FTFSCW-IPM motor improved sliding mode torque observer feedforward compensation control method

Abstract

The invention provides an improved sliding mode torque observer feed-forward compensation control method for an FTFSCW-IPM motor, 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 integral sliding mode surface and an improved reaching law to obtain a control law of a five-phase FTFSCW-IPM improved integral sliding mode in a rotating speed loop, and performing controller stability analysis in combination with a Lyapunov theorem; and S2, designing an FTFSCW-IPM sliding mode torque observer, and performing feed-forward compensation by using a torque observation value to participate in controller output in S2. Through the method provided by the invention, the robustness and the anti-interference capability of the five-phase FTFSCW-IPM motor control system can be improved.

Description

Technical Field

[0001] The invention relates to the field of multi-phase motor control, and in particular to an improved sliding mode torque observer feedforward compensation control method for an FTFSCW-IPM motor. Background Art

[0002] With the rapid development of electric vehicles and automation equipment, the requirements for motor performance are getting higher and higher. The five-phase FTFSCW-IPM motor has gradually become a research hotspot due to its unique advantages, such as higher reliability, lower torque pulsation and wider speed regulation range. In the traditional control of five-phase motors, sliding mode control can achieve better control effects than traditional PI controllers when dealing with systems with significant nonlinear characteristics or unexpected interference.

[0003] In sliding mode control, its main advantage is its insensitivity to dynamic changes of system parameters and disturbances. However, due to the high-frequency switching of control signals on the sliding mode surface, traditional sliding mode control has a chattering phenomenon. It not only affects the control accuracy, but may also cause damage to the actuator. At the same time, in actual motor operation, the motor operation has the problem of slow speed response and poor control effect under complex working conditions of load disturbance.

[0004] Therefore, in order to solve the above problems, it is necessary to propose an improved approach rate and an improved sliding mode torque observer method feedforward compensation strategy on the premise of reducing system jitter and improving the motor's ability to respond to load disturbances. Through this method, the robustness and anti-interference ability of the five-phase FTFSCW-IPM motor control system can be improved. Summary of the invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the background technology, the present invention discloses a FTFSCW-IPM motor improved sliding mode torque observer feedforward compensation control method; in the torque observer design, this method establishes a five-phase FTFSCW-IPM torque mathematical model, and constructs an estimated and actual error sliding surface, and finally observes the input torque of the system, and feeds the observed value back to the torque current through the sliding mode load torque observer, so that the controller can respond quickly to load changes. At the same time, the demand for the reaching law parameter value is reduced, thereby reducing the amplitude of the sliding mode control gain, which can weaken the jitter phenomenon and improve the robustness and anti-interference ability of the five-phase five-phase built-in motor control system.

[0006] Technical solution: The improved sliding mode torque observer feedforward compensation control method of the FTFSCW-IPM motor 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 integral sliding surface and improved reaching law, obtain the control law of the five-phase FTFSCW-IPM improved integral sliding mode in the speed loop, and analyze the controller stability by combining Lyapunov theorem;

[0009] S3. Design the FTFSCW-IPM sliding mode torque observer and use the torque observation value to participate in the controller output in S2 for feedforward compensation.

[0010] Among them, in S1:

[0011] Motor stator flux equation:

[0012] ψ s =L s I s +ψ m (25)

[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] represents the permanent magnet flux matrix of the rotor permanent magnet coupled in each phase, represents the electrical angle, γ is a constant of 0.4π;

[0017] 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;

[0018] 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;

[0019] The mathematical model of the five-phase motor voltage in the rotating dq coordinate is:

[0020]

[0021] 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;

[0022] The mechanical motion equation of the five-phase FTFSCW-IPM motor is:

[0023]

[0024] Where: T e is the electromagnetic torque, T l is the load torque, J is the moment of inertia, ωe is the mechanical angular velocity, and B is the friction coefficient of the drive system;

[0025] The fault-tolerant IPM torque equation becomes:

[0026]

[0027] To facilitate modeling and controller design, the torque equation is simplified to:

[0028]

[0029] Furthermore, in S2:

