Feedforward control method based on nonlinear inertia system of servo press

Abstract

Provided is a feedforward control method based on a nonlinear inertia system of a servo press. In the method, torque calculation of the servo press is achieved by using a kinetic model of the system, the nonlinear inertia of the servo press is calculated online, the calculation process of a torque observer is accurately adapted, a torque feedforward control method is used, a control system exhibits high robustness in the presence of a motor load disturbance, particularly when the servo press meets a heavy load, and the real-time curve error of the servo press is greatly reduced, improving position control precision, and reducing position control error.

Description

A feedforward control method based on nonlinear inertia system of servo press TECHNICAL FIELD

[0001] The application belongs to the field of power electronics and motor control, and particularly relates to a feedforward control method based on nonlinear inertia system of servo press. BACKGROUND

[0002] There are many control methods for servo press, such as the patent with the name of "servo press full-closed loop nonlinear predictive control method and system" and the authorization announcement number CN110077028B, which discloses one of the control methods, but most of the control methods do not consider that a large error will be generated between the target given position and the feedback position when the servo press slider is in the downward forming process and encounters a large load, thereby affecting the final workpiece forming quality of the servo press. SUMMARY

[0003] The application provides a feedforward control method based on nonlinear inertia system of servo press to solve the problems in the prior art.

[0004] The application provides a feedforward control method based on nonlinear inertia system of servo press, which comprises the following steps:

[0005] Step 1: the dynamics equation of the servo press is established by using the Lagrange equation, and the established dynamics equation is converted into the following equation:

[0006] wherein M (θ c ) is an inertia coefficient; N (θ c ) is a centrifugal coefficient of the press; is the feedback angular acceleration of the crank; is the feedback angular velocity of the crank;

[0007] Then, the formula (12) is introduced into the state feedback e c to improve the tracking control effect, and the crank torque τ c is calculated as follows:

[0008] wherein e c = θ c * - θ c ; θ c * is the given angle of the crank; is the given angular velocity of the crank; is the given angular acceleration of the crank; k d represents a speed error coefficient, which is a constant; k pThis represents the position error coefficient, which is a constant.

[0009] Step 2: Utilize the rotational inertia J of the servo press viewed from the motor side and the rotational inertia J of the servo press viewed from the crank side. p Based on the mathematical relationship between them, the formula for calculating the moment of inertia J of the servo press as viewed from the motor side is:

[0010] Where n is the reduction ratio of the reducer;

[0011] Step 3: Based on the stator voltage equation of the permanent magnet synchronous motor, and using Euler's forward approximation method, the feedback value i of the direct-axis current at time k+1 can be obtained. d The feedback values ​​i of the quadrature-axis current at time (k+1) and time (k+1) q (k+1):

[0012] Among them, i q (k) is the feedback value of the quadrature-axis current at time k; i q (k+1) is the feedback value of the quadrature-axis current at time k+1; i d (k) is the feedback value of the direct-axis current at time k; i d (k+1) is the feedback value of the direct-axis current at time k+1; T s For control cycle; V d (k) is the direct-axis voltage at time k; V q (k) is the quadrature-axis voltage at time k; R is the stator resistance; ω e It is the electric angular velocity; L d It is a direct-axis inductor; L q It is a quadrature-axis inductance; ψ f It is a permanent magnet flux chain;

[0013] Step 4: Using the mechanical model equations of the permanent magnet synchronous motor and the moment of inertia J of the servo press as viewed from the motor side calculated in Step 2, combined with a first-order low-pass filter algorithm, the estimated value of the motor load torque is obtained. Calculate using the estimated value of motor load torque. Replace the actual motor load torque value T L The estimated value of motor load torque With crank torque τ c The corresponding values ​​on the motor side are added together to obtain the given torque T of the motor. e * Then, based on the given value i of the motor's quadrature-axis current... q * With the given torque T of the motor e * The linear relationship is used to obtain the given value i of the quadrature-axis current of the motor at time k+1.q (k+1) is calculated as follows:

[0014] where p is the number of motor pole pairs;

[0015] Step five: in the control strategy i d * (k+1) = 0, the value function is set as: g = |i q (k+1) - i q (k+1) | + |i d (k+1) - i d (k+1) | (57),

[0016] where i d * (k+1) represents the given value of the direct-axis current at the k+1 time;

[0017] The eight voltage vectors of the three-phase two-level PWM inverter are respectively brought into the value function, and the voltage vector with the minimum g is defined as the optimal vector, and the optimal vector acts on the power module to output the PWM wave to control the motor operation.

[0018] In the present application, the servo press selects the transmission structure of the crank connecting rod, the motor adopts the surface-mounted permanent magnet synchronous motor, and the driver adopts the three-phase two-level inverter.

