Anti-backlash control method and device for single-inverter dual-motor parallel system based on extended state observer

Abstract

The invention discloses an anti-backlash control method and device for a single-inverter dual-motor parallel system based on an extended state observer. Comprising the following steps: acquiring mechanical angular speeds of two motors, direct-axis current feedback, quadrature-axis current feedback and position feedback of a first motor; obtaining an average angular velocity observation value and a disturbance observation value by using an extended state observer according to the mechanical angular velocities of the two motors and the quadrature-axis current feedback of the first motor; obtaining a rotating speed reference value according to the position feedback and a preset position reference; obtaining a quadrature-axis current reference according to the rotating speed reference value, the average angular speed observation value and the disturbance observation value; obtaining an alpha-axis voltage reference and a beta-axis voltage reference of the first motor according to the quadrature-axis current reference, the direct-axis current feedback and the quadrature-axis current feedback of the first motor and the position feedback; and controlling the three-phase input voltage of the two motors according to the alpha-axis voltage reference and the beta-axis voltage reference of the first motor. According to the method, stable speed control and accurate position tracking can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a backlash elimination control method and device for a single inverter dual motor parallel system based on an extended state observer. Background Art

[0002] With the increasing power demand from users in many fields such as electric vehicles, wind power generation, and mining, dual motor coordinated control has become a research hotspot in recent years. In order to reduce the system size and cost, the structure of one inverter driving two motors has become one of the focuses of experts. Due to the problem of easy loss of step of permanent magnet synchronous motors, the control structure is currently mostly applied to induction motors. It is challenging to overcome system disturbances and ensure the stable operation of single inverter dual parallel permanent magnet synchronous motors.

[0003] In the process of driving high inertia loads, gear transmission inevitably has tooth backlash, which will affect the dynamic response and static accuracy of the system, leading to increased position tracking error and system vibration, and even causing system instability in severe cases. Therefore, how to design a control method that can effectively compensate for tooth backlash disturbance and improve system stability and control accuracy has become an urgent problem to be solved. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a method and device for eliminating backlash in a single inverter dual motor parallel system based on an extended state observer. The present invention effectively compensates for the disturbance caused by backlash and improves the control performance of the system through the design and application of an extended state observer.

[0005] The technical solution adopted by the present invention is:

[0006] 1. A backlash control method for a single inverter dual motor parallel system based on an extended state observer The backlash control method comprises the following steps:

[0007] S1, obtaining the mechanical angular velocity of the two motors, the direct-axis current feedback and quadrature-axis current feedback of the first motor, and the position feedback.

[0008] The step S1 specifically includes: collecting the mechanical angular velocities of the two motors and the three-phase current of the first motor, performing coordinate transformation on the three-phase current to obtain direct-axis current feedback and quadrature-axis current feedback of the first motor, inputting the mechanical angular velocities of the two motors into the backlash model, and obtaining position feedback.

[0009] S2. Use an extended state observer to obtain an average angular velocity observation value and a disturbance observation value according to the mechanical angular velocities of the two motors and the quadrature-axis current feedback of the first motor.

[0010] Specifically, in step S2, the extended state observer is set in the following manner: the average value of the mechanical angular velocity of the two motors and the system disturbance of the single inverter dual motor parallel system are respectively set as the first state variable and the second state variable of the extended state observer, and the first state variable and the second state variable constitute the state vector of the extended state observer; the observation value of the first state variable and the observation value of the second state variable are the average angular velocity observation value and the disturbance observation value respectively; the quadrature axis current feedback of the first motor is set as the input variable of the extended state observer; the output control variable of the extended state observer is set according to the first state variable. The gain coefficient of the extended state observer is set according to the bandwidth of the extended state observer.

[0011] Furthermore, the extended state observer is set according to the following equation:

[0012]

[0013] Where z represents the observed value of the state vector of the extended state observer, which consists of the observed value of the first state variable and the observed value of the second state variable; represents the derivative of the observation value z of the state vector of the extended state observer; u represents the input variable of the extended state observer; y represents the output control variable of the extended state observer, represents the observed value of the output control variable y of the extended state observer; A, B, C represent the system matrix, input matrix and output matrix respectively; L represents the parameter matrix;

[0014] Among them, the system matrix, input matrix, and output matrix are set according to the following formulas:

[0015]

[0016] In the formula, A, B, and C represent the system matrix, input matrix, and output matrix respectively, and b represents the influence coefficient of the input variable of the extended state observer on the first state variable;

[0017] Among them, the parameter matrix is ​​set according to the following formula:

[0018] L=[l1 l2] T

[0019] Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively.

[0020] The first gain coefficient and the second gain coefficient of the extended state observer are set according to the following formulas:

[0021] l1=2ω o

[0022] l2=ωo 2

[0023] Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer, respectively, and ω o represents the bandwidth of the extended state observer.

[0024] Specifically, in the extended state observer, the average angular velocity observation value and the disturbance observation value are obtained according to the mechanical angular velocities of the two motors and the quadrature-axis current feedback of the first motor by the following formula:

[0025]

[0026] In the formula, x1 and x2 represent the first state variable and the second state variable respectively; x1' and x2' represent the observed value of the first state variable and the observed value of the second state variable respectively; l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively; u represents the input variable of the extended state observer; b represents the influence coefficient of the input variable of the extended state observer on the first state variable.

