Permanent magnet double-inertia system model-free fast integration terminal sliding mode control method and system

Abstract

The invention discloses a permanent magnet synchronous motor double-inertia system model-free fast integration terminal sliding mode control method and system based on an enhanced fast terminal sliding mode extended disturbance observer, and the adopted model-free fast integration terminal sliding mode control method based on the enhanced fast terminal sliding mode extended disturbance observer is used. Compared with traditional PI control and a model-free sliding-mode controller based on an extended sliding-mode observer, the method can effectively improve the response speed and control precision under parameter perturbation and external disturbance, reduces the dependence of the controller on a system model, is more suitable for nonlinear systems such as a permanent magnet synchronous motor double-inertia system, and has a wide application prospect. Meanwhile, the total disturbance of the system is estimated by adopting an enhanced fast terminal sliding mode extended disturbance observer, so that the robustness of the method is enhanced, and the anti-interference capability of the permanent magnet synchronous motor system is effectively improved; according to the method, current harmonics and torque ripples generated by parameter perturbation and external disturbance can be effectively suppressed, and the overall control performance of the double-inertia system is further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motors, and more specifically, particularly relates to a model-free fast integral terminal sliding mode control method and system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer. Background Art

[0002] In recent years, due to obvious advantages such as high efficiency, high power density, high power factor, and reliable operation, permanent magnet synchronous motors have been widely used in fields such as industrial robots, aircraft control, ship control, and transportation. In the mechanical cooperative control working scenario, transmission devices such as couplings and transmissions are commonly used to connect the motor and the load device to drive the motor system to move. The operating systems of the permanent magnet synchronous motor and the load can be equivalently regarded as a permanent magnet synchronous motor double-inertia system.

[0003] However, during the movement of the permanent magnet synchronous motor double-inertia system, obvious deformations will occur due to elastic factors, which will seriously damage the stability of the double-inertia system and reduce the control accuracy. At the same time, during the operation of the motor and the load, the overall control performance of the system is also affected by unknown disturbances such as friction, unmodeled parts, parameter mismatches, and external disturbances, affecting the overall smooth operation. To solve the adverse effects brought by the above factors, mechanical means can be adopted, such as changing the structural damping or the motor moment of inertia, etc., but this easily destroys the structural stability of the system and reduces the service life of the equipment. To avoid the disadvantages brought by the mechanical method, control methods such as the traditional PI strategy can be adopted for control, but the anti-disturbance and chattering suppression effects are not good and cannot adapt to the application scenarios of high-precision control. Therefore, in order to ensure the stable operation of the permanent magnet synchronous motor double-inertia system under parameter perturbation, new control methods need to be sought to achieve efficient and reliable operation of the permanent magnet synchronous motor double-inertia system under parameter perturbation. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a model-free fast integral terminal sliding mode control method and system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer in view of the deficiencies and defects of the prior art.

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

[0006] A model-free fast integral terminal sliding mode control method for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer, characterized by including the following steps:

[0007] Step 1: Establish a speed loop super-local model of the permanent magnet synchronous motor double-inertia system, ; where, is the electrical angular velocity of the motor; A and B are parameters to be designed and can be in , is selected within the range; is the moment of inertia of the motor, is the number of pole pairs of the motor, is the permanent magnet flux linkage; is the shaft torsional damping coefficient, is the friction coefficient of the motor; is the total system disturbance, D = 1 J M [ b s L ? k s ( e ? L ) ] +? m , represents the stiffness coefficient of the shaft, is the electrical angular velocity of the load, is the electrical angle of the motor, is the electrical angle of the load, is the total disturbance on the motor side, including internal parameter perturbations, external disturbances, and non - linear parts;

[0008] Step 2: Design an enhanced fast terminal sliding mode extended disturbance observer to estimate the total system disturbance :

[0009] Step 2.1, taking the electrical angular velocity of the motor and the total system disturbance as state variables, and defining the stator current of the shaft and the electrical angular velocity of the motor as the input and output of the system respectively, the extended state equation of the speed loop can be obtained as:

[0010] [ B e D B ] = [ B 1 0 0 ] [ e D ] + [ A 0 ] [ i q 0 ] + [ 0 ( t ) ]

[0011] where, is the change rate of the unknown total disturbance , which is a bounded function;

[0012] Step 2.2, construct an enhanced fast terminal sliding mode extended disturbance observer as:

[0013] [ ^ B e D ^ B ] = [ B 1 0 0 ] [ ^ e D ^ ] + [ A 0 ] u + [ 1 ] smo

[0014] In the formula, is the estimated value of the electrical angular velocity of the motor, is the estimated value of the total system disturbance , is the sliding mode control law of the observer, is the observer gain to be designed, and > 0;

[0015] Let , is the observed error of the electrical angular velocity of the motor; Let , be the observed error of the total disturbance; The error dynamic equation can be obtained as:

[0016] [ e B 1 e B D ] = [ B 1 0 0 ] [ e 1 e D ] + [ 1 ] smo ? [ 0 ( t ) ]

[0017] Step 2.3, taking the observed error of the electrical angular velocity of the motor as the state variable, select the fast terminal sliding mode surface as ; In the formula, , are constants greater than zero to be designed; , are positive odd numbers to be designed;

[0018] To reduce chattering during the sliding mode motion and improve the response speed, adopt a new type of double power reaching law:

[0019] ; Among them, and are normal constants to be designed, is a parameter to be designed, and ; is the sign function;

[0020] Step 2.4, the sliding mode control law of the observer is designed as

[0021] where is the equivalent control law, is the switching control law, which are respectively

[0022]

[0023] sw =? 0 t [ 1 e B 1 + 2 m n e 1 m / n ? 1 e B 1 + 1 ( | e 1 | | s 1 | ) 1 ? h 1 sgn( s 1 ) + 1 | s 1 | 1 + h 1 sgn( s 1 ) ] d

[0024] Among them, is the integral symbol, is the integral variable;

[0025] Step 3: Design a model-free fast integral terminal sliding mode controller for the speed loop:

[0026] Step 3.1, select the state error as the control objective, where is the given electrical angular velocity; Introduce the state variable , ;

[0027] Step 3.2, to weaken the system chattering, adopt a new type of fast integral terminal sliding mode surface:

[0028] s = x 1 + 0 t [ k 1 sgn ( x 1 ( ) ) + k 2 | x 1 ( ) | p / q sgn ( x 1 ( ) ) ] d ; where, , , , are positive numbers to be designed, , are positive odd numbers, and ; is the sign function; where, is the integral symbol, is the integration variable;

[0029] Step 3.3, in order to reduce chattering during the sliding mode motion and improve the response speed, a new double power reaching law is adopted:

[0030] ; where, and are positive constants to be designed, is a parameter to be designed, and ;

[0031] Step 3.4, the model-free fast integral terminal sliding mode controller can be designed as ;

[0032] where, is the equivalent control law: ;

[0033] is the switching control law: .

[0034] Furthermore, for the enhanced fast terminal sliding mode extended disturbance observer, the fast terminal sliding mode surface and the sliding mode control law are selected, and the state error e 1 will converge in finite time, and at this time there is .

[0035] Furthermore, for the model-free fast integral terminal sliding mode controller, the improved fast integral terminal sliding mode surface and the new double power reaching law are selected, and the system state of the model-free fast integral terminal sliding mode controller will converge in finite time, and the designed model-free fast integral terminal sliding mode controller is stable.

[0036] A model-free fast integral terminal sliding mode control system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer, characterized in that it includes an enhanced fast terminal sliding mode extended disturbance observer module (11) and a model-free fast integral terminal sliding mode control module (10), where:

[0037] The enhanced fast terminal sliding mode extended disturbance observer module (11) is respectively connected to the Park transformation module (7), the position and speed detection module (14), and the model-free fast integral terminal sliding mode control module (10). According to the axis current and the electrical angular velocity of the permanent magnet synchronous motor the total disturbance observation value of the system is observed , and the total disturbance observation value of the system is output to the model-free fast integral terminal sliding mode control module (10);

[0038] The model-free fast integral terminal sliding mode control module (10) is respectively connected to the position and speed detection module (14), the position and speed detection module (15), and the enhanced fast terminal sliding mode extended disturbance observer module (11), and outputs the axis current reference value ;

[0039] Furthermore, the vector control strategy is adopted. The axis reference current value is subtracted from the d-axis current output by the Park transformation module (7), and is transmitted to the axis current controller module (9) to obtain the axis reference voltage value ; The axis reference current value is respectively subtracted from the q-axis current output by the Park transformation (7), and is transmitted to the axis current controller module (8) to obtain the axis reference voltage value ; The , are transmitted to the Park inverse transformation module (4) to obtain the axis reference voltage value , axis reference current value ; The , are transmitted to the SVPWM control module (3) to obtain trigger pulses and transmitted to the inverter module (2), and three-phase voltages are output to drive the permanent magnet synchronous motor (1); the permanent magnet synchronous motor (1) drives the load (12) through the drive system module (13).