[0019] The present application has the advantages that the torque calculation control method of the servo press is realized by using the dynamic model of the system, the nonlinear inertia of the servo press is calculated online, the calculation process of the torque observer is accurately adapted, the torque feedforward control method is adopted, the control system exhibits strong robustness in the case of motor load disturbance, especially when the servo press encounters large load, the real-time curve error of the servo press is greatly reduced, the position control precision is improved, and the position control error is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0020] Fig. 1 is a control algorithm block diagram of the present application;

[0021] Fig. 2 is a curve graph of the change of the rotational inertia J of the servo press from the motor side with the crank feedback angle θ c ;

[0022] Fig. 3 is a derivative graph of the rotational inertia J of the servo press from the motor side with the crank feedback angle θ c . DETAILED DESCRIPTION

[0023] The following gives a specific embodiment of the present application, and it should be noted that the present application is not limited to the following specific embodiments, and any equivalent transformation made on the basis of the technical solutions of the present application falls within the protection scope of the present application.

[0024] The technical solutions of the present application are as follows:

[0025] (I) calculating the crank torque τ c

[0026] This step is realized by using the torque control method based on Lagrange equation in the servo drive to calculate the crank torque τ c The inputs of this method include the crank given angle, crank given angular velocity and crank given angular acceleration, and the crank feedback angle and crank feedback angular velocity, and the output is the calculated crank torque.

[0027] The dynamics equation of the servo press is established by using Lagrange equation:

[0028] Wherein, Γ is the Lagrange function, Γ = E k -E p (2); E k is the kinetic energy of the crank connecting rod mechanical structure; E p is the gravitational potential energy of the press transmission system, which can be regarded as E p = 0.

[0029] The kinetic energy E k of the crank connecting rod mechanical structure in the above formula (2) is calculated as follows: E k = E c + E l + E s + E m (3),

[0030] Wherein, E c represents the kinetic energy of the crank; E l represents the kinetic energy of the connecting rod; E s represents the kinetic energy of the slider; E m represents the kinetic energy of the motor and the speed reducer; the expressions of each kinetic energy are as follows:

[0031] Wherein,

[0032] Wherein, J p is the rotational inertia of the servo press from the crank side; J c is the rotational inertia of the crank rotating around the center rotation point of the crank structure; J l is the rotational inertia of the connecting rod rotating around the mass center of the slider; J g is the rotational inertia of the motor and the speed reducer; v l is the speed of the connecting rod midpoint; v s is the speed of the slider; ωm is the angular velocity of the motor; m s is the mass of the slider; m l is the mass of the connecting rod; θ c is the crank feedback angle; is the crank feedback angular velocity; φ is the angle of the connecting rod rotating clockwise from the top dead center to the current position; r is the crank radius; l is the connecting rod length; n is the reduction ratio of the reduction machine.

[0033] Substituting the above formulas (2)-(11) into formula (1), the dynamics equation of the servo press can be changed into the following equation:

[0034] where M(θ c ) is the inertia coefficient, i.e., the moment of inertia J p of the servo press from the crank side; N(θ c ) is the centrifugal coefficient of the press; is the crank feedback angular acceleration; the expressions of M(θ c ) and N(θ c ) are as follows: M(θ c ) = A1 + A2 + A3 + A4 + A5 + A6 + J g *n 2 (13), N(θ c ) = B1 + B2 + B3 + B4 + B5 + B6 + B7 + B8 + B9 (14),

[0035] where A1 = J c (15), A2 = J l r 2 cos 2 (θ c ) / B0 2 (16), A3 = 2ar 2 sin 2 (θ c ) (17), A4 = 2br 3 sin 2 (θ c )cos(θ c ) / B0 (18), A5 = 2cr 4 sin 2 (θ c )cos 2 (θ c ) / B0 2 (19), A6 = m l r 2 / 4 (20), B1 = J l r 4sin(θ c )cos 3 (θ c ) / B0 4 (21), B2 = J l r 2 sin(θ c )cos(θ c ) / B0 2 (22), B3 = 2ar 2 sin(θ c )cos(θ c ) (23), B4 = blr 3 sin(θ c )cos 2 (θ c )*cos(F) / B0 2 (24), B5 = -br 3 sin(θ c ) / B0 (25), B6 = 2br 5 sin 3 (θ c )cos 2 (θ c ) / B0 3 (26), B7 = 2clr 4 sin(θ c )cos 2 (θ c )cos(F) / B0 3 (27), B8 = -2cr 4 sin 3 (θ c )cos(θ c ) / B0 2 (28), B9 = 2cr 6 sin 3 (θ c )cos 3 (θ c ) / B0 4 (29), F = asin(rsin(θ c ) / l) (30),

[0036] The formula (12) is introduced into the state feedback e c to improve the tracking control effect, and finally the crank torque τ c calculation formula is obtained:

[0037] wherein, is the given angle of the crank; giving the angular velocity of the crank; giving the angular acceleration of the crank;k d denotes the speed error coefficient, which is a constant;k p denotes the position error coefficient, which is a constant.

