Five-phase FTFSCW-IPM novel approach rate FTSMC control method based on time-varying ESO

Abstract

The invention provides a five-phase FTFSCW-IPM novel approach rate FTSMC control method based on time-varying ESO, and the method comprises the following steps: building a five-phase FTFSCW-IPM motor mathematical model which comprises a flux linkage, a voltage, a torque and a motion equation; designing a fast terminal sliding mode surface and an improved reaching law to obtain a control law of a five-phase FTFSCW-IPM improved reaching rate fast terminal sliding mode in a rotating speed loop, and performing controller stability analysis in combination with a Lyapunov theorem; a time-varying parameter ESO is designed to be used for five-phase FTFSCW-IPM disturbance observation estimation, the characteristics and parameters of an observer are analyzed, an improved index reaching rate control method is introduced, a feedforward compensation strategy based on a time-varying extended state observer is combined, and the robustness and anti-interference performance of a five-phase FTFSCW-IPM motor control system are improved.

Description

Technical Field

[0001] The present invention relates to the field of multi-phase motor control, and in particular to a novel approach rate FTSMC control method of a five-phase FTFSCW-IPM based on a time-varying ESO. Background Art

[0002] With the development of electric vehicles, robots and other high-end automation equipment, the performance requirements of motor systems are increasing. Five-phase FTFSCW-IPM has gradually become a research hotspot in academic and industrial fields due to its advantages in reliability, torque pulsation suppression and wide speed regulation range. However, how to design more efficient and reliable control strategies to fully tap the potential of this type of motor is still the current research focus.

[0003] Although the five-phase FTFSCW-IPM motor has many advantages, its complex electromagnetic coupling, multiple-input multiple-output (MIMO) characteristics and nonlinear problems pose challenges to the design of the control system. In sliding mode control, its main advantage lies in its insensitivity to dynamic changes in system parameters and disturbances. Compared with traditional PI controllers, sliding mode control can achieve better control effects when dealing with systems with significant nonlinear characteristics or unexpected interference. However, since sliding mode control frequently switches control signals on the sliding surface, high-frequency jitter is prone to occur. This not only reduces the control accuracy, but may also cause wear or damage to the actuator. In addition, in actual motor operation, complex load disturbances often cause the system to respond slowly, making it difficult to achieve ideal control effects and affecting overall performance.

[0004] Therefore, in order to solve the above problems, it is necessary to reduce the motor system jitter while enhancing its ability to cope with internal and external disturbances. Summary of the invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the background technology, the present invention requests to disclose a new approach rate FTSMC control method of a five-phase FTFSCW-IPM based on time-varying ESO. On the basis of the existing sliding mode control, this method adopts a fast terminal sliding mode surface and optimizes the traditional exponential reaching law to reduce system jitter and shorten the response time. At the same time, a time-varying extended state observer is adopted to observe the disturbance in the system and feed forward it to the q1-axis current, thereby realizing effective compensation for the disturbance and improving the anti-disturbance capability of the system.

[0006] Technical solution: The novel approach rate FTSMC control method of the five-phase FTFSCW-IPM based on time-varying ESO disclosed in the present invention comprises the following steps:

[0007] S1. Establish a mathematical model of the five-phase FTFSCW-IPM motor, including flux, voltage, torque and motion equations;

[0008] S2. Design the fast terminal sliding surface and the new reaching law, obtain the control law of the five-phase FTFSCW-IPM new reaching rate fast terminal sliding mode in the speed loop, and analyze the controller stability by combining Lyapunov theorem;

[0009] S3. Design a time-varying parameter ESO for five-phase FTFSCW-IPM disturbance observation estimation, and analyze the characteristics and parameters of the observer.