[0040] Furthermore, the current sensor (5) detects the permanent magnet synchronous motor current information and ; The current and The input is sent to the Clark transformation module (6) to obtain the current in the α-β coordinate system and ; the position and speed detection module (14) detects the electrical position angle of the permanent magnet synchronous motor ; the current , and the electrical position angle of the permanent magnet synchronous motor are transmitted to the Park transformation module (7) to obtain the current in the d-q axis coordinate system , .

[0041] The present invention adopts a model-free fast integral terminal sliding mode control (MFFITSMC) method based on an enhanced fast terminal sliding mode extended disturbance observer (EFTSMEDO). Compared with the traditional PI controller and the traditional model-free sliding mode control (MFSMC) based on an extended sliding mode observer (ESMO), it can reduce the dependence of the controller on the system model and is more suitable for non-linear and multi-coupled systems such as the permanent magnet synchronous motor double-inertia system; at the same time, an enhanced fast terminal sliding mode extended disturbance observer (EFTSMEDO) is used to observe the unknown total disturbance. Compared with the traditional extended sliding mode observer (ESMO), the unknown part of the observed system is more accurate, the steady-state error and chattering are smaller, and the robust performance of the method of the present invention is enhanced; the control method of the present invention has a fast response speed and high control accuracy, ensures the high-performance control of the permanent magnet synchronous motor double-inertia system, and has a certain fault-tolerant control function for parameter perturbation, enabling the permanent magnet synchronous motor double-inertia system to operate efficiently and reliably under parameter perturbation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a system structure block diagram of an embodiment of the present invention;

[0043] In the figure, 1 - Permanent Magnet Synchronous Motor (PMSM), 2 - Inverter, 3 - SVPWM, 4 - Park inverse transformation, 5 - Current transformer, 6 - Clark transformation, 7 - Park transformation, 8 - q-axis current loop controller, 9 - d-axis current loop controller, 10 - Model Fast Integral Terminal Sliding Mode Controller (MFFITSMC), 11 - Enhanced Fast Terminal Sliding Mode Extended Disturbance Observer (EFTSMEDO), 12 - Load, 13 - Transmission system, 14 - Position and speed detection, 15 - Position and speed detection.

[0044] Figure 2 This is an embodiment of the present invention: Comparison diagram of motor-side rotational speeds of PI control, IMFSMC, and MFFITSMC under parameter perturbation and external disturbance.

[0045] Figure 3 This is an embodiment of the present invention: Comparison diagram of load-side rotational speeds of PI control, IMFSMC, and MFFITSMC under parameter perturbation and external disturbance.

[0046] Figure 4 This is an embodiment of the present invention: Comparison diagram of q-axis current responses of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0047] Figure 5 This is an embodiment of the present invention: Comparison diagram of electromagnetic torques of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0048] Figure 6 This is an embodiment of the present invention: Comparison diagram of motor-side electrical angular velocities of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0049] Figure 7 This is an embodiment of the present invention: Comparison diagram of load-side electrical angular velocities of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0050] Figure 8 This is an embodiment of the present invention: Comparison diagram of motor-side angular accelerations of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0051] Figure 9 This is an embodiment of the present invention: Comparison diagram of load-side angular accelerations of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0052] Figure 10 This is an embodiment of the present invention: Comparison diagram of motor-side angular positions of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load variation.

[0053] Figure 11 For an embodiment of the present invention: Comparison diagram of the load - side angular position of PI control, IMFSMC, and MFFITSMC under parameter perturbation and load change.

[0054] Figure 12 For an embodiment of the present invention: Comparison diagram of the rotational speed tracking errors of ESMDO and EFTSMEDO under parameter perturbation and load change.

