Model-free superhelix fast integration terminal sliding mode control method for permanent magnet synchronous motor

Abstract

The invention provides a novel model-free fast integration terminal sliding mode controller method for a permanent magnet synchronous motor based on an improved extended nonsingular terminal sliding mode disturbance observer, and the method is compared with a PI control method and a model-free sliding mode control method based on an extended sliding mode observer. The method can reduce the dependence of a controller on a specific mathematical model of a controlled system, is more suitable for nonlinear and strong coupling systems such as a permanent magnet synchronous motor, employs an improved extended nonsingular terminal sliding mode disturbance observer to estimate unknown total disturbance, and enhances the robustness and anti-interference capability of the method. The control method has high response speed and high control precision, and has a good fault-tolerant control function on the parameter perturbation of the motor, so that the permanent magnet synchronous motor can operate efficiently, stably and reliably under the parameter perturbation condition.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motors, and more specifically to a permanent magnet synchronous motor model-free super-helical fast integral terminal sliding mode control method based on an improved extended non-singular terminal sliding mode disturbance observer. Background Art

[0002] In recent years, permanent magnet synchronous motor drive systems have been widely used in engineering applications such as high-speed railways, aerospace, electric vehicles, and robots due to their compact structure, high efficiency, and excellent dynamic performance. Traditional PI controllers are widely used in motor drive systems due to their simple structure and easy implementation; however, these traditional controllers have limitations such as integral saturation, and permanent magnet synchronous motors are nonlinear, strongly coupled systems, and the system model has uncertainty.

[0003] In engineering practice, due to the complex and changeable operating conditions of permanent magnet synchronous motors, affected by uncertain factors such as temperature and external operating environment, the parameters of permanent magnets, resistors, and inductors will change, causing electrical parameter perturbations of the motors; mechanical parameters such as moment of inertia and friction damping will also change; at the same time, there are unmodeled dynamics in the system; these are collectively referred to as "unknown total disturbances". Existing predictive control methods with fault-tolerant control functions have certain feasibility and effectiveness, but these methods are all model-based control methods. Therefore, in order to ensure the stable operation of permanent magnet synchronous motors under unknown total disturbances, it is necessary to seek new control methods to achieve efficient and reliable operation of the motors. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a permanent magnet synchronous motor model-free super-helical fast integral terminal sliding mode control method based on an improved extended non-singular terminal sliding mode disturbance observer in view of the shortcomings and defects of the existing technology.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A novel model-free super-helical fast integral terminal sliding mode control method for a permanent magnet synchronous motor based on an improved extended non-singular terminal sliding mode disturbance observer is characterized by comprising the following steps:

[0007] Step 1: Establish a hyperlocal model of the speed loop in the permanent magnet synchronous motor control system, which is specifically expressed as ,in represents the electrical angular velocity, represents the q-axis current, represents the q-axis current coefficient, represents the gain of the speed loop, represents the unknown total disturbance;

[0008] Step 2: Design a novel model-free fast integral terminal sliding mode controller for the speed loop:

[0009] Step 2.1, select state error For the control target, is a given electrical angular velocity;

[0010] Step 2.2, select the state error e 1 As a variable, an improved fast integral terminal sliding surface is designed

[0011] (1)

[0012] in, , and All are normal numbers to be designed; , is a positive odd number and satisfies ; is a symbolic function; is a terminal item; is the integral symbol, is the integration variable;

[0013] Step 2.3, introduce a new supercoil control law:

[0014] (2)

[0015] in, , , and is the coefficient to be designed;

[0016] ;

[0017] ;

[0018] in, , , , , , , and is the coefficient to be designed;

[0019] Step 2.4, the new model-free fast integral terminal sliding mode controller can be designed as:

[0020]

[0021] in, is the given value of q-axis current; for An estimated value of For a given electrical angular velocity The derivative of for The second derivative of is a symbolic function; is the integral symbol, is the integration variable;