[0010] Among them, in S1:

[0011] Motor stator flux equation:

[0012] ψ s =L s I s +ψ m (29)

[0013] in: Represents the total flux matrix of each phase;

[0014] represents the stator winding inductance matrix;

[0015] represents the five-phase current matrix;

[0016] It represents the permanent magnet flux moment of the rotor permanent magnet coupled in each phase,

[0017] Represents the electrical angle, γ is a constant 0.4π;

[0018] Where: a ,ψ b ,v c ,ψ d ,ψ e ,v PM They are the armature winding flux and permanent magnet flux amplitude respectively; i a ,i b ,i c ,i d ,i e , are the currents of each phase of the five-phase armature winding; L aa =L bb =L cc =L dd =L ee =L s is the self-inductance of each phase winding,

[0019] M xy =L m(x=a,b,c,d,e,y=a,b,c,d,e,x≠y) is the mutual inductance between the phase windings;

[0020] The mathematical model of the five-phase motor voltage in the rotating dq coordinate is:

[0021]

[0022] Where: u dq ,i dq ,ψ f , respectively represent the dq axis components of stator voltage, current and flux; L d ,L q Represents the AC and DC axis inductance of the motor; ω e is the rotor electrical angular speed;

[0023] Five-phase FTFSCW-IPM mechanical motion equation:

[0024]

[0025] Where: Te is the electromagnetic torque, T l is the load torque, J is the moment of inertia, and B is the friction coefficient of the drive system;

[0026] The five-phase FTFSCW-IPM torque equation becomes:

[0027]

[0028] The torque equation simplifies to:

[0029]

[0030] Furthermore, in S2:

[0031] The control model is established based on the mathematical model of S1:

[0032]

[0033] Define the following system state variables:

[0034]

[0035] in: is the reference speed of the motor; ω m is the actual motor speed;

[0036] According to the above formula:

[0037]

[0038] Design of fast terminal sliding surface:

[0039] Consider a second-order uncertain nonlinear dynamic system:

[0040]

[0041] Where: x = [x1, x2] T ,b(x)≠0,d(x,t) represents uncertainty and external interference,d(x,t)≤D.

[0042] Design the controller as:

[0043]

[0044] Where η>0;

[0045] Considering the linear sliding mode and the fast Terinal sliding mode comprehensively, the fast Terinal sliding mode is changed to:

[0046]

[0047] Where: α, β, q, p>0, (p>q) is an odd number;

[0048] The terminal sliding surface ensures that the system can converge to the sliding surface in a finite time. It can converge to the equilibrium state from any initial state x(0)≠0. The time required is:

[0049]

[0050] Stability analysis of the sliding surface:

[0051]

[0052] but

[0053]

[0054] From formula (14), we can see that This can cause strange problems, so

[0055] Design Improvement Convergence Rate

[0056] The traditional sliding mode reaching law design adopts the exponential reaching law form:

[0057]

[0058] Improved exponential reaching law:

[0059]

[0060] For this control rate, the Y(s,δ) function is used instead of the sgn(s) function for smoothing, where the Y(s,δ) function is:

[0061]

[0062] Where: ρ≠0,δ>0, take ρ=-6,δ1, and we can get the function curve;

[0063] The new approach rate is:

[0064]

[0065] Further, the exponential reaching law analysis is improved:

[0066] When the state in the system is far away from the sliding surface, that is, s→∞, f(s)→1 in the constant speed reaching law, and the function f(s) has no effect on the rapid response of the system; when s→0, the exponential reaching law qs→0, and the constant speed reaching law f(s)→1 / 2, the speed at which the system state approaches the sliding surface is slower than before the improvement, the chattering phenomenon of the motor will be alleviated, and the control accuracy will be improved;

[0067] According to Lyapunov stability analysis, the Lyapunov function is selected as:

[0068]

[0069] but:

[0070]

[0071] It can be seen that -sεsgn(s)<0, f(s)>0, q>0, so The sliding surface function selected by the sliding mode control satisfies the reachability condition, which can ensure that the system is asymptotically stable when entering the sliding mode dynamic state from the approaching mode, and reaches the origin within a limited time;

[0072] To sum up, the output is defined According to equations (8), (11) and (18), the controller output is:

[0073]

[0074] Furthermore, in S3:

[0075] Five-phase FTFSCW-IPM disturbance analysis:

[0076] The motion equation of the five-phase FTFSCW-IPM can be rewritten from equation (3):

[0077]

[0078] Where: g=Δdi q1 -(τ+Δτ)ω-(c+Δc)TL represents the comprehensive disturbance; where

[0079] Δd, Δτ, Δc are the change values ​​of parameters; T L =T L0 +ΔT L ;