[0030] The speed and the integral of the speed are used as the input of the sliding mode controller to reduce the impact of speed fluctuations on the system;

[0031] In the speed loop, let the error be:

[0032]

[0033] System variables:

[0034]

[0035] By introducing the integral of the state variable, the integral sliding surface is obtained:

[0036] s=c∫edt+e=cx 1 +x 2 (32)

[0037] In the design control rate

[0038] Differentiate equation (8) to get:

[0039]

[0040] The general form of common exponential reaching laws is as follows:

[0041]

[0042] Where: ks is the exponential approach term. When s is large, the system state can approach the sliding surface at a large speed. εsgn(s) is the constant speed approach term. When s approaches zero, the approach speed is ε.

[0043] Improved exponential reaching law:

[0044]

[0045] Where: 0<α<1, β>1, when |s| is large, the approaching speed of the variable speed approaching term is It can speed up the sliding mode approaching motion speed; when |s| is small, the approaching speed of the variable speed approaching term is Can reduce chattering; use Y(s,δ) function instead of sgn(s) function for smoothing, where Y(s,δ) function:

[0046]

[0047] Where: ρ≠0,δ>0, take ρ=-6,δ=1, and obtain the function curve;

[0048] 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.

[0049] In summary:

[0050]

[0051] The controller output is:

[0052]

[0053] To analyze the stability of sliding mode control, the Lyapunov function is selected:

[0054]

[0055] From formula (10) and formula (11), we can get:

[0056]

[0057] It can be seen from formula (17) that the improved sliding mode control law satisfies the Lyapunov theorem, ensuring that the system can enter the sliding mode.

[0058] Furthermore, in S3:

[0059] The state equation with rotor electrical angular velocity and load torque as state variables is obtained from the motor torque and motion equation as follows:

[0060]

[0061] Taking the motor electrical angular velocity and load torque as observation variables, a sliding mode observer is constructed as shown in the following formula:

[0062]

[0063] Where: k is the sliding mode gain, is the observed value of electrical angular velocity, g is the feedback coefficient, is the observed value of load torque;

[0064] Substituting equation (18)-(19) to obtain the observer error equation is:

[0065]

[0066] In the formula, is the load torque estimation error,

[0067] Select the speed difference as the switching function and define the sliding surface as

[0068] According to the convergence condition of generalized sliding mode motion It can be seen that:

[0069]

[0070] From formula (21), the possible range of sliding mode gain k is:

[0071]

[0072] According to the sliding mode control law, when the observer approaches the sliding surface, the condition is satisfied. Substituting it into formula (20), we get:

[0073]

[0074] The error equation of the observed torque is obtained from formula (23):

[0075]

[0076] Where c is a constant and the torque observation error is It converges to zero rapidly at an exponential speed. The speed of convergence depends on the size of the feedback coefficient g. From formulas (23) and (24), it can be seen that the dynamic performance of the observer is determined by k and g. By selecting appropriate sliding mode gain k and feedback coefficient g, it is ensured that the torque observation value can track the true torque value in real time and accurately.

[0077] Furthermore, it also includes S4: using the MATLAB / Simulink simulation platform to build a 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 sliding mode observer in accurately estimating the load torque.

[0078] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0079] (1) By feeding back the observed value to the torque current through the load torque observer, the controller can respond quickly to load changes and reduce the demand for the reaching law parameter value, thereby reducing the amplitude of the sliding mode control gain and weakening the chattering phenomenon;

[0080] (2) The problem that the traditional sliding mode torque observer uses a sign function to construct the reaching law, which causes the observer state to exhibit a chattering phenomenon near the sliding surface, causing the estimated result to fluctuate back and forth above the actual value, which has a direct impact on the estimated result, is solved;

[0081] (3) In the case of sudden changes or load fluctuations, feedforward compensation can significantly reduce the change in motor speed and improve the stability of the speed. Load torque observation feedforward control provides an effective performance improvement method for motor control systems, especially for applications that require fast response and high stability.