[0027] S3. Obtain a speed reference value according to the position feedback and a preset position reference.

[0028] The step S3 specifically includes: presetting a position reference, performing a difference between the position reference and the position feedback, and inputting the obtained difference into a proportional controller (P controller) to obtain a speed reference value.

[0029] S4. Obtain a quadrature-axis current reference according to the speed reference value, the average angular velocity observation value and the disturbance observation value.

[0030] The step S4 is specifically as follows: subtracting the speed reference value from the average angular velocity observation value, inputting the obtained difference into a first proportional integral controller (PI controller) to obtain a speed compensation value, subtracting the speed compensation value from the disturbance observation value, inputting the obtained difference into a second proportional integral controller to obtain a quadrature-axis current reference.

[0031] S5, according to the quadrature-axis current reference, the direct-axis current feedback and quadrature-axis current feedback of the first motor, and the position feedback, obtain the α-axis voltage reference and β-axis voltage reference of the first motor; according to the α-axis voltage reference and β-axis voltage reference of the first motor, obtain the compensation control signal, and use a single inverter to control the three-phase input voltage of the two motors according to the compensation control signal. The step S5 is specifically as follows:

[0032] S5.1, set the direct-axis current reference to 0, make a difference between the quadrature-axis current reference and the quadrature-axis current feedback, make a difference between the direct-axis current reference and the direct-axis current feedback, input the obtained two differences as the quadrature-axis current error and the direct-axis current error into two proportional-integral controllers, the two proportional-integral controllers output quadrature-axis voltage compensation and direct-axis voltage compensation respectively, perform coordinate transformation on the quadrature-axis voltage compensation and the direct-axis voltage compensation in combination with the position feedback, and obtain the α-axis voltage reference and the β-axis voltage reference;

[0033] S5.2. Input the α-axis voltage reference and β-axis voltage reference of the first motor into the space vector pulse width modulator to obtain the three-phase duty cycle as a compensation control signal; input the three-phase duty cycle into the inverter, and the inverter controls the three-phase input voltage of the two motors according to the three-phase duty cycle signal.

[0034] The single inverter dual motor parallel system of the present invention adopts master-slave control, that is, the first motor is the master motor and the other motor is the slave motor.

[0035] 2. A backlash control device for a single inverter dual motor parallel system based on an extended state observer The backlash control device comprises:

[0036] An acquisition and calculation module is used to obtain the mechanical angular velocities of the two motors, the direct-axis current feedback and the quadrature-axis current feedback of the first motor, and the position feedback;

[0037] An extended state observer is used to obtain an average angular velocity observation value and a disturbance observation value according to the mechanical angular velocities of the two motors and the quadrature axis current feedback of the first motor;

[0038] A position loop control module, used for obtaining a speed reference value according to position feedback and a preset position reference;

[0039] A speed loop control module is used to obtain a quadrature axis current reference according to a speed reference value, an average angular velocity observation value and a disturbance observation value;

[0040] A current loop control module, used to obtain an α-axis voltage reference and a β-axis voltage reference of the first motor in a two-phase stationary coordinate system according to a quadrature-axis current reference, a direct-axis current feedback and a quadrature-axis current feedback and a position feedback of the first motor;

[0041] A space vector pulse width modulator, used for obtaining a three-phase duty ratio according to an α-axis voltage reference and a β-axis voltage reference of the first motor and using the duty ratio as a compensation control signal;

[0042] The inverter is used for controlling the three-phase input voltages of the two motors according to the compensation control signal.

[0043] The beneficial effects of the present invention are:

[0044] 1. The present invention proposes a control structure that regards the speed loops of two motors as a whole, and combines an extended state observer to observe and compensate for the disturbance caused by the tooth gap, thereby achieving stable speed control and precise position tracking.

[0045] 2. The present invention can estimate the nonlinear disturbance caused by the backlash through real-time observation of the motor shaft torque through the extended state observer, and generate corresponding compensation control signals, thereby reducing the impact of the backlash on the system. The compensation process can significantly improve the positioning accuracy of the system and effectively suppress the vibration and noise caused by the backlash.

[0046] 3. The control method of the present invention not only effectively solves the influence of tooth clearance on system performance and improves the control accuracy and stability of the system, but also can realize the coordinated control of dual motors under various complex working conditions, laying a technical foundation for further promoting the application of parallel motor systems in the industrial field. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of the topological structure of the single inverter dual motor parallel system in the present invention;

[0048] Figure 2 It is a structural schematic diagram of the tooth gap model in the present invention;

[0049] Figure 3 is a control block diagram of an extended state observer in an embodiment of the present invention;

[0050] Figure 4 is a control block diagram of the control method in the present invention;

[0051] Figure 5 4 is a comparison diagram of compensation effects in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] A first aspect of the present invention provides a backlash elimination control method for a single inverter dual motor parallel system based on an extended state observer, which specifically comprises the following steps:

[0054] S1. Obtain the mechanical angular velocity of the two motors in the single inverter dual-motor parallel system, the direct-axis current feedback and quadrature-axis current feedback of the first motor, and the position feedback. Specifically: Use sensors to collect the mechanical angular velocity of the two motors and the three-phase current of the first motor in real time. Perform coordinate transformation on the three-phase current (i.e., perform Clarke transformation and Park transformation in sequence) to obtain the direct-axis current feedback and quadrature-axis current feedback of the first motor in the orthogonal dq coordinate system. Input the mechanical angular velocity of the two motors into the pre-built backlash model to obtain the position feedback in the form of electrical angle.