[0055] Figure 13 For an embodiment of the present invention: Comparison diagram of ESMDO and EFTSMEDO in unknown disturbance observation under parameter perturbation and load change. Specific implementation manner

[0056] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

[0057] Figure 1 It is a block diagram of an embodiment of a model - free fast - integral terminal sliding - mode control method and system for a permanent - magnet synchronous motor double - inertia system. Figure 1 Among them, the current sensor (5) transmits the detected stator current information of the permanent - magnet synchronous motor (PMSM) and transmits it to the Clarke transformation module (6) to obtain axis current 、 axis current ; The position and speed detection module (14) detects the electrical position angle and electrical angular velocity of the permanent - magnet synchronous motor; Then, the electrical position angle 、 - axis current 、 are transmitted to the Park transformation module (7) to output d - q axis currents 、 ; The position and speed detection module (15) detects the load - side position angle and angular velocity ; The electrical angular velocity and axis current of the permanent - magnet synchronous motor are transmitted to the enhanced fast - terminal sliding - mode extended disturbance observer module (11) to obtain the total system disturbance observation value ; The permanent - magnet synchronous motor position angle and electrical angular velocity , load - side position angle and angular velocity , total system disturbance observation value , load - side reference angular velocity , transmitted to the model-free fast integral terminal sliding mode control module (10) to obtain the q-axis current reference value ; Using vector control strategy, reference current value of the and the d-axis current output by the Park transformation (7) are subtracted and transmitted to the q-axis current controller module (9) to obtain the reference voltage value of the q-axis ; the reference current value of the d-axis are respectively subtracted from the q-axis current output by the Park transformation (7) and transmitted to the d-axis current controller module (8) to obtain the reference voltage value of the d-axis ; The d-q axis reference voltage values , are transmitted to the Park inverse transformation module (4) to obtain the reference voltage value of the α-axis , the reference current value of the β-axis ; , are transmitted to the SVPWM (i.e., Space Vector Pulse Width Modulation) module (3), and the obtained trigger pulses are transmitted to the inverter module (2) to output three-phase voltages to drive the permanent magnet synchronous motor (1); The permanent magnet synchronous motor (1) drives the load (12) through the drive system module (13).

[0058] Ignoring core saturation and losses, not considering permanent magnet hysteresis and eddy current losses, and not considering parameter perturbations, the stator voltage equation of the PMSM in the d-q axis coordinate system can be obtained as

[0059] (1)

[0060] where , are respectively the stator d-q axis voltage components; , are respectively the stator d-q axis current components; is the electrical angular velocity of the motor; is the nominal value of the stator phase winding resistance; , are respectively the nominal values of the stator phase winding d-q axis inductances; is the nominal value of the permanent magnet flux linkage.

[0061] The electromagnetic torque equation in the d-q coordinate system is:

[0062] T e = 1 . 5 p n ( d i q ? q i d ) = 1 . 5 p n [ r i q + ( L d ? L q ) i d i q ] (2)

[0063] Where T e is the electromagnetic torque; is the number of pole pairs.

[0064] Under normal circumstances, in the motor and load system, when the stiffness of the drive shaft is relatively large, the motor and the load can be regarded as a rigid whole. However, for the actual system, the stiffness of the drive shaft is limited, and there will be a certain degree of elastic deformation. Generally, it is equivalent to a two-inertia system with an elastic shaft connecting the motor and the load. The electromagnetic torque T e and the shaft torque T s act together on the motor side and jointly determine the mechanical speed ω m of the motor. On the other side, the load torque T L and the shaft torque T s act together on the load side and jointly determine the mechanical angular velocity ω l of the load. The motion equation of the two-inertia drive system can be expressed as:

[0065] { B m = [ T e ? T s ? b m m ] / J M B l = [ T s ? T L ? b L l ] / J L T s = b s ( m ? l ) + k s ( m ? l ) B m = m B l = l B m = a m B l = a l (3)

[0066] Wherein, is the mechanical angular velocity of the motor, is the mechanical angular velocity of the load; is the mechanical angle of the motor, is the mechanical angle of the load; is the moment of inertia of the motor, is the moment of inertia of the load; represents the stiffness coefficient of the shaft, is the torsional damping coefficient of the shaft; is the friction coefficient of the motor, is the friction coefficient of the load; and , , , , where, is the number of pole pairs; is the electrical angular velocity of the motor, is the electrical angular velocity of the load; is the electrical angle of the motor, is the electrical angle of the load.