[0082] (4) The calculation method used is simple and efficient, easy to operate in practice, and helps to transform theoretical innovation into engineering practice and practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 The five-phase FTFSCW-IPM motor control block diagram of the present invention;

[0084] Figure 2 This is a control block diagram of the improved sliding mode controller of the present invention;

[0085] Figure 3 The improved sliding mode torque observer of the present invention;

[0086] Figure 4 is the switching function graph;

[0087] Figure 5 It is the five-phase FTFSCW-IPM motor speed diagram;

[0088] Figure 6It is the torque observation diagram of the five-phase FTFSCW-IPM;

[0089] Figure 7 is the electromagnetic torque of the five-phase FTFSCW-IPM motor;

[0090] Figure 8 This is the A-phase current diagram of the five-phase FTFSCW-IPM motor. DETAILED DESCRIPTION

[0091] The following is a detailed description in conjunction with the specific implementation methods and the accompanying drawings.

[0092] like Figure 1 The improved sliding mode torque observer feedforward compensation control method of the FTFSCW-IPM motor shown includes the following steps:

[0093] S1. Establish a mathematical model of the five-phase FTFSCW-IPM motor, including flux, voltage, torque and motion equations;

[0094] Motor stator flux equation:

[0095] ψ s =L s I s +ψ m (49)

[0096] in: Represents the total flux matrix of each phase;

[0097] represents the stator winding inductance matrix;

[0098] represents the five-phase current matrix;

[0099] represents the permanent magnet flux matrix of the rotor permanent magnet coupled in each phase, represents the electrical angle, γ is a constant of 0.4π;

[0100] 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 =Lee =L s is the self-inductance of each phase winding;

[0101] 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;

[0102] The mathematical model of the five-phase motor voltage in the rotating dq coordinate is:

[0103]

[0104] 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;

[0105] The mechanical motion equation of the five-phase FTFSCW-IPM motor is:

[0106]

[0107] Where: T e is the electromagnetic torque, T l is the load torque, J is the moment of inertia, ωe is the mechanical angular velocity, and B is the friction coefficient of the drive system;

[0108] The fault-tolerant IPM torque equation becomes:

[0109]

[0110] There is no third harmonic in the back EMF of the five-phase FTFSCW-IPM motor 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:

[0111]

[0112] S2. Design the fast integral sliding surface and improved reaching law, obtain the control law of the five-phase FTFSCW-IPM improved integral sliding mode in the speed loop, and analyze the controller stability in combination with Lyapunov theorem;

[0113] In general sliding surface design, the error between velocity and acceleration is usually used as the input of sliding mode control. Acceleration is generally obtained by the differential of velocity, and the differential will lead to the amplification of noise signals, resulting in a large error in the acceleration signal. Therefore, the present invention adopts an integral sliding surface such as Figure 2 shown.

[0114] The speed and the integral of the speed are used as the input of the sliding mode controller to reduce the impact of speed fluctuations on the system;

[0115] In the speed loop, let the error be:

[0116]

[0117] System variables:

[0118]

[0119] By introducing the integral of the state variable, the integral sliding surface is obtained:

[0120] s=c∫edt+e=cx 1 +x 2 (56)

[0121] In the design control rate

[0122] Differentiate equation (8) to obtain:

[0123]

[0124] The general form of common exponential reaching laws is as follows:

[0125]

[0126] Where: ks is the exponential approach term. When s is large, the system state can approach the sliding surface at a large speed. εsgn(s) is the constant speed approach term. When s approaches zero, the approach speed is ε.

[0127] Improved exponential reaching law:

[0128]

[0129] Where: 0<α<1, β>1, when |s| is large, the approaching speed of the variable speed approaching term is It can speed up the sliding mode approaching motion speed; when |s| is small, the approaching speed of the variable speed approaching term is Can reduce chattering; use Y(s,δ) function instead of sgn(s) function for smoothing, where Y(s,δ) function:

[0130]

[0131] Where: ρ≠0,δ>0, take ρ=-6,δ=1, and get the function curve as Figure 4 As shown;

[0132] 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.

[0133] In summary:

[0134]

[0135] The controller output is:

[0136]

[0137] To analyze the stability of sliding mode control, the Lyapunov function is selected:

[0138]

[0139] From formula (10) and formula (11), we can get:

[0140]

[0141] It can be seen from formula (17) that the improved sliding mode control law satisfies the Lyapunov theorem, ensuring that the system can enter the sliding mode.