[0055] In a specific implementation, the backlash model may adopt a dead zone model or other models.

[0056] S2. Use an extended state observer to obtain the average angular velocity observation value of the two motors and the disturbance observation value of the single inverter dual-motor parallel system according to the mechanical angular velocity of the two motors and the quadrature-axis current feedback of the first motor.

[0057] The extended state observer in this step adopts a linear first-order extended state observer and is set in the following manner: the average value of the mechanical angular velocity of the two motors (ω1+ω2) / 2 and the system disturbance f of the single inverter dual-motor parallel system are set as the first state variable x1 and the second state variable x2 of the extended state observer respectively. The first state variable and the second state variable constitute the state vector x of the extended state observer, x=[x1 x2] T The observed value x1' of the first state variable and the observed value x2' of the second state variable are the average angular velocity observed value (ω1+ω2)' / 2 and the disturbance observed value f' respectively; the quadrature axis current feedback i of the first motor is q1 Set as the input variable u of the extended state observer; according to the first state variable x1, combined with the preset output matrix C, set the output control variable y of the extended state observer; according to the bandwidth ω of the extended state observer o Set the gain coefficients l1 and l2 of the extended state observer.

[0058] In this step, the extended state observer is used to calculate the mechanical angular velocities ω1 and ω2 of the two motors and the quadrature axis current feedback i of the first motor using the following formula: q1 Get the average angular velocity observation and disturbance observation:

[0059]

[0060] Wherein, x1 and x2 represent the first state variable and the second state variable, i.e., the average value of the mechanical angular velocity of the two motors (ω1+ω2) / 2 and the system disturbance f of the single inverter dual motor parallel system, respectively; x1' and x2' represent the observed value of the first state variable and the observed value of the second state variable, i.e., the average angular velocity observation value [(ω1+ω2)' / 2 and the disturbance observation value f', respectively; l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer, respectively; u represents the input variable of the extended state observer, i.e., the quadrature-axis current feedback i of the first motor. q1 ; b represents the influence coefficient of the input variable of the extended state observer on the first state variable.

[0061] Among them, the influence coefficient b of the input variable of the extended state observer on the first state variable is set according to the following formula:

[0062] b=K t / J m

[0063] In the formula, K t Represents the torque coefficient, J m Indicates the moment of inertia of each motor.

[0064] Furthermore, the equation of the extended state observer is specifically:

[0065]

[0066] Where z represents the observed value of the state vector of the extended state observer, which is composed of the observed value x1' of the first state variable and the observed value x2' of the second state variable, z = [x1'x2'] T ; ω represents the derivative of the observed value z of the state vector of the extended state observer; u represents the input variable of the extended state observer, that is, the quadrature axis current feedback i of the first motor q1 ; y represents the output control variable of the extended state observer, represents the observed value of the output control variable of the extended state observer; A, B, C represent the system matrix, input matrix and output matrix respectively; L represents the parameter matrix;

[0067] Among them, the system matrix, input matrix, and output matrix are set as:

[0068] B=[b 0] T , C = [1 0]

[0069] In the formula, A, B, and C represent the system matrix, input matrix, and output matrix respectively, and b represents the influence coefficient of the input variable of the extended state observer on the first state variable;

[0070] Among them, the parameter matrix is ​​set as:

[0071] L=[l1 l2] T

[0072] Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively.

[0073] The first gain coefficient and the second gain coefficient of the extended state observer are set according to the following formulas:

[0074] l1=2ω o

[0075] l2=ω o 2

[0076] Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer, respectively, and ω o represents the bandwidth of the extended state observer.

[0077] In the specific implementation, the equation of the extended state observer is constructed according to the following system state equation:

[0078]

[0079] Where x represents the state vector of the extended state observer, represents the derivative of the state vector x, A, B, and C represent the system matrix, input matrix, and output matrix, respectively, y represents the output control variable of the extended state observer, and u represents the input variable of the extended state observer, that is, the quadrature-axis current feedback i of the first motor. q1 .

[0080] S3, obtaining a speed reference value according to the position feedback obtained in step S1 and the preset position reference. Step S3 specifically includes: presetting a position reference in the form of electrical angle, subtracting the position reference in the form of electrical angle and the position feedback in the form of electrical angle, and inputting the obtained difference as a position error into a proportional controller (P controller) to obtain a speed reference value.

[0081] S4, obtain the quadrature axis current reference according to the speed reference value obtained in step S3, the average angular velocity observation value obtained in step S2, and the disturbance observation value. Step S4 is specifically as follows: subtract the speed reference value from the average angular velocity observation value, input the obtained difference as a speed error into a first proportional integral controller (PI controller), obtain a speed compensation value, subtract the speed compensation value from the disturbance observation value, input the obtained difference as a speed backlash elimination error into a second proportional integral controller (PI controller), and obtain the quadrature axis current reference.

