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

Abstract

The present application belongs to the field of power electronics and motor control, and particularly relates to a feedforward control method based on a nonlinear inertia system of a servo press, which realizes torque calculation control of the servo press by using a dynamic model of the system, online calculates the nonlinear inertia of the servo press, accurately adapts the calculation process of a torque observer, adopts a torque feedforward control method, and exhibits strong robustness of the control system in the case of motor load disturbance, especially when the servo press encounters a 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.

Description

Technical Field

[0001] This invention belongs to the field of power electronics and motor control, specifically relating to a feedforward control method based on a nonlinear inertia system of a servo press. Background Technology

[0002] There are many control methods for servo presses. For example, the patent with authorization announcement number CN110077028B entitled "Full Closed-Loop Nonlinear Predictive Control Method and System for Servo Press" discloses one such control method. However, most control methods do not consider the situation where a large error will occur between the target given position and the feedback position when the servo press slide encounters a large load during the forming process, which will affect the final workpiece forming quality of the servo press. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a feedforward control method based on a nonlinear inertia system of a servo press.

[0004] This invention discloses a feedforward control method based on a nonlinear inertia system of a servo press, comprising the following steps:

[0005] Step 1: Establish the dynamic equations of the servo press using the Lagrange equations, and then transform the established dynamic equations into the following equations:

[0006]

[0007] Where M(θ) c ) is the inertia coefficient; N(θ) c ) is the centrifugal coefficient of the press; This refers to the crank feedback angular acceleration; The crank feedback angular velocity;

[0008] Then, formula (12) is introduced into the state feedback e. c To improve the tracking control effect, the crank torque τ is obtained. c Calculation formula:

[0009]

[0010] Among them, e c =θ c * -θ c ; θ c * Give the crank an angle; Give the crank an angular velocity; Give the crank an angular acceleration; k d The velocity error coefficient is represented by k, which is a constant. pThis represents the position error coefficient, which is a constant.

[0011] 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:

[0012]

[0013] Where n is the reduction ratio of the reducer;

[0014] 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):

[0015]

[0016] 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;

[0017] Step 4: Using the mechanical model equations of the permanent magnet synchronous motor and the moment of inertia J of the servo press calculated in Step 2 from the motor side, 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 The formula for calculating *(k+1) is:

[0018]

[0019] Where p is the number of pole pairs of the motor;

[0020] Step 5: In control strategy i d * When (k+1)=0, the value function is set as follows:

[0021] g = |i q *(k+1)-i q (k+1)|+|i d *(k+1)-i d (k+1)|(57),

[0022] Among them, i d * (k+1) represents the given value of the direct-axis current at time k+1;

[0023] The eight voltage vectors of the three-phase two-level PWM inverter are respectively substituted into the value function, and the voltage vector that achieves the minimum value of g is defined as the optimal vector. The optimal vector acts on the PWM wave output by the power module to control the motor operation.

[0024] In this invention, the servo press uses a crank-connecting rod transmission structure, the motor is a surface-mounted permanent magnet synchronous motor, and the driver is a three-phase two-level inverter.

[0025] The advantages of this invention are that it utilizes the dynamic model of the system to realize the control method for torque calculation of the servo press, calculates the nonlinear inertia of the servo press online, accurately adapts to the calculation process of the torque observer, and adopts the torque feedforward control method. The control system exhibits strong robustness under motor load disturbances. In particular, when the servo press encounters a large load, the real-time curve error of the servo press is greatly reduced, improving the position control accuracy and reducing the position control error. Attached Figure Description

[0026] Figure 1 This is a block diagram of the control algorithm of the present invention;

[0027] Figure 2 To show the moment of inertia J of the servo press as a function of the crank feedback angle θ, viewed from the motor side. c The change curve;

[0028] Figure 3 To measure the moment of inertia J of the servo press relative to the crank feedback angle θ from the motor side.c The derivative graph. Detailed Implementation

[0029] The following are specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments. All equivalent modifications made based on the technical solutions of this application fall within the protection scope of the present invention.

[0030] The technical solution for implementing this invention is as follows:

[0031] (I) Calculating the crank torque τ c

[0032] This step involves using a torque control method based on the Lagrange equation in the servo drive to calculate the crank torque τ. c The inputs to this method include crank given angle, crank given angular velocity, and crank given angular acceleration, as well as crank feedback angle and crank feedback angular velocity. The output of this method is the calculated crank torque.