[0142] S3. Design the FTFSCW-IPM sliding mode torque observer and use the torque observation value to participate in the controller output in S2 for feedforward compensation.

[0143] The state equation with rotor electrical angular velocity and load torque as state variables is obtained from the motor torque and motion equation as follows:

[0144]

[0145] Since the mechanical motion time constant of the system is much larger than the time constant of the current loop, it can be assumed that the load change is negligible and remains basically unchanged during the current control period, that is, Taking the motor electrical angular velocity and load torque as observation variables, a sliding mode observer is constructed as shown in the following formula:

[0146]

[0147] Where: k is the sliding mode gain, is the observed value of electrical angular velocity, g is the feedback coefficient, is the observed value of load torque;

[0148] Substituting equation (18)-(19) to obtain the observer error equation is:

[0149]

[0150] In the formula, is the load torque estimation error,

[0151] Select the speed difference as the switching function and define the sliding surface as

[0152] According to the convergence condition of generalized sliding mode motion It can be seen that:

[0153]

[0154] From formula (21), the possible range of sliding mode gain k is:

[0155]

[0156] According to the sliding mode control law, when the observer approaches the sliding mode surface, the condition is satisfied. Substituting it into formula (20), we get:

[0157]

[0158] The error equation of the observed torque is obtained from formula (23):

[0159]

[0160] Where c is a constant, torque observation error It converges to zero quickly at an exponential rate, and the speed of convergence depends on the size of the feedback coefficient g. It can be observed from formulas (23) and (24) that the dynamic performance of the observer is determined by k and g. The sliding mode gain k should not be set too large, because this may cause jitter of the torque observation value, which in turn affects the stability of the speed control loop. By selecting appropriate control parameters such as the sliding mode gain k and the feedback coefficient g, we can ensure that the torque observation value can track the true torque value in real time and accurately. This can be constructed as follows Figure 3 The observer system framework is shown.

[0161] 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 sliding mode observer in accurately estimating load torque.

[0162] The simulation results are as follows Figure 5-8 shown.

[0163] Figure 5The five-phase FTFSCW-IPM motor is shown accelerating from no load to 800 r / min, then suddenly adding a load of 10 N·m at 0.1s, suddenly reducing the load to 0 at 0.2s, and suddenly increasing the speed setting from 800 r / min to 900 r / min at 0.3s;

[0164] Figure 6 The waveform diagram of the sliding mode load torque observation is shown;

[0165] Figure 7 It is the electromagnetic torque diagram of the motor corresponding to the speed change;

[0166] Figure 8 This is the change diagram of phase A current during motor operation;

[0167] By observing Figures (5), (6), (7) and (8), it can be seen that in the present invention, the five-phase FTFSCW-IPM motor using the sliding mode load torque observer feedforward control 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 0.02s, and the speed only drops by 9r / min; when the load is reduced to 0, the motor recovers to 800r / min in 0.015s, and the speed only rises by 12r / min; the sliding mode load torque observer has a smaller value at startup and has less impact on the controller startup. The response time at 0.1s loading is 0.015s, and the observation error is maintained within the range of ±0.05N·m. The response time at 0.2s load reduction is 0.005s, and the observation error is maintained within the range of ±0.05N·m. The effect on the controller at 0.3 acceleration is very small. From the electromagnetic torque diagram of the motor, the electromagnetic pulsation is small during the stable operation of the motor. When the load is cut, there is no large electromagnetic pulsation phenomenon, and the motor has good operating performance. From the A-phase current waveform, it can be seen that the current is a sine wave, and the third harmonic is well controlled, which makes the controller have better control performance in the fundamental wave space.

[0168] These results show that the five-phase FTFSCW-IPM motor in the present invention exhibits a rapid dynamic response and has no speed overshoot problem; when the load torque increases or decreases, the sliding mode load torque observer can quickly and accurately estimate the load torque of the motor, so that the motor speed can follow the set value in time, and also shows a rapid dynamic response when the motor accelerates; these data prove the effectiveness of the five-phase FTFSCW-IPM motor control method based on sliding mode load torque observer feedforward compensation proposed in the present invention.