[0082] S5, according to the quadrature-axis current reference obtained in step S4, the direct-axis current feedback and quadrature-axis current feedback and position feedback of the first motor obtained in step S1, obtain the α-axis voltage reference and β-axis voltage reference of the first motor in the two-phase stationary coordinate system; obtain the compensation control signal according to the α-axis voltage reference and β-axis voltage reference of the first motor, and use a single inverter to control the three-phase input voltage of the two motors according to the compensation control signal. Step S5 is specifically:

[0083] S5.1, set the direct-axis current reference to 0, make a difference between the quadrature-axis current reference and the quadrature-axis current feedback, make a difference between the direct-axis current reference and the direct-axis current feedback, input the obtained two differences into two proportional-integral controllers as the quadrature-axis current error and the direct-axis current error respectively, the two proportional-integral controllers output the quadrature-axis voltage compensation and the direct-axis voltage compensation respectively, and perform coordinate transformation on the quadrature-axis voltage compensation and the direct-axis voltage compensation in combination with the position feedback in the form of electrical angle to obtain the α-axis voltage reference and the β-axis voltage reference;

[0084] S5.2. Input the α-axis voltage reference and β-axis voltage reference of the first motor into the space vector pulse width modulator (SVPWM), and the space vector pulse width modulator outputs a three-phase duty cycle as a compensation control signal; input the three-phase duty cycle into the inverter, and the inverter controls the three-phase input voltage of the two motors according to the three-phase duty cycle signal.

[0085] A second aspect of the present invention provides a backlash elimination control device for a single inverter dual motor parallel system based on an extended state observer, the backlash elimination control device comprising:

[0086] An acquisition and calculation module is used to obtain the mechanical angular velocities of the two motors, the direct-axis current feedback and the quadrature-axis current feedback of the first motor, and the position feedback;

[0087] The extended state observer is used to calculate the mechanical angular velocity of the two motors and the quadrature axis current feedback of the first motor i q Get the average angular velocity observation value and the disturbance observation value;

[0088] A position loop control module, used for obtaining a speed reference value according to position feedback and a preset position reference;

[0089] A speed loop control module is used to obtain a quadrature axis current reference according to a speed reference value, an average angular velocity observation value and a disturbance observation value;

[0090] The current loop control module is used to obtain an α-axis voltage reference and a β-axis voltage reference of the first motor in a two-phase stationary coordinate system according to a quadrature-axis current reference, a direct-axis current feedback and a quadrature-axis current feedback of the first motor, and a position feedback; specifically, the current loop control module adopts a master-slave control, with the first motor as the master motor, and the direct-axis current and the quadrature-axis current of the master motor as negative feedback for current closed-loop control, while the second motor is used as a slave motor and adopts open-loop control;

[0091] A space vector pulse width modulator, used for obtaining a three-phase duty ratio according to an α-axis voltage reference and a β-axis voltage reference of the first motor and using the duty ratio as a compensation control signal;

[0092] The inverter is used to simultaneously control the three-phase input voltage of the first motor and the second motor according to the compensation control signal.

[0093] The third aspect of the present invention provides a single inverter dual motor parallel system using the above-mentioned backlash elimination control device. The single inverter dual motor parallel system includes a backlash elimination control device, a DC power supply, a first motor, a second motor and a load motor; the DC input end of the inverter in the backlash elimination control device is electrically connected to the output end of the DC power supply to receive the electric energy provided by the DC power supply, the AC output end of the inverter is connected in parallel with the first motor and the second motor, and the output shafts of the first motor and the second motor are transmission-connected to the output shaft of the load motor through gears.

[0094] The specific embodiments of the present invention are as follows:

[0095] Example

[0096] This embodiment is based on the topological structure diagram as shown in Figure 1 The single inverter dual motor parallel system shown is used to further illustrate the design and principle of the anti-backlash control method of the present invention.

[0097] Figure 1 In the inverter of the gap elimination control device, a three-phase inverter is used. The DC input terminal of the three-phase inverter is electrically connected to the DC power supply. The DC bus voltage of the DC power supply corresponds to Figure 1 U dc The three-phase inverter has a first phase bridge arm, a second phase bridge arm and a third phase bridge arm connected in parallel, and the upper and lower bridge arms of the first phase bridge arm correspond to Figure 1 S a , S a ', the upper and lower bridge arms of the second phase bridge arm correspond to Figure 1 S b , S b ', the upper and lower bridge arms of the third phase bridge arm correspond to Figure 1 S c , S c '.

[0098] Both motors are permanent magnet synchronous motors. The first motor and the second motor correspond to Figure 1 PMSM1 and PMSM2 in the three-phase inverter. The two motors are controlled by master-slave, that is, the first motor PMSM1 is used as the master motor and the second motor PMSM2 is used as the slave motor. The upper bridge arm and the lower bridge arm of the first phase bridge arm, the second phase bridge arm and the third phase bridge arm in the three-phase inverter are respectively connected to the two ends of the first phase, the second phase and the third phase of each motor. The output shafts of the first motor and the second motor are connected to the output shaft of the same load motor through gears.