[0080] Design of time-varying parameter ESO:

[0081] Design Fal function:

[0082]

[0083] Where, e is the function input; α, δ are adjustable parameters; Sign( ) is the sign function;

[0084] The value range of α is 0<α<1;

[0085] Design a time-varying parameter disturbance observer based on the hyperbolic tangent function, and define the hyperbolic tangent nonlinear function as:

[0086] tanh(Fal(e,β,c))=βtanh(ce) (52)

[0087] In the formula, e is the input variable of the function, β, c are adjustable variables used to change the amplitude and change rate of the Fal(e, β, c) function;

[0088] According to the velocity dynamic equation of formula (22) and combined with the extended state observer theory, the disturbance observer of the velocity loop is designed as follows:

[0089]

[0090] Where: is the estimated value of the rotation speed; is the medium disturbance of the speed loop; β1, β2, c are the parameters of ESO;

[0091] Using the saturation property of the hyperbolic tangent function, the time-varying parameter β 01 , β 02 Replace β1 and β2; a smaller gain is used when ESO starts running. As the running time t increases, the observer parameter will gradually increase to stability;

[0092] The time-varying parameter ESO is expressed as:

[0093]

[0094] Where: t is the time when the observer is put into operation; β 01 , β 02is the time-varying parameter of ESO; b1 and b2 are the changing rates of the control parameters;

[0095] As the unknown disturbance estimation value of the five-phase FTFSCW-IPM motor system, the q1-axis current required for the unknown disturbance is calculated using formula (26) and then directly compensated to the q1-axis, thereby improving the anti-disturbance performance of the system;

[0096]

[0097] Considering the disturbance compensation of the motor, the controller output is:

[0098]

[0099] Furthermore, it also includes S4, building a corresponding control simulation model using the MATLAB / Simulink simulation platform to test the performance of the control strategy in terms of rapid response of the motor speed and verify the effectiveness of the time-varying ESO in estimating motor disturbances.

[0100] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0101] (1) The present invention uses the total disturbance of the system (including internal nonlinearity and external disturbance) by the time-varying parameter ESO and compensates it into the control strategy. Compared with the traditional ESO, the estimation performance of the time-varying ESO is better, which can better adapt to the dynamically changing system state and further improve the control accuracy;

[0102] (2) Fast terminal sliding mode control ensures that the system reaches the sliding surface within a finite time, so that the system can quickly converge to the equilibrium state within a finite time. The time when the system state reaches the equilibrium state can be adjusted by parameters. The selection of a new exponential approach rate improves the fast convergence speed and slows down the vibration;

[0103] (3) The control method of the present invention has broad application prospects in the fields of electric vehicles, industrial automation, and high-precision servo systems, especially in scenarios with strict requirements for high performance and high robustness, such as drive motor control of autonomous vehicles and high-end robot control systems;

[0104] (4) The adopted calculation method is simple and efficient, easy to operate in practice, and helps to transform theoretical innovation into engineering practice and practical application. The fast terminal sliding mode control based on time-varying parameter ESO provides a new solution for the efficient operation of the five-phase FTFSCW-IPM by integrating advanced observer technology and nonlinear control methods, achieving better dynamic performance and robustness under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 This is a five-phase FTFSCW-IPM control block diagram of the present invention;

[0106] Figure 2 Control block diagram of fast terminal sliding mode controller for improving approach rate;

[0107] Figure 3 is the switching function graph;

[0108] Figure 4 This is the Fal function analysis diagram;

[0109] Figure 5 is the graph of βtanh(ce) function;

[0110] Figure 6 It is the five-phase FTFSCW-IPM speed diagram;

[0111] Figure 7 It is the electromagnetic torque diagram of the five-phase FTFSCW-IPM;

[0112] Figure 8 It is the A phase current diagram of the five-phase FTFSCW-IPM;

[0113] Fig. 9 The third harmonic plane of the five-phase FTFSCW-IPM is d3 、i q3 Current diagram. DETAILED DESCRIPTION

[0114] The following is a detailed description in conjunction with the specific implementation methods and the accompanying drawings.