[0067] Considering that the motor operation is affected by unknown disturbance changes, the speed loop model of the PMSM two-inertia system with unknown disturbances can be obtained as:

[0068] { d e dt = 1 J M [ 3 2 n p 2 r i q ? b s ( e ? L ) ? k s ( e ? L ) ] ? b m e J M +? m d L dt = 1 J L [ b s ( e ? L ) + k s ( e ? L ) ? T L ? b L L ] +? l (4)

[0069] In the formula, , ,

[0070] ? m = ? 3 J M n p 2 r 2 J M ( J M + J M ) i q + J M ( b s + b m ) J M ( J M + J M ) e + 1 ( J M + J M ) [ ? b s L ? k s ( e ? L ) ? b m e ] ,

[0071] ? l = 1 J L + J L [ ? n p T L + b s ( e ? L ) + k s ( e ? L ) ] ? ( b L + b L ) J L + J L L ;

[0072] Among them, 、 are respectively the non-linear friction resistance parts on the motor side and the load side, and are respectively the external disturbances on the motor and load sides, and are disturbed by the parameter mismatches on the motor side and the load side, and are respectively the parameter perturbation amounts of the moments of inertia on the motor and load sides, and are respectively the changes in the friction coefficients of the motor and the load, 、 are respectively the total disturbances of the systems on the motor and load sides, and are bounded and differentiable, including the disturbances caused by internal parameter perturbations, external disturbances and non-linear parts.

[0073] The speed controller of the traditional permanent magnet synchronous motor control system is a PI controller and an improved model-free sliding mode controller (Improved Model-free Sliding Mode Control, IMFSMC) based on an extended sliding mode observer (Extended Sliding Mode Observer, ESMO), and it cannot well adapt 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 model-free fast integral terminal sliding mode control (Model-free Fast Integral Terminal Sliding Mode Control, MFFITSMC) method based on an enhanced fast terminal sliding mode extended disturbance observer (Enhanced Fast Terminal Sliding Mode Extended Disturbance Observer, EFTSMEDO).

[0074] S1 Establish a speed loop super-local model of the permanent magnet synchronous motor double-inertia system

[0075] To solve the problem of unknown disturbances reducing the system control performance, a method of model-free fast integral terminal sliding mode control (MFFITSMC) is proposed to feedback control the motor speed, which not only reduces the dependence of the motor on the precise mathematical model, but also suppresses the system chattering and improves the dynamic response speed of the system.

[0076] According to the PMSM speed loop double-inertia system model in Equation (4), the speed loop super-local model of the PMSM double-inertia system is established as:

[0077] (5)

[0078] In the formula, A and B are parameters to be designed and can be selected within 、 ; is the moment of inertia of the motor, is the number of pole pairs of the motor, is the permanent magnet flux linkage; is the shaft torsional damping coefficient, is the friction coefficient of the motor; D is the non-linear unknown part on the motor side, D = 1 J M [ b s L ? k s ( e ? L ) ] +? m , represents the stiffness coefficient of the shaft, is the electrical angular velocity of the load, is the electrical angle of the motor, is the electrical angle of the load, is the total disturbance on the motor side.

[0079] S2 Design an enhanced fast terminal sliding mode extended disturbance observer to estimate the total system disturbance D

[0080] Taking the electrical angular velocity of the motor and the total system disturbance as state variables, and defining the shaft stator current and the electrical angular velocity of the motor as the input and output of the system respectively, the speed loop extended state equation can be obtained as:

[0081] [ B e D B ] = [ B 1 0 0 ] [ e D ] + [ A 0 ] [ i q 0 ] + [ 0 ( t ) ] (6)

[0082] where is the change rate of the unknown total disturbance and is a bounded function.

[0083] According to Equation (6), an enhanced fast terminal sliding mode extended disturbance observer is constructed as:

[0084] [ ^ B e D ^ B ] = [ B 1 0 0 ] [ ^ e D ^ ] + [ A 0 ] [ i q 0 ] + [ 1 ] smo (7)

[0085] In the formula, is the estimated value of the electrical angular velocity, is the estimated value of the total system disturbance, is the sliding mode control law, is the parameter to be designed.

[0086] Let , be the rotational speed observation error; Let , be the disturbance observation error. Subtracting equation (6) from equation (7) gives the dynamic equation of the observation error:

[0087] [ e B 1 e B D ] = [ B 1 0 0 ] [ e 1 e D ] + [ 1 ] smo ? [ 0 ( t ) ] (8)

[0088] Taking the rotational speed observation error as the state variable, the fast terminal sliding mode surface is selected as

[0089] (9)

[0090] In the formula, , are constants greater than zero to be designed; , are all positive odd numbers.