[0099] 1. Construct a mathematical model of a single inverter dual motor parallel system considering backlash

[0100] In the dual-motor parallel system, the two motors are connected to the load through gears with a specific reduction ratio. Therefore, when the load is transmitted through the gears, it is distributed to the two motors. Therefore, the dynamic equation of the system is constructed as:

[0101]

[0102] In the formula, J m Represents the moment of inertia of each motor, J L Indicates the moment of inertia of the load motor, θ1, θ2, θ L Respectively represent the position angles of the first motor, the second motor, and the load motor, Respectively represent the first-order derivative and second-order derivative of the corresponding position angle, B L Indicates the dynamic friction factor of the load motor; T e1 , T e2 Respectively represent the torque of the first motor and the second motor; T sh1 , T sh2 Respectively represent the shaft torque of the first motor and the second motor; N s Indicates the reduction ratio.

[0103] In this embodiment, a dead zone model is used to construct a nonlinear backlash model to describe the actual gear rotation process. The schematic diagram of the backlash model is shown in Figure 2, where K s represents the stiffness coefficient of the tooth gap, and 2a represents the tooth gap width.

[0104] The specific backlash model is:

[0105]

[0106] In the formula, K s represents the stiffness coefficient of the tooth gap; C represents the damping coefficient of the tooth gap; 2a represents the tooth gap width, that is, the distance between the two gear meshing surfaces; θ d Represents the angular displacement difference between the motor and the load motor; Represents θ d The first derivative of T sh Represents the shaft torque of each motor.

[0107] Among them, the angular displacement difference θ between the motor and the load motor d Specifically:

[0108] θ d =θ i / N s -θ L , i=1,2

[0109] In the formula, θ i represents the position angle of the first motor (i=1) or the second motor (i=2), θL Indicates the position angle of the load motor, N s Indicates the reduction ratio.

[0110] Combining the system's dynamic equation and backlash model, it can be seen that in the system's dynamic equation, the shaft torque T of the first motor and the second motor is sh1 , T sh2 The values ​​of are related to the tooth gap width, but in actual operation, the value of the tooth gap width is unknown, which leads to nonlinearity of the shaft torque. Therefore, the existence of tooth gap will seriously affect the control performance of the system.

[0111] 2. Constructing the extended state observer equation

[0112] The dynamic equation of the system is modified into the following form:

[0113]

[0114] Where ω represents the mechanical angular velocity of the main motor, Represents the derivative of the mechanical angular velocity of the main motor, T e Represents the electromagnetic torque of the main motor, J m Indicates the moment of inertia of the main motor, B m Indicates the dynamic friction factor of the main motor, T sh Indicates the shaft torque of the main motor, N s Indicates the reduction ratio.

[0115] The sum of the above disturbances is regarded as the total disturbance of the system and set to f, thereby modifying the system dynamics equation to:

[0116]

[0117] In the formula, Represents the derivative of the mechanical angular velocity of the main motor, T e Represents the electromagnetic torque of the main motor, J m represents the moment of inertia of the main motor, and f represents the system disturbance of the single-inverter dual-motor parallel system.

[0118] Combined with the electromagnetic torque formula of the surface-mounted permanent magnet synchronous motor, the system dynamics equation is further modified as follows:

[0119]

[0120] In the formula, represents the derivative of the mechanical angular velocity of the main motor, f represents the system disturbance of the single inverter dual motor parallel system, i q represents the quadrature axis current feedback, b represents the influence coefficient of the input variable of the extended state observer on the first state variable, J m Indicates the rotational inertia of the main motor.

[0121] The system state equation is constructed based on the system dynamics equation. The system state equation is specifically:

[0122]

[0123] Where x represents the state vector of the extended state observer, represents the derivative of the state vector x, A, B, and C represent the system matrix, input matrix, and output matrix respectively, y represents the output control variable of the extended state observer, and u represents the input variable of the extended state observer, namely, the quadrature-axis current feedback of the first motor.

[0124] Among them, the state vector x consists of two state variables, that is, x = [x1 x2] T , the first state variable x1 and the second state variable x2 are respectively the average value of the mechanical angular velocity of the two motors (ω1+ω2) / 2 and the system disturbance f of the single inverter dual-motor parallel system, where ω1 and ω2 represent the mechanical angular velocity of the first motor and the second motor respectively.

[0125] Among them, the system matrix, input matrix, and output matrix are set as:

[0126] B=[b 0] T , C = [1 0]

[0127] Where A, B, and C represent the system matrix, input matrix, and output matrix, respectively, and b represents the influence coefficient of the input variable of the extended state observer on the first state variable.

[0128] Then, the equation of the extended state observer is constructed based on the system state equation. The equation of the extended state observer is specifically:

[0129]

[0130] Where z represents the observation vector of the state vector of the extended state observer, that is, z = [x1'x2'] T , which is composed of the observation value x1' of the first state variable and the observation value x2' of the second state variable. The observation value of the first state variable and the observation value of the second state variable are the average angular velocity observation value x1' and the disturbance observation value x2' respectively; represents the derivative of the observation value z of the state vector of the extended state observer; u represents the input variable of the extended state observer, that is, the quadrature-axis current feedback of the first motor; y represents the output control variable of the extended state observer, represents the observed value of the output control variable of the extended state observer; A, B, C represent the system matrix, input matrix and output matrix respectively; L represents the parameter matrix;

[0131] Among them, the parameter matrix is ​​set as:

[0132] L=[l1 l2] T

[0133] Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively.