[0038] (II) Calculate the moment of inertia J of the servo press from the motor side

[0039] This step uses the mathematical relationship between the moments of inertia to obtain the moment of inertia J of the servo press from the motor side, which is used to calculate the motor load torque estimate.

[0040] Moment of inertia J of the servo press from the crank side p , which is the inertia coefficient M(θ c ) described above, i.e. p J c =M(θ q ), then the calculation formula of the moment of inertia J of the servo press from the motor side is:

[0041] where n is the reduction ratio of the reduction machine.

[0042] (III) Calculate i d (k+1) and i d (k+1)

[0043] This step uses the stator voltage equation of the permanent magnet synchronous motor to calculate the k+1 time of the cross-axis and direct-axis current in the dq coordinate system, and then used in the value function calculation in the model predictive current control.

[0044] The servo press of this embodiment selects the crank connecting rod transmission structure, the motor uses the surface-mounted permanent magnet synchronous motor, and the driver uses the three-phase two-level inverter.

[0045] The mathematical model of the surface-mounted permanent magnet synchronous motor in the rotating coordinate system, the stator voltage equation is:

[0046] where: ψ d =L d i f +ψ q =L q i q ,

[0047] The above, V d is the direct-axis voltage; V q is the cross-axis voltage; i d is the direct-axis current; i q is the cross-axis current; R is the stator resistance; ωe is the electrical angular velocity; ψ d is the direct-axis stator flux linkage; ψ q is the quadrature-axis stator flux linkage; ψ f is the permanent magnet flux linkage; L d is the direct-axis inductance; L q is the quadrature-axis inductance.

[0048] According to the stator voltage equation described above, the current value at the k+1 moment can be calculated by using the current value at the k moment by using the Euler forward approximation rule:

[0049] The Euler forward approximation rule is:

[0050] According to the stator voltage equation, the following can be obtained:

[0051] where, i q (k) is the feedback value of the quadrature-axis current at the k moment; i q (k+1) is the feedback value of the quadrature-axis current at the k+1 moment; i d (k) is the feedback value of the direct-axis current at the k moment; i d (k+1) is the feedback value of the direct-axis current at the k+1 moment; T s is the control period; V d (k) is the direct-axis voltage at the k moment; V q (k) is the quadrature-axis voltage at the k moment.

[0052] (Four) calculating the given value i q *(k+1)

[0053] This step uses the mechanical model equation of the permanent magnet synchronous motor and the real-time calculated rotational inertia of the servo press from the motor side, combines a first-order low-pass filter algorithm, and completes the calculation of the motor load torque estimation value. The above motor load torque estimation value and the corresponding value of the crank torque at the motor side are added, which is the given torque of the motor. According to the linear relationship between the given current and the given torque of the motor, the given current of the motor is obtained.

[0054] The mechanical model equation of the permanent magnet synchronous motor can be expressed as:

[0055] where, θ m is the rotational mechanical angle of the motor; T e is the electromagnetic torque of the motor; T L is the load torque of the motor, which includes the real load, friction and other disturbances; and p is the number of motor pole pairs.

[0056] In practical application, the moment of inertia J of the servo press from the motor side changes with the crank feedback angle θ c as shown in Fig. 2, where the vertical coordinate is the moment of inertia J of the servo press from the motor side, and the horizontal coordinate is the crank feedback angle θ c . The actual J constantly changes with θ c , and is not the traditional default constant J of the system. Fig. 3 is the derivative of the moment of inertia J of the servo press from the motor side with respect to the crank feedback angle θ c . It can be seen that

[0057] Since the rotational mechanical angle θ m of the motor and the crank feedback angle θ c are in a linear relationship, the expression is θ m = nθ c

[0058] (46),

[0059] Therefore,

[0060] where n is the reduction ratio of the reduction machine, and n is generally less than 50. It can be seen that is times of , and it is known that is closer to 0 than

[0061] Substituting into formula (45) gives:

[0062] Therefore,

[0063] Formula (49) is transformed from the time domain to the frequency domain by Laplace transformation, and T L = T e -Jsω m (50),

[0064] where s is a differential operator.

[0065] Then, formula (50) is combined with the design of a first-order low-pass filter to obtain the motor load torque estimate , which has the following expression:

[0066] where g1 is the cutoff frequency of the first-order low-pass filter. Thereafter, the motor load torque estimate is used to replace the actual motor load torque value T L , that is

[0067] In order to improve the accuracy of the data model and reduce the error influence of the differential operator s, the formula (51) can be transformed into:

[0068] The J in the above formula (52) is calculated according to the formula (36), and then the first-order low-pass filter is used to complete the calculation of the motor load torque estimation value . In the subsequent calculation process, the motor load torque estimation value is used to replace the actual motor load torque value T L .

