discrete mathematical model of the permanent magnet synchronous motor constructed in step 1, according to the neural network technology and the principle of backstepping, a discrete finite time adaptive backstepping controller of the permanent magnet synchronous motor based on the minimum operator is designed; Step 3. Utilize the permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on the minimum operator designed in step 2 to enable the permanent magnet synchronous motor to quickly track the desired signal.

2. The method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor according to claim 1, characterized in that: The step 1 is specifically as follows: The dq coordinate axis mathematical model of the permanent magnet synchronous motor is established as shown in formula (1): Among them, θ represents the rotor angle of the permanent magnet synchronous motor, ω represents the rotor angular velocity, J represents the moment of inertia of the permanent magnet synchronous motor, and n p Indicates the number of pole pairs of the permanent magnet synchronous motor, L d and L q is the stator inductance in the dq coordinate system; i d and i q are the excitation currents on the d and q axes respectively; φ f represents the flux generated by the permanent magnet of the permanent magnet synchronous motor, B represents the friction coefficient of the permanent magnet synchronous motor, T L Represents the load torque of the permanent magnet synchronous motor, R s Indicates the stator resistance of the permanent magnet synchronous motor; u d and u q Respectively represent the d and q axis voltages, u d and u q is the input signal of the permanent magnet synchronous motor system; The permanent magnet synchronous motor is described as a discrete mathematical model as shown in formula (2) using the Euler method: Among them, Δ T represents the sampling time, θ(k) and θ(k+1) represent the rotor angle of the permanent magnet synchronous motor at time k and time k+1 respectively, ω(k) and ω(k+1) represent the rotor angular velocity at time k and time k+1 respectively; i d (k) and i d (k+1) are the excitation currents on the d-axis at time k and time k+1, i q (k) and i q (k+1) are the excitation currents on the q axis at time k and time k+1 respectively; u d (k) and u q (k) represents the voltage on the d and q axes at time k respectively; Define the following variables: x1(k)=θ(k),x2(k)=ω(k),x3(k)=i q (k),x4(k)=i d (k); The simplified discrete mathematical model of the permanent magnet synchronous motor dq coordinate axis is as shown in formula (3):

3. The method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2.

1. Define the system errors e1(k), e2(k), e3(k), and e4(k) as shown in formula (4): Among them, x d (k) is the preset tracking position signal, α1(k) and α2(k) are virtual control functions; Step 2.

2. According to formula (3), the first and second equations in the system error defined by formula (4) are obtained: The virtual control function α1(k) based on the minimum operator is constructed by the backstepping method as shown in formula (6): Where f1(k)=x1(k)-x d (k+1), κ1 represents the control gain, κ1>0; γ is a positive constant, 0<γ<1; Substituting formula (6) into formula (5) yields: Step 2.

3. According to formula (3), the second and third equations in the system error defined by formula (4) are obtained: where f2(k) = (1 + a2Δ T )x2(k) + a3Δ T x3(k)x4(k) + a4Δ T T L -α1(k + 1); The virtual control function α2(k) based on the minimum operator is constructed by the backstepping method as shown in formula (9): Where, κ2 represents the control gain, κ2>0; Substituting formula (9) into formula (8) yields: Step 2.

4. According to formula (3), the third equation in the system error defined by formula (4) is obtained: where f3(k) = (1 + b1Δ T )x3(k) + b2Δ T x2(k) + b3Δ T x2(k)x4(k) - α2(k + 1); Considering the RBF neural network approximation theorem, there exists an RBF neural network W3 T S3[Z3(k)], such that: <h2 style=";text-align:left;direction:ltr">f3(k) = W3<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> S3[Z3(k)]+τ3 (12) Where W3 is the weight column vector of the RBF neural network, S3[Z3(k)] represents the basis function vector of the RBF neural network, and Z3(k) = [x1(k), x2(k), x3(k), x4(k), x d (k),x d (k+1),x d (k+2),x d (k+3)] T , τ3 is the approximation error, and satisfies |τ3|≤ε3, where ε3 is a constant, and ε3>0; According to the backstepping method, the control law based on the minimum operator shown in formula (13) and the adaptive law shown in formula (14) are selected: Where, κ3 represents the control gain, κ3>0; is the estimated network weight of W3, is the weight approximation error, δ3 is a bounded positive constant; Substituting formula (13) into formula (11), we obtain: Step 2.

5. According to formula (3), the fourth equation in the system error defined by formula (4) is obtained: where, f4(k) = (1 + c1Δ T )x4(k) + c2Δ T x2(k)x3(k); Considering the RBF neural network approximation theorem, there exists an RBF neural network W4 T S4[Z4(k)], such that: f4(k)=W4 T S4[Z4(k)]+τ4 (17) Where W4 is the weight column vector of the RBF neural network, S4[Z4(k)] represents the RBF neural network basis function vector, Z4(k)=[x2(k),x3(k),x4(k)] T , τ4 is the approximation error, and satisfies |τ4|≤ε4, where ε4 is a constant and ε4>0; According to the backstepping method, the control law based on the minimum operator shown in formula (18) and the adaptive law shown in formula (19) are selected: Where, κ4 represents the control gain, κ4>0; is the estimated network weight of W4, is the weight approximation error, δ4 is a bounded positive constant; Substituting formula (18) into formula (16) yields: The discrete finite-time adaptive backstepping controller of permanent magnet synchronous motor based on the minimum operator is designed as follows:

4. The method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor according to claim 1, characterized in that: In the step 2, After completing the design of a discrete finite-time adaptive backstepping controller for permanent magnet synchronous motors based on the minimum operator, the stability analysis of the permanent magnet synchronous motor system controlled by the discrete finite-time adaptive backstepping controller for permanent magnet synchronous motors based on the minimum operator is carried out.