[0022] Step 3: Design an improved extended non-singular terminal sliding mode disturbance observer to observe the unknown total disturbance :

[0023] Step 3.1, the electrical angular velocity and the unknown total disturbance F as state variables, the quadrature axis current is the control input, electrical angular velocity As the system output, the speed loop extended state equation can be obtained as follows:

[0024]

[0025] In the formula, is the unknown total disturbance The rate of change of

[0026] The improved extended non-singular terminal sliding mode disturbance observer is specifically expressed as:

[0027]

[0028] in, is the electrical angular velocity Observed value of is the control input of the observer; for The rate of change of is the observer gain;

[0029] From this, the dynamic error equation of the observer can be obtained as:

[0030]

[0031] In the formula, represents the speed observation error of the observer; represents the observation error of the unknown total disturbance;

[0032] Step 3.2, select a fast non-singular terminal sliding surface:

[0033] (3)

[0034] in, is the speed observation error of the observer; is a positive constant to be designed, ;

[0035] Step 3.3, select the double power reaching law:

[0036] (4)

[0037] in, and is the normal number to be designed, , ; is a symbolic function;

[0038] Step 3.4, the control input of the improved extended non-singular terminal sliding mode disturbance observer is designed as:

[0039]

[0040] in, is the integral symbol, is the integration variable.

[0041] Furthermore, the novel model-free fast integral terminal sliding mode controller selects the fast integral terminal sliding mode surface improved by formula (1) and the super-helical control law improved by formula (2), and the state error e 1 will converge in finite time.

[0042] Furthermore, the improved extended non-singular terminal sliding mode disturbance observer selects the fast non-singular terminal sliding mode surface of formula (3) and the double power reaching law of formula (4). or When the state error of the improved extended non-singular terminal sliding mode disturbance observer is It will converge in a finite time, and the designed model-free superhelical fast terminal sliding mode controller is stable. At this time, .

[0043] The present invention adopts a novel model-free super-twisting fast integral terminal sliding mode control (MFSITSMC) method of permanent magnet synchronous motor based on improved extended non-singular terminal sliding mode disturbance observer (IENTSMDO) for the speed loop, which is different from PI controller and traditional model-free sliding mode control (Model-free Sliding Mode Control, ESMO) based on extended sliding mode observer (ESMO). Compared with the traditional MFSMC, the controller can reduce its dependence on the system model and is more suitable for nonlinear and multi-coupled systems such as permanent magnet synchronous motors. At the same time, an improved extended non-singular terminal sliding mode disturbance observer is used to observe the unknown total disturbance. Compared with the extended sliding mode observer, the observed unknown part of the system is more accurate, the steady-state error and jitter are smaller, and the robust performance of the method of the present invention is enhanced. The control method of the present invention has fast response speed and high control accuracy, and has a certain fault-tolerant control function for parameter perturbations, so that the permanent magnet synchronous motor can maintain efficient and reliable operation under parameter perturbations. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a structural block diagram of a control system according to an embodiment of the present invention;

[0045] In the figure, 1—permanent magnet synchronous motor (PMSM), 2—three-phase inverter, 3—SVPWM module (i.e., space vector pulse width modulation), 4—Park inverse transform, 5—current transformer, 6—Clark transform, 7—Park transform, 8—q-axis current controller, 9—d-axis current controller, 10—new model-free super-helical fast integral terminal sliding mode controller, 11—improved extended non-singular terminal sliding mode disturbance observer, 12—MTPA, 13—position and speed sensors.

[0046] Figure 2 This is a comparison diagram of the speed response of an embodiment of the present invention under parameter perturbation and PI control.

[0047] Figure 3 The figure is a comparison diagram of the speed response of an embodiment of the present invention under parameter perturbation and that of the traditional model-free control (MFSMC).

[0048] Figure 4 This is a comparison diagram of the d-axis current response of an embodiment of the present invention under parameter perturbation and PI control.