[0069] The above formula (45) can be obtained: Further, the following formula can be obtained:

[0070] Since i q and i q * are in a linear proportional relationship, the following formula can be obtained from formula (53):

[0071] Where i q * represents the given value of the motor cross-axis current; T e * is the given torque of the motor;

[0072] The motor load torque estimation value is used to replace the actual motor load torque value T L , and the given torque T e of the motor is: *

[0073] The given value i q *(k+1) of the motor cross-axis current at the k+1 time is:

[0074] (Five) Model predictive current control

[0075] The current values required by the value function in the above predictive current control have been calculated and directly brought into the corresponding value function. The voltage vector corresponding to the minimum value of the value function is applied to the power module to output and control the motor rotation.

[0076] In the case of the control strategy i d * (k+1) = 0, here i d *(k+1) represents the given value of the direct-axis current at the k+1 time, the value function at the k+1 time can be obtained by optimizing the suitable control rate, and the value function is set as: g = |i q *(k+1)-i q (k+1)|+|i d *(k+1)-i d (k+1)| (57),

[0077] Finally, the optimization step is obtained by bringing the eight voltage vectors of the three-phase two-level PWM (pulse width modulation) inverter into the value function respectively, and the voltage vector with the minimum g is defined as the optimal vector, and the optimal vector acts on the power module output PWM wave to control the motor operation.

[0078] Note: the above letters are above the dot, which means derivation, for example represents the derivation of θ c in the specification, which will not be explained one by one.

[0079] The present application can also have other various examples, and those skilled in the art can make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application, but these corresponding changes and modifications should belong to the protection scope of the claims attached to the present application.

Claims

1. A feedforward control method based on the nonlinear inertia system of a servo press, characterized by: Comprising the following steps: Step one: the dynamics equation of servo press is established by using Lagrange equation, and the established dynamics equation is converted into the following equation: where M(θ c ) is the inertia coefficient; N(θ c ) is the centrifugal coefficient of the press; to crank feedback angle acceleration; Feedback angular velocity for the crank; Then the formula (12) is introduced into the state feedback e c to improve the tracking control effect, and the crank torque τ c Calculation formula: where e c = θ c * - θ c ; θ c * θ is given to the crank; to give the crank an angular velocity; to give the crank an angular acceleration; k d denotes a velocity error coefficient, which is constant; k p denotes a position error coefficient, which is constant; Step two: using the mathematical relationship between the moment of inertia J of the servo press from the motor side and the moment of inertia J of the servo press from the crank side p The calculation formula of the moment of inertia J of the servo press from the motor side is: Wherein n is the reduction ratio of the reduction gear; Step three: According to the stator voltage equation of the permanent magnet synchronous motor, the feedback value of the direct-axis current i d (k+1) at the k+1 moment and the feedback value of the quadrature-axis current i q (k+1) at the k+1 moment can be obtained by using Euler forward approximation rule. where i q (k) is the feedback value of the kth moment of the quadrature axis current; i q (k+1) is the feedback value of the k+1th moment of the quadrature axis current; i d (k) is the feedback value of the kth moment of the direct axis current; i d (k+1) is the feedback value of the k+1th moment of the direct axis current; T s is the control period; V d (k) is the kth moment of the direct axis voltage; V q (k) is the kth moment of the quadrature axis voltage; R is the stator resistance; ω e is the electrical angular velocity; L d is the direct axis inductance; L q is the quadrature axis inductance; ψ f is the permanent magnet flux linkage; Step four: using the mechanical model equation of the permanent magnet synchronous motor and the rotational inertia J of the servo press from the motor side calculated in step two, combined with a first-order low-pass filter algorithm, the motor load torque estimation value is completed Calculation, motor load torque estimate substitute motor load torque value T L motor load torque estimated value with the crank torque τ c The corresponding values at the motor side are added to obtain the given torque T e * Then, the given value i q * of the motor's cross-axis current at the k+1 time is obtained according to the linear relationship between the given torque T e * of the motor and the given value i q ​ Wherein p is the number of motor pole pairs; Step five: In control policy i d * In case (k+1) = 0, the value function is set to: g = |i q (k+1) - i q (k+1) + i d (k+1) - i d (k+1) + i where i d * (k+1) denotes the given value of the direct-axis current at the k+1 instant. The eight voltage vectors of the three-phase two-level PWM inverter are respectively brought into the value function, and the voltage vector that makes g minimum is defined as the optimal vector, and the optimal vector acts on the power module output PWM wave to control the motor operation.

2. The method of feed forward control based on the non-linear inertia system of servo press according to claim 1, characterized in that: The servo press selects the transmission structure of the crank connecting rod, the motor adopts the surface-mounted permanent magnet synchronous motor, and the driver adopts the three-phase two-level inverter.

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