[0115] A novel approach rate FTSMC control method for five-phase FTFSCW-IPM based on time-varying ESO is proposed. Figure 1 As shown, the following steps are included:

[0116] S1. Establish a mathematical model of the five-phase FTFSCW-IPM motor, including flux, voltage, torque and motion equations;

[0117] S2. Design the fast terminal sliding surface and improved reaching law, obtain the control law of the five-phase FTFSCW-IPM with improved reaching rate and fast terminal sliding mode in the speed loop, and analyze the controller stability by combining Lyapunov theorem;

[0118] S3. Design a time-varying parameter ESO for five-phase FTFSCW-IPM disturbance observation estimation, and analyze the characteristics and parameters of the observer;

[0119] S4. The corresponding control simulation model was constructed using the MATLAB / Simulink simulation platform to test the performance of the control strategy in terms of rapid response of motor speed and to verify the effectiveness of the time-varying ESO in estimating motor disturbances.

[0120] Specifically, in S1:

[0121] Motor stator flux equation:

[0122] ψ s =L s I s +ψ m (57)

[0123] in: Represents the total flux matrix of each phase;

[0124] represents the stator winding inductance matrix;

[0125] represents the five-phase current matrix;

[0126] It represents the permanent magnet flux moment of the rotor permanent magnet coupled in each phase,

[0127] Represents the electrical angle, γ is a constant 0.4π;

[0128] Where: a ,ψ b ,ψ c ,ψ d ,ψ e ,ψ PM They are the armature winding flux and permanent magnet flux amplitude respectively; i a ,i b ,i c ,i d ,i e , are the currents of each phase of the five-phase armature winding; L aa =L bb =L cc =L dd =L ee =L s is the self-inductance of each phase winding,

[0129] M xy =L m (x=a,b,c,d,e,y=a,b,c,d,e,x≠y) is the mutual inductance between the phase windings;

[0130] The mathematical model of the five-phase motor voltage in the rotating dq coordinate is:

[0131]

[0132] Where: u dq ,i dq ,ψ f , respectively represent the dq axis components of stator voltage, current and flux; L d ,L q represents the AC and DC axis inductance of the motor; ωe is the rotor electrical angular velocity;

[0133] Five-phase FTFSCW-IPM mechanical motion equation:

[0134]

[0135] Where: Te is the electromagnetic torque, T l is the load torque, J is the moment of inertia, and B is the friction coefficient of the drive system;

[0136] The five-phase FTFSCW-IPM torque equation becomes:

[0137]

[0138] There is no third harmonic in the back EMF of the five-phase FTFSCW-IPM corresponding to the present invention, and the salient pole effect is not obvious. To facilitate modeling and controller design, the torque equation is simplified to:

[0139]

[0140] In S2:

[0141] The control model is established based on the mathematical model of S1:

[0142]

[0143] Define the following system state variables:

[0144]

[0145] in: is the reference speed of the motor, which is generally a constant; ω m is the actual motor speed;

[0146] According to the above formula:

[0147]

[0148] Design of fast terminal sliding surface:

[0149] Consider a second-order uncertain nonlinear dynamic system:

[0150]

[0151] Where: x = [x1, x2] T ,b(x)≠0,d(x,t) represents uncertainty and external interference,d(x,t)≤D.

[0152] Design the controller as:

[0153]

[0154] Where η>0;

[0155] In traditional terminal sliding mode control, when the system is close to equilibrium, the convergence of nonlinear sliding mode is slower than that of linear sliding mode dynamics (p = 1). Considering the linear sliding mode and fast Terinal sliding mode, the fast Terinal sliding mode is changed to:

[0156]

[0157] Where: α, β, q, p>0, (p>q) is an odd number;

[0158] The terminal sliding surface ensures that the system can converge to the sliding surface in a finite time. It can converge to the equilibrium state from any initial state x(0)≠0. The time required is:

[0159]

[0160] Stability analysis of the sliding surface:

[0161]

[0162] but

[0163]

[0164] From formula (14), we can see that This can cause strange problems, so

[0165] Design Improvement Convergence Rate

[0166] The traditional sliding mode reaching law design adopts the exponential reaching law form:

[0167]

[0168] When the system state is far away from the sliding surface, it will approach the sliding surface quickly at an exponential speed; when the system state is close to the sliding surface, its approach speed will slow down and continue to approach at a constant speed. If the parameter ε is set to a small value, the system will approach the sliding surface slowly, resulting in a long adjustment process, and the dynamic performance of the system will not be ideal. On the contrary, if ε is set to a large value, the system will approach the sliding surface quickly, and the adjustment process will be shortened accordingly, but this will easily cause the control target to reach the sliding surface too quickly, thereby causing the system to vibrate.