[0091] To reduce chattering during the sliding mode motion and improve the response speed, a new double power reaching law is adopted:

[0092] (10)

[0093] Among them, and are normal constants to be designed, is the parameter to be designed, and ; is the sign function;

[0094] The sliding mode control law of the observer is designed as

[0095] (11)

[0096] Among them, is the equivalent control law, is the switching control law, which are respectively

[0097] (12)

[0098] sw =? 0 t [ 1 e B 1 + 2 m n e 1 m / n ? 1 e B 1 + 1 ( | e 1 | | s 1 | ) 1 ? h 1 sgn( s 1 ) + 1 | s 1 | 1 + h 1 sgn( s 1 ) ] d (13)

[0099] Among them, is the integral symbol, is the integration variable;

[0100] Then we can obtain

[0101] (14)

[0102] where, , , assume is bounded.

[0103] Select the Lyapunov function

[0104] (15)

[0105] Taking the derivative of it, we can get

[0106] (16)

[0107] When , there is

[0108] (17)

[0109] When , there is

[0110] (18)

[0111] According to Lyapunov stability, the observed state error variable of the system can reach the sliding mode surface within a finite time and slide along the sliding mode surface, and the state error converges to 0 within a finite time.

[0112] S3 Design the model-free fast integral terminal sliding mode controller for the speed loop

[0113] Let the given electrical angular velocity of the motor be , assume is continuous and differentiable. Introduce the state variable

[0114] (19)

[0115] To weaken the system chattering, a new type of fast integral terminal sliding mode surface is proposed:

[0116] s = x 1 + 0 t [ k 1 sgn ( x 1 ( ) ) + k 2 | x 1 ( ) | p / q sgn ( x 1 ( ) ) ] d (20)

[0117] where, , , , are positive numbers to be designed, , is a positive odd number, and ; is the sign function; where is the integral symbol, is the integration variable;

[0118] In order to reduce chattering during the sliding mode motion and improve the response speed, a new double power reaching law is adopted:

[0119] (21)

[0120] where and are positive constants to be designed, is a parameter to be designed, and .

[0121] From the speed loop super-local model of the PMSM double-inertia system in Equation (5) and the new fast integral terminal sliding mode surface in Equation (20), the equivalent control law is obtained as follows:

[0122] (22)

[0123] To eliminate the adverse effects of uncertain factors on the system, a switching control law is designed as:

[0124] (23)

[0125] Therefore, the designed model-free fast integral terminal sliding mode controller is

[0126] (24)

[0127] Construct the following Lyapunov function:

[0128] (25)

[0129] Taking the derivative of it gives

[0130] V B = s s B = s ( x 2 + k 1 sgn ( x 1 ) + k 2 | x 1 | p / q sgn ( x 1 ) ) = s [ B e * ? 1 J M ( A iq * + B e + D ) + k 1 sgn ( x 1 ) + k 2 | x 1 | p / q sgn ( x 1 ) ] = s ( ? ( | x | | s | ) 1 ? h sgn( s ) ? | s | 1 + h sgn( s ) + D ^ ? D ) | s | ( ? ( | x | | s | ) 1 ? h ? | s | 1 + h + D ) (26)

[0131] where is the observed value of , is the disturbance observation error, which is a bounded quantity. When the disturbance observation is accurate, then . Since , so there is , , obviously .

[0132] According to the Lyapunov stability criterion theorem and LaSalle's invariance principle, it can be known that the state variables will converge to zero along the sliding mode surface in a finite time, and the designed controller reaches the stability condition, and the state variables asymptotically converge in a finite time. Therefore, the speed error of the model-free fast integral terminal sliding mode controller designed in this embodiment will converge in a finite time.

[0133] In addition, in order to suppress chattering, a saturation function is introduced to replace the sign function. The saturation function adopts switching control outside the boundary layer and continuous control inside the boundary layer.

[0134] (27)

[0135] where , is the boundary layer.

[0136] Next, the double-inertia system of the permanent magnet synchronous motor is modeled and simulated. The system model is as Figure 1 . The speed loop controller of the control system adopts model-free fast integral terminal sliding mode control (MFFITSMC) based on an enhanced fast terminal sliding mode extended disturbance observer (EFTSMEDO) for control, and the current loop adopts PI control. Further, the proposed MFFITSMC control strategy based on EFTSMEDO is used for the speed loop, and a comparative simulation analysis is carried out with the speed loop using a traditional PI regulator and the speed loop using a model-free sliding mode control (MFSMC) algorithm based on an extended sliding mode observer (ESMO). The parameters of the permanent magnet synchronous motor double-inertia system are shown in Table 1:

[0137] Table 1 Parameters of the permanent magnet synchronous motor double-inertia system