[0049] Figure 5 The figure is a comparison diagram of the q-axis current response of an embodiment of the present invention under parameter perturbation and PI control.

[0050] Figure 6 The figure is a comparison diagram of torque response of an embodiment of the present invention under parameter perturbation and PI control.

[0051] Figure 7 This is a comparison diagram of the d-axis current response of an embodiment of the present invention and that of MFSMC under parameter perturbation.

[0052] Figure 8 This is a comparison diagram of the q-axis current response of an embodiment of the present invention and that of MFSMC under parameter perturbation.

[0053] Fig. 9 The figure is a comparison diagram of the torque response of an embodiment of the present invention and MFSMC under parameter perturbation.

[0054] Fig.10 The figure is a comparison diagram of the speed tracking error of an embodiment of the present invention and the extended sliding mode observer (ESMO) under parameter perturbation.

[0055] Fig.11 This is a comparison diagram of the unknown part F observed by ESMO under parameter perturbation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be further described below in conjunction with specific implementation modes.

[0057] Ignoring stator core saturation, eddy current and hysteresis loss, the stator voltage equation of the permanent magnet synchronous motor (PMSM) in the ideal dq rotating coordinate system is:

[0058] (6)

[0059] In the formula, , Respectively represent the stator d-axis and q-axis voltage components; is the stator phase winding resistance; , Respectively represent the stator d-axis and q-axis current components; , They represent the stator d-axis and q-axis inductances respectively; is the electrical angular velocity; is the rotor permanent magnet flux.

[0060] When the permanent magnet synchronous motor is in actual operation, the internal parameters of the motor, such as resistance, inductance, and flux linkage, will be perturbed. Considering the influence of the perturbation of electromagnetic parameters, the stator voltage equation of the PMSM is:

[0061] (7)

[0062] In the formula, and Indicated by stator phase winding resistance , stator d-axis inductance , stator q-axis inductance And the rotor permanent magnet flux The d-axis and q-axis voltage disturbances caused by isoelectric parameter perturbations are expressed as:

[0063] (8)

[0064] In the case of electrical parameter perturbation, the electromagnetic torque equation of PMSM is expressed as

[0065] T e = 3 2 n p [ ψ r + ( L d − L q ) i d ] i q + Δ T e = 3 2 n p ψ e x t i q + Δ T e (9)

[0066] In the formula, is the electromagnetic torque; represents the number of pole pairs; Represents effective magnetic linkage; Δ T e = 3 2 n p [ ψ r + ( Δ L d − Δ L q ) i d ] i q The electromagnetic torque perturbation represents the parameter perturbation.

[0067] In the case of mechanical parameter perturbations, the mechanical motion equation of the PMSM can be expressed as:

[0068] (10)

[0069] In the formula, represents the electrical angular velocity, represents the mechanical angular velocity, ; represents the load torque; represents the torque damping coefficient, represents the damping torque, represents the moment of inertia; represents the mechanical parameter perturbation;

[0070] Substituting equation (9) into equation (10), the speed state equation of the permanent magnet synchronous motor considering the unknown total disturbances such as electrical parameter perturbation, mechanical parameter perturbation, external disturbance and unmodeled dynamics is obtained as follows:

[0071] (11)

[0072] In the formula, is the unknown disturbance of load torque; are the “unmodeled dynamics” in the system, including sensor detection errors, friction damping, cogging torque, etc.

[0073] The speed controller of the traditional permanent magnet synchronous motor control system is a PI controller and a traditional model-free sliding mode control (MFSMC) based on an extended sliding mode observer (ESMO), which cannot adapt well to the application occasions where the permanent magnet synchronous motor control system faces complex working conditions, especially when there are unknown disturbances such as electrical parameter perturbations, mechanical parameter perturbations, external disturbances and unmodeled dynamics. This embodiment proposes a new model-free super-twisting fast integral terminal sliding mode control (MFSITSMC) method for permanent magnet synchronous motors based on an improved extended nonsingular terminal sliding mode disturbance observer (IENTSMDO).