[0169] Aiming at the shortcomings of the traditional exponential reaching law, an improved exponential reaching law is designed:

[0170]

[0171] For this control rate, the Y(s,δ) function is used instead of the sgn(s) function for smoothing, where the Y(s,δ) function is:

[0172]

[0173] Where: ρ≠0,δ>0, taking ρ=-6,δ=1, we can get the function curve, such as Figure 3 As shown;

[0174] The new approach rate is:

[0175]

[0176] The function Y(s,δ) is flatter than the saturation function sat(s), and has different effects with different values ​​of ρ and δ. Appropriate values ​​can be selected according to actual conditions to meet engineering requirements.

[0177] Improved exponential reaching law analysis:

[0178] When the state in the system is far away from the sliding surface, that is, s→∞, f(s)→1 in the constant speed reaching law, and the function f(s) has no effect on the rapid response of the system; when s→0, the exponential reaching law qs→0, and the constant speed reaching law f(s)→1 / 2, the speed at which the system state approaches the sliding surface is slower than before the improvement, the chattering phenomenon of the motor will be alleviated, and the control accuracy will be improved;

[0179] According to Lyapunov stability analysis, the Lyapunov function is selected as:

[0180]

[0181] but:

[0182]

[0183] It can be seen that -sεsgn(s)<0, f(s)>0, q>0, so The sliding surface function selected by the sliding mode control satisfies the reachability condition, which can ensure that the system is asymptotically stable when entering the sliding mode dynamic state from the approaching mode, and reaches the origin within a limited time;

[0184] To sum up, the output is defined According to equations (8), (11) and (18), the controller output is:

[0185]

[0186] The control block diagram is shown in Figure (2). The controller adds an integral term, which not only weakens the bucket vibration phenomenon of the sliding mode control, but also improves the control quality.

[0187] In S3, the uncertain disturbances existing in the actual operation of the motor are taken into account. In order to offset the impact of these disturbances on the system, a five-phase FTFSCW-IPM disturbance observer is designed. Therefore, disturbance variables should be introduced when designing the speed controller.

[0188] Five-phase FTFSCW-IPM disturbance analysis:

[0189] The motion equation of the five-phase FTFSCW-IPM can be rewritten from equation (3):

[0190]

[0191] Where: g=Δdi q1 -(τ+Δτ)ω-(c+Δc)T L represents the comprehensive disturbance; where

[0192] Δd, Δτ, Δc are the change values ​​of parameters; T L =T L0 +ΔT L ;

[0193] Design of time-varying parameter ESO:

[0194] In the extended state observer (ESO) proposed by Professor Han Jingqing, the Fal function is a key nonlinear function, which has important applications in control engineering. The design concept of the Fal function is based on the principle of "large error, small gain; small error, large gain", and its expression is:

[0195]

[0196] In the formula, e is the function input; α, δ are adjustable parameters; Sign() is the symbol function;

[0197] exist Figure 4The characteristics of non-smooth Fal function with different parameters are given.

[0198] When 0<α<1, δ is the non-smooth interval threshold. When |e|<δ, the function is linear. The purpose is to avoid high-frequency jitter caused by high gain of the sign function when the error is small. When |e|>δ, it is non-smooth. When δ=0.1α=0, the curve approximates the sign function. When α=1, it is linear. Therefore, the value range of α is 0<α<1.

[0199] Design a time-varying parameter disturbance observer based on the hyperbolic tangent function, and define the hyperbolic tangent nonlinear function as:

[0200] tanh(Fal(e,β,c))=βtanh(ce) (80)

[0201] Where e is the input variable of the function, β and c are adjustable variables used to change the amplitude and rate of change of the Fal(e,β,c) function.