[0138] parameter numerical value <![CDATA[DC side voltage U dc > 350 V <![CDATA[Stator resistance R s > 1.9 Ω <![CDATA[Direct-axis inductance L d > 3.34 mH <![CDATA[Quadrature axis inductance L d > 3.34 mH <![CDATA[Permanent magnet flux linkage ψ r > 0.171 Wb <![CDATA[Coefficient of viscous friction b m > 0.000106 N.m.s / rad <![CDATA[Motor moment of inertia J M > <![CDATA[0.025 kg.m 2 > <![CDATA[Number of pole pairs n p > 4 <![CDATA[System torsional stiffness k s > 300 N.m / rad <![CDATA[Axial torsional damping b s > 0.8 N.m.s / rad <![CDATA[Load moment of inertia J L > <![CDATA[0.00025 kg.m 2 >

[0139] Under parameter perturbation: at 0 s, the motor moment of inertia increases by 1.4 times from 0.025 kg·m 2 , and the motor viscous friction coefficient increases by 3 times from 0.000106 N·m·s / rad; at 0.5 s, the motor speed steps from 1000 r / min to 1500 r / min; at 1 s, the load end increases from 10 N·m to 3.5 times; the remaining parameters are nominal values. The set running time is 1.5 s. The simulation waveforms are as Figures 2 to 13 shown.

[0140] When the motor undergoes parameter perturbation, from Figure 2 and Figure 3From the rotational speed change curve, it can be seen that compared with the PI control and the MFSMC method based on ESMO, the MFFITSMC control method based on EFTSMEDO has the fastest speed response, the smallest overshoot, and can recover to the given speed in an extremely short time.

[0141] From Figures 4 - 5 From the q-axis current response and torque response in [reference], it can be seen that compared with the PI control and the MFSMC method based on ESMO, the MFFITSMC control method based on EFTSMEDO has smaller q-axis current and torque ripples, a smoother waveform, and better transient and steady-state performance of the motor.

[0142] From Figures 6 - 11 is the electrical angular velocity of the motor , the angular velocity at the load end , the acceleration on the motor side , the acceleration on the load side , the mechanical angular position of the motor and the position angle at the load end In the comparison diagram of [parameters], it can be seen from the figure that the MFFITSMC control method based on EFTSMEDO has the fastest dynamic response performance and the smallest overshoot.

[0143] From Figures 12 - 13 From the observed curves of the rotational speed tracking error and the total system disturbance in [reference], it can be seen that compared with ESMO, the waveform of the unknown part observed by IENTSMDO is smoother, the system response is also faster, and almost no chattering phenomenon occurs.

[0144] In summary, compared with the PI control and the MFSMC method based on ESMO, the MFSITSMC method based on IENTSMDO can effectively suppress the ripples of torque and current, accelerate the system response speed, effectively improve the steady-state response of the system, improve the overall control performance of the motor, and also have a good control effect on the load side. It has a certain fault tolerance function during motor parameter perturbation, further enhancing the robustness of the PMSM dual-inertia system.

[0145] The above-described embodiments are only preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention.

Claims

1. A model-free fast integral terminal sliding mode control method for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer, Characterized in that, It includes the following steps: Step 1: Establish a super-local model of the speed loop of the permanent magnet synchronous motor double-inertia system, ; where, is the electrical angular velocity of the motor; A and B are parameters to be designed and can be selected within , range; is the moment of inertia of the motor, is the number of pole pairs of the motor, is the permanent magnet flux linkage; is the shaft torsional damping coefficient, is the friction coefficient of the motor; is the total disturbance of the system, , represents the stiffness coefficient of the shaft, is the electrical angular velocity of the load, is the electrical angle of the motor, is the electrical angle of the load, is the total disturbance on the motor side, including internal parameter perturbations, external disturbances and non-linear parts; Step 2: Design an enhanced fast terminal sliding mode extended disturbance observer to estimate the total system disturbance : Step 2.1, taking the electrical angular velocity of the motor and the total system disturbance as state variables, and defining the stator current of the axis and the electrical angular velocity of the motor as the input and output of the system respectively, the extended state equation of the speed loop can be obtained as follows: , where unknown total disturbance with a bounded function for the rate of change; Step 2.2, construct an enhanced fast terminal sliding mode extended disturbance observer as: , where is the estimated value of the electrical angular velocity of the motor, and is the estimated value of the total system disturbance . is the sliding mode control law of the observer, is the observer gain to be designed, and > 0; Let , be the observed error of the electrical angular velocity of the motor; Let , the observed error of the total disturbance; The error dynamic equation can be obtained as follows: ； Step 2.3, taking the electrical angular velocity observation error of the motor as the state variable, select the fast terminal sliding mode surface as ; where, , are constants greater than zero to be designed; , are positive odd numbers to be designed; In order to reduce chattering during the sliding mode motion and improve the response speed, a new double-power reaching law is adopted: ; among them, and are positive constants to be designed, is a parameter to be designed, and ; is the sign function; Step 2.4, the sliding mode control law of the observer is designed as , where is the equivalent control law, is the switching control law, and they are respectively , , where, is the integral symbol, is the integration variable; Step 3: Design a model-free fast integral terminal sliding mode controller for the speed loop: Step 3.1, select the state error as the control target, where is the given electrical angular velocity; introduce the state variables , ; Step 3.2, in order to weaken the system chattering, a new fast integral terminal sliding mode surface is adopted: ; among them, , , , are positive numbers to be designed, , are positive odd numbers, and ; is the sign function; among them, is the integral sign, is the integration variable; Step 3.3, in order to reduce chattering during the sliding mode motion and improve the response speed, a new double-power reaching law is adopted: ; Among them, and are positive constants to be designed, is a parameter to be designed, and ; Step 3.4, the model-free fast integral terminal sliding mode controller can be designed as ; Among them, is the equivalent control law: ; is the switching control law: .