[0033] The dynamic equations of the servo press are established using the Lagrange equations:

[0034]

[0035] Where Γ is the Lagrange function, Γ = E k -E p (2); E k E represents the kinetic energy of the crank-connecting rod mechanical structure. p The gravitational potential energy of the press transmission system can be considered as E p =0;

[0036] In the above formula (2), the kinetic energy E of the crank-connecting rod mechanical structure k The calculation is as follows:

[0037] E k =E c +E l +E s +E m (3),

[0038] Where E c E represents the kinetic energy of the crankshaft. l E represents the kinetic energy of the connecting rod. s E represents the kinetic energy of the slider. m This represents the kinetic energy of the motor and the reducer; the expressions for each kinetic energy are as follows:

[0039]

[0040]

[0041] in,

[0042] Among them, J p The moment of inertia of the servo press as viewed from the crank side; J c J is the moment of inertia of the crankshaft as it rotates around the central point of rotation of the crankshaft structure; l J is the moment of inertia of the connecting rod rotating around the center of mass of the slider; g It is the moment of inertia of the motor and the reducer; v l It is the velocity at the midpoint of the connecting rod; v s It is the velocity of the slider; ω m It is the angular velocity of the motor; m s It is the mass of the slider; m l It is the mass of the connecting rod; θ c It is the crank feedback angle; φ is the crank feedback angular velocity; φ is the angle of clockwise rotation of the connecting rod 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 reducer.

[0043] Substituting the above formulas (2)-(11) into formula (1), the dynamic equation of the servo press can be transformed into the following equation:

[0044]

[0045] Where M(θ) c The coefficient of inertia is J, which is the moment of inertia of the servo press as viewed from the crank side. p N(θ) c ) is the centrifugal coefficient of the press; The crank feedback angular acceleration; M(θ) c ) and N(θ c The expressions for ) are as follows:

[0046] M(θ c )=A1+A2+A3+A4+A5+A6+J g *n 2 (13),

[0047] N(θ c )=B1+B2+B3+B4+B5+B6+B7+B8+B9(14),

[0048] in,

[0049] A1 = J c (15),

[0050] A2 = J l r 2 cos 2 (θc ) / B0 2 (16),

[0051] A3=2ar 2 sin 2 (i c )(17),

[0052] A4=2br 3 sin 2 (i c )cos(θ c ) / B0 (18),

[0053] A5=2cr 4 sin 2 (i c )cos 2 (i c ) / B0 2 (19),

[0054] A6=m l r 2 / 4 (20),

[0055] B1=J l r 4 sin(θ c )cos 3 (i c ) / B0 4 (21),

[0056] B2=J l r 2 sin(θ c )cos(θ c ) / B0 2 (22),

[0057] B3=2ar 2 sin(θ c )cos(θ c )(23),

[0058] B4=blr 3 sin(θ c )cos 2 (i c )*cos(F) / B0 2 (24),

[0059] B5=-br 3 sin(θ c ) / B0 (25),

[0060] B6=2br 5 sin3 (θ c cos 2 (θ c ) / B0 3 (26),

[0061] B7 = 2clr 4 sin(θ c cos 2 (θ c cos(F) / B0 3 (27),

[0062] B8 = -2cr 4 sin 3 (θ c cos(θ) c ) / B0 2 (28),

[0063] B9 = 2cr 6 sin 3 (θ c cos 3 (θ c ) / B0 4 (29),

[0064] F = asin(rsin(θ) c ) / l) (30),

[0065]

[0066] Introduce formula (12) into the state feedback e c To improve the tracking control effect, the crank torque τ can ultimately be obtained. c Calculation formula:

[0067]

[0068] Among them, e c =θ c * -θ c ; θ c * Give the crank an angle; Give the crank an angular velocity; Give the crank an angular acceleration; k d The velocity error coefficient is represented by k, which is a constant. p This represents the position error coefficient, which is a constant.

[0069] (II) Calculate the moment of inertia J of the servo press as viewed from the motor side.

[0070] This step utilizes the mathematical relationship between moments of inertia to obtain the moment of inertia J of the servo press as viewed from the motor side, which is used to calculate the estimated value of the motor load torque.

[0071] The moment of inertia J of the servo press viewed from the crank side p This is the aforementioned inertia coefficient M(θ) c ), that is, J p =M(θ) c Then, the formula for calculating the moment of inertia J of the servo press as viewed from the motor side is:

[0072]

[0073] Where n is the reduction ratio of the reducer.

[0074] (III) Calculate i based on the stator voltage equation q (k+1) and i d (k+1)

[0075] This step utilizes the stator voltage equation of the permanent magnet synchronous motor to calculate the quadrature and direct axis currents at time k+1 in the dq coordinate system, and then uses them to calculate the value function in model predictive current control.

[0076] In this embodiment, the servo press uses a crank-connecting rod transmission structure, the motor is a surface-mounted permanent magnet synchronous motor, and the driver is a three-phase two-level inverter.

[0077] The mathematical model of the surface-mounted permanent magnet synchronous motor in the rotating coordinate system, and the stator voltage equation are as follows:

[0078]

[0079] in:

[0080] ψ d =L d i d +ψ f (39),

[0081] ψ q =L q i q (40),

[0082] The above, V d It is the direct-axis voltage; V q It is the quadrature-axis voltage; i d It is the direct-axis current; i q It is the quadrature-axis current; R is the stator resistance; ω e It is the electric angular velocity; ψ d It is a direct-axis stator flux linkage; ψ q It is the cross-axis stator flux linkage; ψ f It is a permanent magnet flux linkage; Ld It is a direct-axis inductor; L q It is a quadrature axis inductor.