[0202] Figure 5 The characteristic curve of the hyperbolic tangent function is given. When the input e is greater than the threshold, the absolute value of the function output value is β. The smaller c is, the smoother the transition of the function value near zero is.

[0203] According to the velocity dynamic equation of formula (22) and combined with the extended state observer theory, the disturbance observer of the velocity loop is designed as follows:

[0204]

[0205] Where: is the estimated value of the rotation speed; is the medium disturbance of the speed loop; β1, β2, c are the parameters of ESO;

[0206] The accuracy and bandwidth of ESO can be improved by adjusting the parameters β1 and β2. If the initial value of the observed value is significantly different from the actual speed value of the motor, the high gain of ESO will have a differential peak. As can be seen from formula (25), the differential term of the speed includes the estimated value of the disturbance, so the existence of the peak phenomenon will reduce the accuracy of the disturbance observation and affect the quality of the system. In order to eliminate the differential peak phenomenon of the disturbance observer and improve the convergence effect of ESO, the present invention utilizes the saturation property of the hyperbolic tangent function and uses the time-varying parameter β 01 , β 02 Replace β1 and β2; a smaller gain is used when ESO starts running. As the running time t increases, the observer parameter will gradually increase to stability;

[0207] The time-varying parameter ESO is expressed as:

[0208]

[0209] Where: t is the time when the observer is put into operation; β 01 , β 02 is the time-varying parameter of ESO; b1 and b2 are the changing rates of the control parameters;

[0210] As the unknown disturbance estimation value of the five-phase FTFSCW-IPM motor system, the q1-axis current required for the unknown disturbance is calculated using formula (26) and then directly compensated to the q1-axis, thereby improving the anti-disturbance performance of the system;

[0211]

[0212] Considering the disturbance compensation of the motor, the controller output is:

[0213]

[0214] The present invention introduces an improved exponential approach rate control method and combines it with a feedforward compensation strategy based on a time-varying extended state observer to improve the robustness and anti-interference performance of a five-phase FTFSCW-IPM motor control system.

[0215] In FTSMC, firstly, a fast terminal sliding surface is used, which can make the system state converge to the equilibrium point within a finite time, and has both high response speed and vibration suppression ability. Secondly, a new exponential approach rate is introduced in the design of sliding mode approach rate. When the sliding surface error is large, this method can speed up the approach speed; when the error is small, the variable speed approach term will automatically reduce the approach speed, thereby effectively reducing the vibration. In addition, the Y(s,δ) function is used instead of the sgn(s) function for smoothing, which retains the dynamic performance of sgn(s), and does not have a large vibration problem like sgn(s) near 0. Thirdly, the output is output in the form of integral, thus solving the problem of controller output vibration.

[0216] The role of ESO is to estimate the total disturbance in the system (including internal nonlinearity and external disturbance) in real time and compensate it in the control strategy. Compared with traditional ESO, time-varying parameter ESO has better estimation performance, eliminates the differential peak phenomenon of disturbance observer, can better adapt to the dynamically changing system state, and further improve control accuracy.

[0217] S4: The corresponding control simulation model was constructed using the MATLAB / Simulink simulation platform to test the performance of the control strategy in terms of rapid response of the motor speed and to verify the effectiveness of the time-varying ESO in estimating motor disturbances. The simulation results are shown in Figure 6-9 shown.