2. A model-free fast integral terminal sliding mode control method for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer according to claim 1, Characterized in that, For the enhanced fast terminal sliding mode extended disturbance observer, a fast terminal sliding mode surface and a sliding mode control law are selected, and the state error e 1 will converge within a finite time, and at this time, there is .

3. A model-free fast integral terminal sliding mode control method for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer according to claim 1, Characterized in that, For the model-free fast integral terminal sliding mode controller, an improved fast integral terminal sliding mode surface and a new double-power reaching law are selected, and the system state will converge in a finite time, and the designed model-free fast integral terminal sliding mode controller is stable.

4. A model-free fast integral terminal sliding mode control system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer, Characterized in that, It includes an enhanced fast terminal sliding mode extended disturbance observer module (11) and a model-free fast integral terminal sliding mode control module (10), where: The enhanced fast terminal sliding mode extended disturbance observer module (11) is respectively connected to the Park transformation module (7), the position and speed detection module (14), and the model-free fast integral terminal sliding mode control module (10). According to the axis current , the electrical angular velocity of the permanent magnet synchronous motor , the total disturbance observation value of the system is observed , and the total disturbance observation value of the system is output to the model-free fast integral terminal sliding mode control module (10); the model-free fast integral terminal sliding mode control module (10) is respectively connected to the position and speed detection module (14), the position and speed detection module (15), and the enhanced fast terminal sliding mode extended disturbance observer module (11), and outputs the axis current reference value ; The model-free fast integral terminal sliding mode control system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer adopts any one of the model-free fast integral terminal sliding mode control methods for a permanent magnet synchronous motor double-inertia system described in claims 1-3.

5. A model-free fast integral terminal sliding mode control system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer according to claim 4, Characterized in that, It further includes: Adopt 's vector control strategy, Axis reference current value Subtract from the d-axis current output by the Park transformation module (7), and transmit it to Axis current controller module (9), and obtain Axis reference voltage value ; ; Axis reference current value Respectively subtract from the q-axis current output by the Park transformation (7), and transmit it to Axis current controller module (8), and obtain Axis reference voltage value ; Transmit ; Transmit , To the Park inverse transformation module (4), and obtain Axis reference voltage value , Axis reference current value ; Transmit , To the SVPWM module (3), obtain the trigger pulse and transmit it to the inverter module (2), output three-phase voltage to drive the permanent magnet synchronous motor (1); the permanent magnet synchronous motor (1) drives the load (12) through the drive system module (13).

6. A model-free fast integral terminal sliding mode control system for a permanent magnet synchronous motor double-inertia system based on an enhanced fast terminal sliding mode extended disturbance observer according to any one of claims 4-5, Characterized in that, The current sensor (5) detects the current information of the permanent magnet synchronous motor and ; the current and is input into the Clark transformation module (6) to obtain the current in the α-β coordinate system 、 ; the position and speed detection module (14) detects the electrical position angle of the permanent magnet synchronous motor ; the current 、 and the electrical position angle of the permanent magnet synchronous motor are transmitted to the Park transformation module (7) to obtain the current in the d-q axis coordinate system 、 .

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