[0074] S1 Establishment of a hyperlocal model of the speed loop of a permanent magnet synchronous motor control system

[0075] The new hyperlocal model of the single-input single-output system can be expressed as:

[0076] (12)

[0077] In the formula, is the state variable; Represents the input of the system; Represents the output of the system; , is a non-physical constant; nonlinear Lipschitz bounded function is the total disturbance of the system, which is the set of the known system parameter perturbation part and the unknown disturbance.

[0078] According to the mechanical motion equation of the permanent magnet synchronous motor considering the unknown total disturbance (11) and the new super-local model formula (12), the speed loop super-local model of the permanent magnet synchronous motor is established as follows:

[0079] (13)

[0080] In the formula, is the q-axis current coefficient of the PMSM stator to be designed; is the speed gain to be designed, and F is the unknown total disturbance.

[0081] S2 Establishment of Model-Free Super Helical Fast Integral Terminal Sliding Mode Controller (MFSITSMC)

[0082] The electrical angular velocity tracking error is defined as

[0083] (14)

[0084] In the formula, For a given electrical angular velocity, is the electrical angular velocity. Select the state error To control the goal.

[0085] Tracking error in electrical angular velocity is the state variable, the state equation is

[0086] (15)

[0087] In order to ensure the finite time convergence and non-singularity of the system, an improved fast integral terminal sliding surface is designed.

[0088] (16)

[0089] In the formula, , and All are normal numbers to be designed; , is a positive odd number and satisfies ; is the integral symbol, is the integral variable; the terminal term introduced It enables the system to reach the sliding surface within a limited time.

[0090] In order to weaken the chattering and accelerate the system state to reach the sliding surface, an improved super-helical control law is introduced:

[0091] (17)

[0092] In the formula, , , and is the coefficient to be designed; ;

[0093] ;

[0094] in, , , , , , , and is the coefficient to be designed;

[0095] For the state equation (15), the improved fast integral terminal sliding mode surface (16) is selected, the improved superhelical control law (17) is selected, and the following model-free fast integral terminal sliding mode speed loop controller is designed:

[0096] (18)

[0097] Then the system can reach the sliding surface in a finite time.

[0098] According to the Lyapunov function , and its derivative can be obtained

[0099] (19)

[0100] According to the Lyapunov stability theorem, the system state will converge in a finite time. Therefore, the speed error of the permanent magnet synchronous motor controlled by the model-free fast integral terminal sliding mode speed loop controller designed in this embodiment will be Converges in finite time.

[0101] S3 Design of a fast terminal sliding mode observer for estimating unknown total disturbances in hyperlocal models

[0102] The electrical angular velocity and the unknown part F as the state variable, the quadrature axis current is the control input, electrical angular velocity As the system output, the speed loop extended state equation can be obtained as follows:

[0103] (20)

[0104] In the formula, is the unknown total disturbance The rate of change of

[0105] The improved and extended non-singular terminal sliding mode disturbance observer designed by equation (20) is:

[0106] (twenty one)

[0107] in, is the electrical angular velocity Observed value of is the control input of the observer; for The rate of change of is the observer gain;

[0108] From equations (20) and (21), we can get the dynamic error equation of the observer:

[0109] (twenty two)

[0110] In the formula, represents the speed observation error of the observer; Represents the observation error of the unknown total disturbance.

[0111] Select speed observation error As state variables, and using fast non-singular terminal sliding surface

[0112] (twenty three)

[0113] In the formula, is the speed observation error of the observer; is a positive constant to be designed, .