[0218] Figure 6The five-phase FTFSCW-IPM is shown accelerating from no-load to 800 r / min, with a sudden application of a load of 10 N·m at 0.1 s, a sudden reduction of the load to 0 at 0.2 s, and then a sudden increase in speed from 800 r / min to 1000 r / min at 0.3 s. Figure 7 is the change of electromagnetic torque of the motor in this process; Figure 8 The dynamic change curve of phase A current during motor operation is presented; Fig. 9 is the third harmonic plane current i of the motor d3 、i q3 Control effect. By observing Figures (6), (7), (8) and (9), it can be known that in the present invention, the five-phase FTFSCW-IPM with feedforward control using time-varying ESO only takes 0.04s to start at no load and accelerate to 800r / min, and there is no speed overshoot; when the load is 10N·m, the motor recovers to 800r / min in 0.015s, and the speed only drops by 12r / min; when the load is reduced to 0, the motor recovers to 800r / min in 0.017s, and the speed only rises by 13r / min; from the electromagnetic torque diagram of the motor, the electromagnetic pulsation is small during the stable operation of the motor, and there is no large electromagnetic pulsation when the load is increased or decreased, and the motor has good operating performance. It can be seen from the A-phase current waveform that the current is a sine wave, which makes the controller have better control performance in the fundamental wave space. The modulation strategy of the present invention adopts the adjacent four-vector control strategy, from the third harmonic current i d3 、i q3 It can be seen that the control is well controlled and the harmonic current is eliminated. These results show that the five-phase FTFSCW-IPM in the present invention uses a new exponential reaching law, which not only effectively reduces the jitter, but also improves the response speed of the system. On this basis, combined with the fast terminal sliding mode surface, a global fast terminal sliding mode speed controller is designed, which enables the system to converge within a finite time, significantly improves the convergence speed of the sliding mode control, and further suppresses the jitter. In addition, in order to deal with disturbances in the system, an ESO with time-varying parameters is designed for disturbance observation and feedforward compensation. Through Figure 6-Figure 9 The results show that the control strategy further accelerates the response speed of the speed regulation system, reduces the steady-state error, and enhances the anti-disturbance ability of the system. These data prove the effectiveness of the new approach rate fast terminal sliding mode control method of the five-phase FTFSCW-IPM based on time-varying parameter ESO proposed in this paper.

Claims

1. A novel approach rate FTSMC control method of five-phase FTFSCW-IPM based on time-varying ESO, characterized in that: The following steps are involved: S1. Establish a mathematical model of the five-phase FTFSCW-IPM motor, including flux, voltage, torque and motion equations; S2. Design the fast terminal sliding surface and improved reaching law, obtain the control law of the five-phase FTFSCW-IPM with improved reaching rate and fast terminal sliding mode in the speed loop, and analyze the controller stability by combining Lyapunov theorem; S3. Design a time-varying parameter ESO for five-phase FTFSCW-IPM disturbance observation estimation, and analyze the characteristics and parameters of the observer.

2. According to the five-phase FTFSCW-IPM novel approach rate FTSMC control method based on time-varying ESO according to claim 1, it is characterized in that: In S1: Motor stator flux equation: ψ s =L s I s +ψ m (1) in: Represents the total flux matrix of each phase; represents the stator winding inductance matrix; represents the five-phase current matrix; It represents the permanent magnetic flux linkage moment of the rotor permanent magnet coupled in each phase, Represents the electrical angle, γ is a constant 0.4π; Where: a , ψ b , ψ c , ψ d , ψ e , ψ PM They are the armature winding flux and permanent magnet flux amplitude respectively; i a ,i b ,i c ,i d ,i e , are the currents of each phase of the five-phase armature winding; L aa =L bb =L cc =L dd =L ee =L s is the self-inductance of each phase winding, M xy =L m (x=a,b,c,d,e,y=a,b,c,d,e,x≠y) is the mutual inductance between the phase windings; The mathematical model of the five-phase motor voltage in the rotating dq coordinate is: Where: u dq ,i dq , ψ f , respectively represent the dq axis components of stator voltage, current and flux; L d , L q represents the AC and DC axis inductance of the motor; ωe is the rotor electrical angular velocity; Five-phase FTFSCW-IPM mechanical motion equation: Where: Te is the electromagnetic torque, Tl is the load torque, J is the moment of inertia, and B is the friction coefficient of the drive system; The five-phase FTFSCW-IPM torque equation becomes: The torque equation simplifies to:

3. The novel approach rate FTSMC control method of the five-phase FTFSCW-IPM based on time-varying ESO according to claim 2 is characterized in that: In S2: The control model is established based on the mathematical model of S1: Define the following system state variables: in: is the reference speed of the motor; ω m is the actual motor speed; According to the above formula: Design of fast terminal sliding surface: Consider a second-order uncertain nonlinear dynamic system: Where: x = [x1, x2] T , b(x)≠0, d(x, y) represents uncertainty and external interference, d(x, t)≤D. Design the controller as: Where η>0; Considering the linear sliding mode and the fast Terinal sliding mode comprehensively, the fast Terinal sliding mode is changed to: Where: α, β, q, p>0, (p>q) is an odd number; The terminal sliding surface ensures that the system can converge to the sliding surface in a finite time. It can converge to the equilibrium state from any initial state x(0)≠0. The time required is: Stability analysis of the sliding surface: but From formula (14), we can see that This can cause strange problems, so Design Improvement Convergence Rate The traditional sliding mode reaching law design adopts the exponential reaching law form: Improved exponential reaching law: For the control rate, the Y(s, δ) function is used instead of the sgn(s) function for smoothing, where the Y(s, δ) function is: Where: ρ≠0, δ>0, take ρ=-6, δ=1, and we can get the function curve; The new approach rate is:

4. The novel approach rate FTSMC control method of the five-phase FTFSCW-IPM based on time-varying ESO according to claim 3 is characterized in that: In S2: Improved exponential reaching law analysis: When the state in the system is far away from the sliding surface, that is, s→∞, f(s)→1 in the constant speed reaching law, and the function f(s) has no effect on the rapid response of the system; when s→0, the exponential reaching law qs→0, and the constant speed reaching law f(s)→1 / 2, the speed at which the system state approaches the sliding surface is slower than before the improvement, the chattering phenomenon of the motor will be alleviated, and the control accuracy will be improved; According to Lyapunov stability analysis, the Lyapunov function is selected as: but: It can be seen that -sεsgn(s)<0, f(s)>0, q>0, so The sliding surface function selected by the sliding mode control satisfies the reachability condition, which can ensure that the system is asymptotically stable when entering the sliding mode dynamic state from the approaching mode, and reaches the origin within a limited time; To sum up, the output is defined According to equations (8), (11) and (18), the controller output is:

5. The novel approach rate FTSMC control method of the five-phase FTFSCW-IPM based on time-varying ESO according to claim 4 is characterized in that: In S3: Five-phase FTFSCW-IPM disturbance analysis: The motion equation of the five-phase FTFSCW-IPM can be rewritten from equation (3): Where: g=Δdi q1 -(T+Δτ)ω-(c+Δc)T L represents the comprehensive disturbance; where Δd, Δτ, Δc are the change values ​​of the parameters; T L =T L0 +△T L ; Design of time-varying parameter ESO: Design Fal function: In the formula, e is the function input; α, δ are adjustable parameters; Sign() is the symbol function; The value range of α is 0<α<1; Design a time-varying parameter disturbance observer based on the hyperbolic tangent function, and define the hyperbolic tangent nonlinear function as: tanh(Fal(e,β,c))=βtanh(ce) (24) In the formula, e is the input variable of the function, β and c are adjustable variables used to change the amplitude and rate of change of the Fal(e, βl, c) function; According to the velocity dynamic equation of formula (22) and combined with the extended state observer theory, the disturbance observer of the velocity loop is designed as follows: Where: is the estimated value of the rotation speed; is the medium disturbance of the speed loop; β1, β2, c are the parameters of ESO; Using the saturation property of the hyperbolic tangent function, the time-varying parameter β 01 , β 02 Replace β1 and β2; a smaller gain is used when ESO starts running. As the running time t increases, the observer parameter will gradually increase to stability; The time-varying parameter ESO is expressed as: Where: t is the time when the observer is put into operation; β 01 , β 02 is the time-varying parameter of ESO; b1 and b2 are the changing rates of the control parameters; As the unknown disturbance estimation value of the five-phase FTFSCW-IPM motor system, the q1-axis current required for the unknown disturbance is calculated using formula (26) and then directly compensated to the q1-axis, thereby improving the anti-disturbance performance of the system; Considering the disturbance compensation of the motor, the controller output is:

6. The novel approach rate FTSMC control method of five-phase FTFSCW-IPM based on time-varying ESO according to claim 1 is characterized in that: It also includes S4, using the MATLAB / Simulink simulation platform to build the corresponding control simulation model to test the performance of the control strategy in terms of rapid response of motor speed and verify the effectiveness of the time-varying ESO in estimating motor disturbances.

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