[0134] Further simplifying the equation of the extended state observer, we can obtain:

[0135]

[0136] In the formula, x1 and x2 represent the first state variable and the second state variable respectively; x1' and x2' represent the observed value of the first state variable and the observed value of the second state variable respectively; l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively; u represents the input variable of the extended state observer, that is, the quadrature-axis current feedback of the first motor; b represents the influence coefficient of the input variable of the extended state observer on the first state variable.

[0137] According to the simplified extended state observer above, we can get Figure 3 The extended state observer control block diagram shown in Figure 3 In the figure, 1 / s indicates an integral operation, + indicates a positive input, and - indicates a negative input.

[0138] The linear control rate of the extended state observer is set according to the following formula:

[0139]

[0140] Where, e0 represents the first linear control rate parameter, K p represents the gain coefficient of the speed loop; ω* represents the speed reference value, and u represents the second linear control rate parameter.

[0141] 3. Calculate the parameter matrix L of the extended state observer

[0142] According to the above system state equation and the equation of the extended state observer, the actual value of the first state variable and the observed value of the first state variable are subtracted to obtain the error matrix:

[0143]

[0144] Where, e represents the difference between the actual value of the first state variable and the observed value of the first state variable, e represents the derivative of the difference e, A and C represent the system matrix and the output matrix respectively; L represents the parameter matrix.

[0145] The closer the observed value e of the first state variable is to its actual value, the better the observer can suppress disturbances. In order to make the actual first state variable infinitely close to the observed value of the first state variable, it is necessary to satisfy that all the eigenvalues ​​of the matrix (A-LC) are located in the left half plane of the s plane, so that the matrix is ​​stable. Therefore, the expression is:

[0146] |(A-LC)-λI|=(λ+ω o ) 2

[0147] Where λ represents the eigenvalue of the error matrix; I represents the unit matrix; ω o represents the bandwidth of the extended state observer.

[0148] From the above formula, we can get l1=2ω o , l2=ω o 2 .

[0149] 4. Stability of the Extended State Observer

[0150] According to the above system state equation and the equation of the extended state observer, the observer transfer function is expressed as:

[0151]

[0152] In the formula, represents the observed value of the first state variable, that is, the average angular velocity observed value, represents the first state variable, that is, the average value of the mechanical angular velocities of the two motors, ω1 and ω2 represent the mechanical angular velocities of the first motor and the second motor respectively, f′ represents the observed value of the second state variable, that is, the disturbance observation value, u represents the input variable of the extended state observer, that is, the quadrature-axis current feedback of the first motor, b represents the influence coefficient of the input variable of the extended state observer on the first state variable; l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively, and s represents the complex variable in the complex plane.

[0153] Therefore, the observed value of the first state variable and the first state variable satisfy the following relationship:

[0154]

[0155] In the formula, represents the observed value of the first state variable, that is, the average angular velocity observed value, represents the first state variable, that is, the average value of the mechanical angular velocities of the two motors, ω1 and ω2 represent the mechanical angular velocities of the first motor and the second motor respectively, l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively, s represents the complex variable in the complex plane, and ω0 represents the bandwidth of the extended state observer.

[0156] When the system is running, the input variable of the extended state observer, that is, the quadrature-axis current feedback of the first motor, can be regarded as a step signal. Therefore, the observed value of the first state variable can be further expressed as:

[0157]

[0158] In the formula, represents the frequency domain form of the observed value of the first state variable, ω1 and ω2 represent the mechanical angular velocities of the first motor and the second motor respectively, s represents the complex variable in the complex plane, and ω0 represents the bandwidth of the extended state observer.

[0159] Performing an inverse Laplace transform on the above equation yields the time domain response, which is the time domain form of the observed value of the first state variable:

[0160]

[0161] In the formula, represents the time domain form of the observed value of the first state variable, ε(t) represents, and ω0 represents the bandwidth of the extended state observer.

[0162] Derivative the above formula, we get the extreme point and the time corresponding to the extreme point is t = 2 / ω ο This time is approximately regarded as the peak time of the output, and the time corresponding to the extreme point is t = 2 / ω ο Substituting into the above formula, we can obtain the peak value of the observed value of the first state variable in the time domain:

[0163]

[0164] It can be seen that the bandwidth ω of the extended state observer is ο The value of does not affect the overshoot of the output variable of the extended state observer.

[0165] 5. The above-mentioned extended state observer is introduced into the three-closed-loop control structure to obtain the control flow chart of the control method of the present invention, as shown in detail. Figure 4 shown.

[0166] The method of this embodiment is used to perform backlash elimination control on a single inverter dual motor parallel system, and the specific process is as follows:

[0167] S1. Use sensors to collect the mechanical angular velocities ω1 and ω2 of the two motors and the three-phase current of the first motor in real time, perform coordinate transformation on the three-phase current (i.e., perform Clarke transformation and Park transformation in sequence), and obtain the direct axis current feedback i of the first motor in the orthogonal dq coordinate system. d1 and quadrature axis current feedback i q1 .