[0114] In order to speed up the convergence of the sliding mode approach motion and improve the system tracking performance, the following double power approach law is selected (twenty four)

[0115] in, and is the normal number to be designed, , ; is a symbolic function;

[0116] For the dynamic error equation expressed by equation (22), combined with the sliding surface in equation (23) and the reaching law in equation (24), the control input of the improved extended non-singular terminal sliding mode disturbance observer is designed as:

[0117] (25)

[0118] in, is the integral symbol, is the integral variable; then the system will converge to the following region in a finite time:

[0119] (26)

[0120] Select function , taking its derivative and combining it with the double power approaching law (24), we can get

[0121] (27)

[0122] Substituting the control law (25) into the state error equation and taking the derivative, we can obtain

[0123] (28)

[0124] From equations (25), (27), and (28), we can get

[0125] (29)

[0126] Formula (29) can be divided into the following two cases:

[0127] (30)

[0128] (31)

[0129] Assumptions when When

[0130] (32)

[0131] At this time area It can guarantee finite-time convergence.

[0132] when When

[0133] (33)

[0134] At this time area It can guarantee finite-time convergence.

[0135] Therefore, according to the Lyapunov stability theorem, the system will converge to the region in finite time , after which it will remain stable on the sliding surface.

[0136] From equation (22), the above observer error equation converges to zero, so we get ,Right now ,in, is the integral symbol, is the integration variable.

[0137] Next, the permanent magnet synchronous motor vector control system was modeled and simulated. The system model is as follows: Figure 1The speed loop controller of the permanent magnet synchronous motor control system adopts the model-free super-helical fast integral terminal sliding mode controller (MFSITSMC) based on the improved extended non-singular terminal sliding mode disturbance observer (IENTSMDO) for control, and the current loop adopts PI control. The proposed MFSITSMC control strategy based on IENTSMDO is further compared with the speed loop and current loop using traditional PI regulators, and the speed loop using the model-free sliding mode control (MFSMC) algorithm based on the extended sliding mode observer (ESMO) and the current loop using PI control. The simulation parameters of the permanent magnet synchronous motor are shown in Table 1:

[0138] Table 1 Permanent magnet synchronous motor parameters Motor parameters unit Numeric <![CDATA[Rated voltage / u N > V 1080 <![CDATA[Rated current / I N > A 200 <![CDATA[Rated torque / T N > N·m 1008 <![CDATA[Rated speed / n N > r / min 1800 <![CDATA[DC side voltage / U dc > V 1500 <![CDATA[Stator resistance / R s > Ω 0.02 <![CDATA[Number of pole pairs / n p > pairs 4 <![CDATA[ d Shaft inductance / L d ]]> H 0.015 <![CDATA[ q Shaft inductance / L q ]]> H 0.036 <![CDATA[Permanent magnet flux linkage / ψ r > Wb 0.892 Moment of inertia / <![CDATA[kg·m 2 ]]> 100

[0139] Under parameter perturbation: the initial speed of the permanent magnet synchronous motor is set to 100 rad / s, which changes to 200 rad / s after 0.5 s; the initial torque is 300 , and increases to 1000 after 1 s. ; The initial value of the motor resistance is 0.02 , 1.5s to 0.04 ; The initial value of the d-axis inductance is 1.5 mH, which increases to 4 mH after 2.0 s; the initial value of the q-axis inductance is 3.6 mH, which increases to 5.57 mH after 2s; the remaining parameters are nominal values. The simulation waveform is as follows Figures 2 to 11 shown.

[0140] When the motor parameters are perturbed, Figure 2 and Figure 3 From the speed change curve, it can be seen that compared with PI control and the MFSMC method based on ESMO, the MFSMC method based on IENTSMDO has the fastest speed response, the smallest overshoot, and can recover to the given speed in a very short time.

[0141] Depend on Figure 4-Figure 9 From the dq axis current response and torque response, it can be seen that compared with PI control and the MFSMC method based on ESMO, the dq axis current and torque pulsation of the MFSMC method based on IENTSMDO is smaller, the waveform is smoother, and the motor transient steady-state performance is better.