Claims

1. An improved sliding mode torque observer feedforward compensation control method for FTFSCW-IPM motor, 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 integral sliding surface and improved reaching law, obtain the control law of the five-phase FTFSCW-IPM improved integral sliding mode in the speed loop, and analyze the controller stability in combination with Lyapunov theorem; S3. Design the FTFSCW-IPM sliding mode torque observer and use the torque observation value to participate in the controller output in S2 for feedforward compensation.

2. The improved sliding mode torque observer feedforward compensation control method of FTFSCW-IPM motor according to claim 1 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; represents the permanent magnet flux matrix of the rotor permanent magnet coupled in each phase, represents the electrical angle, γ is a constant of 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; The mechanical motion equation of the five-phase FTFSCW-IPM motor is: Where: T e is the electromagnetic torque, T l is the load torque, J is the moment of inertia, ωe is the mechanical angular velocity, and B is the friction coefficient of the drive system; The fault-tolerant IPM torque equation becomes: To facilitate modeling and controller design, the torque equation is simplified to:

3. The improved sliding mode torque observer feedforward compensation control method of FTFSCW-IPM motor according to claim 2 is characterized in that: In S2: The speed and the integral of the speed are used as the input of the sliding mode controller to reduce the impact of speed fluctuations on the system; In the speed loop, let the error be: System variables: By introducing the integral of the state variable, the integral sliding surface is obtained: s=c∫edt+e=cx1+x2(8) In the design control rate Differentiate equation (8) to get: The general form of common exponential reaching laws is as follows: Where: ks is the exponential approach term. When s is large, the system state can approach the sliding surface at a large speed. εsgn(s) is the constant speed approach term. When s approaches zero, the approach speed is ε. Improved exponential reaching law: Where: 0 <a<1,β> 1. When |s| is large, the approaching speed of the variable speed approaching term is It can speed up the sliding mode approaching motion speed; when |s| is small, the approaching speed of the variable speed approaching term is Can reduce chattering; use Y(s,δ) function instead of sgn(s) function for smoothing, where Y(s,2) function: Where: ρ≠0,δ>0, take ρ=-6,δ=1, and obtain the function curve; 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. In summary: The controller output is: To analyze the stability of sliding mode control, the Lyapunov function is selected: From formula (10) and formula (11), we can get: It can be seen from formula (17) that the improved sliding mode control law satisfies the Lyapunov theorem, ensuring that the system can enter the sliding mode.

4. The improved sliding mode torque observer feedforward compensation control method of FTFSCW-IPM motor according to claim 3 is characterized in that: In S3: The state equation with rotor electrical angular velocity and load torque as state variables is obtained from the motor torque and motion equation as follows: Taking the motor electrical angular velocity and load torque as observation variables, a sliding mode observer is constructed as shown in the following formula: Where: k is the sliding mode gain, is the observed value of electrical angular velocity, g is the feedback coefficient, is the observed value of load torque; Substituting equation (18)-(19) to obtain the observer error equation is: In the formula, is the load torque estimation error, Select the speed difference as the switching function and define the sliding surface as According to the convergence condition of generalized sliding mode motion It can be seen that: From formula (21), the possible range of sliding mode gain k is: According to the sliding mode control law, when the observer approaches the sliding mode surface, the condition is satisfied. Substituting it into formula (20), we get: The error equation of the observed torque is obtained from formula (23): Where c is a constant and the torque observation error is It converges to zero rapidly at an exponential speed. The speed of convergence depends on the size of the feedback coefficient g. From formulas (23) and (24), it can be seen that the dynamic performance of the observer is determined by k and g. By selecting appropriate sliding mode gain k and feedback coefficient g, it is ensured that the torque observation value can track the true torque value in real time and accurately.

5. The improved sliding mode torque observer feedforward compensation control method of FTFSCW-IPM motor according to claim 1 is characterized in that: It also includes S4: The corresponding control simulation model is 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 sliding mode observer in accurately estimating load torque.

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