[0168] Then the mechanical angular velocities ω1 and ω2 of the two motors are input into the backlash model, and the mechanical angular velocity of each motor is combined with the speed feedback ω L The shaft torque of the side output is obtained. The shaft torque of the side output of the two motors corresponds to Figure 4 T sh1 , T sh2 , according to the shaft torque T output by the first motor side sh1 , the shaft torque T output by the second motor side sh2 and output torque T L Get position feedback θ L , the position feedback θ L Convert it into electrical angle form to obtain position feedback θ1 in electrical angle form.

[0169] ω L Indicates the system feedback speed, T L Represents the output torque, T sh1 , T sh2 are the shaft torques output by the two motor sides respectively;

[0170] S2, using the extended state observer LESO according to the mechanical angular velocities ω1 and ω2 of the two motors, and the quadrature axis current feedback i of the first motor q1 The average angular velocity observation value (ω1+ω2)′ / 2 and the disturbance observation value f′ are obtained.

[0171] S3. In the position loop control module, the position reference θ in the form of a preset electrical angle is * The difference is input into the proportional controller (P controller) to obtain the speed reference value ω * .

[0172] S4, in the speed loop control module, the speed reference value ω output by the position loop * The speed compensation value is obtained by subtracting the speed compensation value from the disturbance observation value f′ output by the extended state observer, and the obtained difference is input into the second proportional integral controller to obtain the quadrature axis current reference i q1 * .

[0173] S5. In the current loop control module, the direct axis current reference i d1 * Set to 0, the quadrature axis current reference i q1 * and quadrature axis current feedback i q1 Make a difference and refer to the direct axis current i d1 * and direct axis current feedback i d1 The quadrature axis current error and the direct axis current error are input into two proportional integral controllers to obtain quadrature axis voltage compensation and direct axis voltage compensation. Then, the quadrature axis voltage compensation and the direct axis voltage compensation are transformed into coordinates in combination with the position feedback θ1 in the form of electrical angle to obtain the α-axis voltage reference U α1 and β-axis voltage reference U β1 ;

[0174] S5.2, the α-axis voltage reference U of the first motor α1 and β-axis voltage reference U β1 Input the space vector pulse width modulator (SVPWM) to obtain the three-phase duty cycle as the compensation control signal; input the three-phase duty cycle into the inverter, and the inverter controls the three-phase input voltage U of the two motors according to the three-phase duty cycle signal a , U b , U c .

[0175] Next, in order to verify the effectiveness of the method proposed in the present invention, an experimental comparison is made between the traditional vector control method and the method of the present invention for a single inverter dual motor parallel system considering backlash under the same working conditions. The specific working conditions are: the position reference is set to a constant value of 6πrad, the slave motor is open-loop controlled, and a load torque of 2Nm is applied.

[0176] The experimental results of the conventional vector control method and the method of the present invention are shown as follows: Figure 5 From top to bottom, the figure shows the load position reference and actual position, position error, master motor three-phase current, slave motor three-phase current, master and slave motors, and actual position comparison of the load.

[0177] like Figure 5 As shown in (a), when the traditional vector control method is used, the tracking time of the load position is 3.2s, the steady-state tracking error of the load position is 0.83°, the three-phase current amplitude of the main motor is 2.27A, and the three-phase current amplitude of the slave motor is 2.59A.

[0178] like Figure 5As shown in (b), when the method of the present invention is adopted, the tracking time of the load position is 2.5s, the steady-state tracking error of the load position is 0.5°, the three-phase current amplitude of the main motor is 1.93A, and the three-phase current amplitude of the slave motor is 1.89A.

[0179] It can be seen that the method proposed in the present invention can effectively reduce the tracking time of the position loop, reduce the steady-state tracking error of the load position, and thus improve the control performance of the system.

[0180] The above two preferred embodiments of the present invention are specifically described, but they are only used as illustrative examples, and the contents of the present invention are not limited to the above examples. For those skilled in the art, any equivalent modifications and substitutions made to the above examples are also covered by the present invention. Therefore, any equivalent modifications and substitutions made without departing from the spirit and scope of the present invention are within the protection scope of the present invention.

Claims

1. A backlash control method for a single inverter dual motor parallel system based on an extended state observer, characterized in that: The following steps are involved: S1, obtaining the mechanical angular velocity of the two motors, the direct-axis current feedback and the quadrature-axis current feedback of the first motor, and the position feedback; S2, using an extended state observer to obtain an average angular velocity observation value and a disturbance observation value according to the mechanical angular velocities of the two motors and the quadrature-axis current feedback of the first motor; S3, obtaining a speed reference value according to the position feedback and a preset position reference; S4, obtaining a quadrature-axis current reference according to a speed reference value, an average angular velocity observation value, and a disturbance observation value; S5. Obtain an α-axis voltage reference and a β-axis voltage reference of the first motor according to a quadrature-axis current reference, direct-axis current feedback and quadrature-axis current feedback of the first motor, and position feedback; obtain a compensation control signal according to the α-axis voltage reference and the β-axis voltage reference of the first motor, and use a single inverter to control the three-phase input voltages of the two motors according to the compensation control signal.

2. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 1, characterized in that: In the step S2, the extended state observer is set in the following manner: the average value of the mechanical angular velocities of the two motors and the system disturbance of the single-inverter dual-motor parallel system are respectively set as the first state variable and the second state variable of the extended state observer, and the first state variable and the second state variable constitute the state vector of the extended state observer; the observation value of the first state variable and the observation value of the second state variable are the average angular velocity observation value and the disturbance observation value, respectively; the quadrature-axis current feedback of the first motor is set as the input variable of the extended state observer; and the output control variable of the extended state observer is set according to the first state variable.

3. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 2, characterized in that: The extended state observer is set as follows: Where z represents the observed value of the state vector of the extended state observer, which consists of the observed value of the first state variable and the observed value of the second state variable; represents the derivative of the observation value z of the state vector of the extended state observer; u represents the input variable of the extended state observer; y represents the output control variable of the extended state observer, represents the observed value of the output control variable y of the extended state observer; A, B, C represent the system matrix, input matrix and output matrix respectively; L represents the parameter matrix; The parameter matrix is ​​set as follows: L＝[l1 l2] T Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively.

4. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 3 is characterized in that: The first gain coefficient and the second gain coefficient of the extended state observer are set according to the following formulas: l1=2ω o l2=ω o 2 Where l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer, respectively, and ω o represents the bandwidth of the extended state observer.

5. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 3, characterized in that: In the extended state observer, the average angular velocity observation value and the disturbance observation value are obtained according to the mechanical angular velocity of the two motors and the quadrature axis current feedback of the first motor by the following formula: In the formula, x1 and x2 represent the first state variable and the second state variable respectively; x1' and x2' represent the observed value of the first state variable and the observed value of the second state variable respectively; l1 and l2 represent the first gain coefficient and the second gain coefficient of the extended state observer respectively; u represents the input variable of the extended state observer; b represents the influence coefficient of the input variable of the extended state observer on the first state variable.

6. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 1, characterized in that: The step S1 specifically includes: collecting the mechanical angular velocities of the two motors and the three-phase current of the first motor, performing coordinate transformation on the three-phase current to obtain direct-axis current feedback and quadrature-axis current feedback of the first motor, inputting the mechanical angular velocities of the two motors into the backlash model, and obtaining position feedback.

7. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 1, characterized in that: The step S3 specifically includes: presetting a position reference, performing a difference between the position reference and the position feedback, and inputting the obtained difference into a proportional controller to obtain a speed reference value.

8. The backlash elimination control method for a single inverter dual motor parallel system based on an extended state observer according to claim 1, characterized in that: The step S4 specifically comprises: subtracting the speed reference value from the average angular velocity observation value, inputting the obtained difference into the first proportional-integral controller to obtain the speed compensation value, subtracting the speed compensation value from the disturbance observation value, inputting the obtained difference into the second proportional-integral controller to obtain the quadrature-axis current reference.

9. The anti-backlash control method of a single inverter dual motor parallel system based on an extended state observer according to claim 1, characterized in that: The step S5 is specifically as follows: S5.1, set the direct-axis current reference to 0, make a difference between the quadrature-axis current reference and the quadrature-axis current feedback, make a difference between the direct-axis current reference and the direct-axis current feedback, input the obtained two differences into two proportional-integral controllers respectively, the two proportional-integral controllers output quadrature-axis voltage compensation and direct-axis voltage compensation respectively, perform coordinate transformation on the quadrature-axis voltage compensation and the direct-axis voltage compensation in combination with the position feedback, and obtain the α-axis voltage reference and the β-axis voltage reference; S5.

2. Input the α-axis voltage reference and β-axis voltage reference of the first motor into the space vector pulse width modulator to obtain the three-phase duty cycle as a compensation control signal; input the three-phase duty cycle into the inverter, and the inverter controls the three-phase input voltage of the two motors according to the three-phase duty cycle signal.

10. An anti-backlash control device for use in the anti-backlash control method according to any one of claims 1 to 9, characterized in that: The anti-backlash control device comprises: An acquisition and calculation module is used to obtain the mechanical angular velocities of the two motors, the direct-axis current feedback and the quadrature-axis current feedback of the first motor, and the position feedback; An extended state observer is used to obtain an average angular velocity observation value and a disturbance observation value according to the mechanical angular velocities of the two motors and the quadrature axis current feedback of the first motor; A position loop control module, used for obtaining a speed reference value according to position feedback and a preset position reference; A speed loop control module is used to obtain a quadrature axis current reference according to a speed reference value, an average angular velocity observation value and a disturbance observation value; A current loop control module, used for obtaining an α-axis voltage reference and a β-axis voltage reference of the first motor according to a quadrature-axis current reference, a direct-axis current feedback and a quadrature-axis current feedback of the first motor, and a position feedback; A space vector pulse width modulator, used for obtaining a three-phase duty ratio according to an α-axis voltage reference and a β-axis voltage reference of the first motor and using the duty ratio as a compensation control signal; The inverter is used for controlling the three-phase input voltages of the two motors according to the compensation control signal.

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