[0142] Depend on Figure 10-11 From the observation curves of the medium-speed tracking error and the unknown part, it can be seen that compared with ESMO, the waveform of the unknown part observed by IENTSMDO is smoother, the system response is faster, and there is almost no jitter phenomenon.

[0143] In summary, compared with PI control and MFSMC method based on ESMO, the MFSITSMC method based on IENTSMDO can effectively suppress the pulsation of torque and current and speed up the system response speed, effectively improve the steady-state response of the system, and improve the overall control performance of the motor. It has a certain fault tolerance function when the motor parameters are perturbed, which further enhances the robustness of the PMSM system to disturbances.

[0144] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or change made by a person skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A novel model-free super-helical fast integral terminal sliding mode control method for permanent magnet synchronous motor based on an improved extended non-singular terminal sliding mode disturbance observer. It is characterized in that The following steps are involved: Step 1: Establish a hyperlocal model of the speed loop in the permanent magnet synchronous motor control system, which is specifically expressed as ,in represents the electrical angular velocity, represents the q-axis current, represents the q-axis current coefficient, represents the gain of the speed loop, represents the unknown total disturbance; Step 2: Design a novel model-free fast integral terminal sliding mode controller for the speed loop: Step 2.1, select state error For the control target, is a given electrical angular velocity; Step 2.2, select the state error e 1 As a variable, an improved fast integral terminal sliding surface is designed (1), where , and All are normal numbers to be designed; , is a positive odd number and satisfies ; is a symbolic function; is a terminal item; is the integral symbol, is the integration variable; Step 2.3, introduce a new supercoil control law: (2) where , , and is the coefficient to be designed; ； ； in, , , , , , , and is the coefficient to be designed; Step 2.4, the new model-free fast integral terminal sliding mode controller can be designed as: ,in, is the given value of q-axis current; for An estimated value of For a given electrical angular velocity The derivative of for The second derivative of is a symbolic function; is the integral symbol, is the integration variable; Step 3: Design an improved extended non-singular terminal sliding mode disturbance observer to observe the unknown total disturbance : Step 3.1, the electrical angular velocity and the unknown total disturbance F as state variables, the quadrature axis current is the control input, electrical angular velocity As the system output, the speed loop extended state equation can be obtained as follows: , where is the unknown total disturbance The rate of change of The improved extended non-singular terminal sliding mode disturbance observer is specifically expressed as: ,in, is the electrical angular velocity Observed value of is the control input of the observer; for The rate of change of is the observer gain; From this, the dynamic error equation of the observer can be obtained as: , where represents the speed observation error of the observer; represents the observation error of the unknown total disturbance; Step 3.2, select a fast non-singular terminal sliding surface: (3), where is the speed observation error of the observer; is a positive constant to be designed, ; Step 3.3, select the double power reaching law: (4), where and is the normal number to be designed, , ; is a symbolic function; Step 3.4, the control input of the improved extended non-singular terminal sliding mode disturbance observer is designed as: in, is the integral symbol, is the integration variable.

2. According to claim 1, a novel model-free super-helical fast integral terminal sliding mode control method for permanent magnet synchronous motor based on an improved extended non-singular terminal sliding mode disturbance observer, It is characterized in that The novel model-free fast integral terminal sliding mode controller selects the fast integral terminal sliding mode surface improved by formula (1) and the super spiral control law improved by formula (2), and the state error will converge in finite time.

3. According to claim 1, a novel model-free super-helical fast integral terminal sliding mode control method for permanent magnet synchronous motor based on improved extended non-singular terminal sliding mode disturbance observer, It is characterized in that The improved extended non-singular terminal sliding mode disturbance observer selects the fast non-singular terminal sliding mode surface of formula (3) and the double power reaching law of formula (4). or When the state error of the improved extended non-singular terminal sliding mode disturbance observer is It will converge in a finite time, and the designed model-free superhelical fast terminal sliding mode controller is stable. At this time, .

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