5. The method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor according to claim 3, characterized in that: In step 2, after completing the controller design, the process of performing stability analysis on the permanent magnet synchronous motor controlled by the permanent magnet synchronous motor discrete finite time adaptive backstepping controller is as follows: According to the design of the discrete finite-time adaptive backstepping controller of the permanent magnet synchronous motor, the finite-time stability analysis of the fourth subsystem shown in formula (20), the third subsystem shown in formula (15), the second subsystem shown in formula (10) and the first subsystem shown in formula (7) are given in sequence, that is, the finite-time stability analysis from the last subsystem to the first subsystem is given; Select the Lyapunov function V of the third and fourth subsystems i (k): V i (k)=|e i (k)| (21) Where i = 3, 4, then V i The first-order difference of (k) ΔV i (k) is: when When , we get: when When , we get: The RBF neural network basis function vector S i [Z i (k)] satisfies ||S i [Z i (k)]||≤ι i The conditions, ι i represents a positive constant, and defines η i =||W i ||, select the Lyapunov function V i,η (k): get: when When , we get: when When , we get: in, for The modulus of , so we get: According to formula (29), select the parameter δ i Make (|(1-δ i )|-1+ι i )<0, we get: among them ψ i =e i +l i |the i |; When the error Established, further obtained is bounded, so u q (k) and u d (k) and are all bounded; therefore χ i is a bounded positive constant; hence: when When i satisfy: Among them, e i (0) indicates the initial value of error; When k ≥ K i When |e i (k)|≤χ i ; The maximum stabilization time of the third and fourth subsystems is K M =max{K3,K4}; Select the Lyapunov function V2(k) of the second subsystem: V2(k)=|e2(k)| (32) Then the first-order difference ΔV2(k) of V2(k) is: Where ζ2=|a1Δ T χ3|; when When , we get: when When , we get: ΔV2(k)≤-|e2(k)|+ζ2 (35) So we get: when When , there is a stable time K2 that satisfies: Among them, e2(0) represents the initial value of error; When k ≥ K2, |e2(k)| ≤ ζ2; Select the Lyapunov function V1(k) of the first subsystem: V1(k)=|e1(k)| (37) Then the first-order difference ΔV1(k) of V1(k) is: where ζ1=|Δ T ζ2|; when When , we get: when When , we get: ΔV1(k)≤-|e1(k)|+ζ1 (40) So we get: when When , there is a stable time K1 that satisfies: Among them, e1(0) represents the initial value of error; Therefore, when When |e1(k)|≤ζ1, the position tracking error e1(k) of the permanent magnet synchronous motor system is ultimately bounded and the system state x1(k) can track the preset expected position signal x in a finite time. d (k).

6. The method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor according to claim 1, characterized in that: In step 3, the process of implementing tracking control of the permanent magnet synchronous motor of the preset reference signal by using the permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on the minimum operator is as follows: Output u of discrete finite-time adaptive backstepping controller for permanent magnet synchronous motor based on minimum operator d and u q , after being converted into actual output by the inverter, the permanent magnet synchronous motor is controlled to achieve finite time stability.

7. The method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor according to claim 6, characterized in that: In step 3, A discrete finite-time adaptive backstepping controller for permanent magnet synchronous motor based on minimum operator is proposed. The future state information is obtained by backstepping recursion method based on minimum operator to overcome the causal contradiction problem. The neural network technology is used to process the unknown nonlinear function of permanent magnet synchronous motor system. The u output by the controller d and u q After the inverter conversion, the actual output is i A 、i B 、i C , thereby achieving finite-time stability of the permanent magnet synchronous motor system.

8. A discrete finite time adaptive backstepping control system for a permanent magnet synchronous motor, characterized in that: Includes the following modules: A model building module is used to build a discrete mathematical model of a permanent magnet synchronous motor; The controller design module is based on the discrete mathematical model of the permanent magnet synchronous motor, and according to the neural network technology and the principle of backstepping, a discrete finite time adaptive backstepping controller of the permanent magnet synchronous motor based on the minimum operator is designed; And a tracking control module, which utilizes a permanent magnet synchronous motor discrete finite time adaptive backstepping controller based on a minimum operator to enable the permanent magnet synchronous motor to quickly track a desired signal.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for discrete finite-time adaptive backstepping control of a permanent magnet synchronous motor as described in any one of claims 1 to 7 are implemented.

Images