[0083] Based on the stator voltage equations above, and using Euler's forward approximation method, the current value at time k+1 can be calculated from the current value at time k:

[0084] Euler's forward approximation law is:

[0085]

[0086] According to the stator voltage equation, we can obtain:

[0087]

[0088] 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.

[0089] (iv) Calculate the given value i of the quadrature-axis current at time k+1. q *(k+1)

[0090] This step utilizes the mechanical model equations of the permanent magnet synchronous motor and the real-time calculated moment of inertia of the servo press viewed from the motor side, combined with a first-order low-pass filter algorithm, to calculate the estimated value of the motor load torque. The estimated value of the motor load torque is added to the corresponding value of the crank torque on the motor side to obtain the given torque of the motor. Based on the linear relationship between the given current and the given torque of the motor, the given current of the motor is obtained.

[0091] The mechanical model equations of a permanent magnet synchronous motor can be expressed as:

[0092]

[0093] Where, θ m It is the mechanical rotation angle of the motor; T e It is the electromagnetic torque of the motor; T L It is the motor load torque, which includes the actual load, friction, and other disturbances; p is the number of pole pairs of the motor.

[0094] In practical applications, the moment of inertia J of a servo press, viewed from the motor side, varies with the crank feedback angle θ.c The change curve is shown in the attached figure. Figure 2 As shown, the vertical axis represents the moment of inertia J of the servo press as viewed from the motor side, and the horizontal axis represents the crank feedback angle θ. c In reality, J varies with θ c The system is constantly changing; it does not, by traditional assumption, treat the system's moment of inertia J as constant. (Appendix) Figure 3 To measure the moment of inertia J of the servo press relative to the crank feedback angle θ from the motor side. c The derivative of can be seen

[0095] Due to the rotational mechanical angle θ of the motor m and crank feedback angle θ c The relationship is linear, expressed as: θ m =nθ c

[0096] (46),

[0097] but

[0098] Where n is the reduction ratio of the reducer, and n is generally less than 50. yes of times, we can know Compare Closer to 0, we get

[0099] Will Substituting into formula (45), we get:

[0100]

[0101] but

[0102] Equation (49) is transformed from the time domain to the frequency domain using the Laplace transform, resulting in:

[0103] T L =T e -Jsω m (50),

[0104] Where s is the differential operator.

[0105] Then, by combining formula (50) with the design of a first-order low-pass filter, the estimated value of the motor load torque is obtained. The expression is as follows:

[0106]

[0107] Where g1 is the cutoff frequency of the first-order low-pass filter; thereafter, the estimated value of the motor load torque is used. Replace the actual motor load torque value T L ,Right now

[0108] To improve the accuracy of the data model and reduce the influence of the error of the differential operator s, formula (51) can be transformed into:

[0109]

[0110] The value of J in the above formula (52) is calculated according to formula (36), and then the motor load torque can be estimated by using a first-order low-pass filter. The calculation is as follows. Subsequent calculations will use the estimated value of the motor load torque. Replace the actual motor load torque value T L .

[0111] From formula (45), we can obtain the following: Furthermore, we can obtain:

[0112]

[0113] Because i q and i q * They are in a linear proportional relationship, therefore, from formula (53) we can obtain:

[0114]

[0115] Where i q * T represents the given value of the quadrature-axis current of the motor. e * This is the given torque for the motor;

[0116] Estimated value of motor load torque Replace the actual motor load torque value T L Then the given torque T of the motor e * The expression is:

[0117]

[0118] Then the given value i of the quadrature-axis current of the motor at time k+1. q The expression for *(k+1) is:

[0119]

[0120] (V) Model Predictive Current Control

[0121] The current values ​​required for the value function in the above predictive current control have been calculated and directly substituted into the corresponding value function. The voltage vector corresponding to the minimum value of the value function is then applied to the power module output to control the motor rotation.

[0122] In control strategy i d * When (k+1)=0, here i d * (k+1) represents the given value of the direct-axis current at time k+1. The value function at time k+1 can be obtained through optimization using a suitable control law. The value function is set as follows:

[0123] g = |i q *(k+1)-i q (k+1)|+|i d *(k+1)-i d (k+1)|(57),

[0124] Finally, the optimization step involves substituting the eight voltage vectors of the three-phase two-level PWM (pulse width modulation) inverter into the value function, and defining the voltage vector that achieves the minimum value of g as the optimal vector. The optimal vector is then applied to the PWM wave output by the power module to control the motor operation.

[0125] Note: The dots above the letters above indicate differentiation, for example... Indicates the relationship with θ c Differentiation will not be explained in detail in the instruction manual.

[0126] This invention may have many other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A feedforward control method based on a nonlinear inertia system of a servo press, characterized in that: Includes the following steps: Step 1: The nonlinear inertia coefficient of the servo press was calculated online. , The dynamic equations of the servo press are established using the Lagrange equations, and then transformed into the following equations: （12）， in, It is the coefficient of inertia; It is the centrifugal coefficient of the press; This refers to the crank feedback angular acceleration; Then, formula (12) is introduced into state feedback. To improve the tracking control effect, a method based on nonlinear inertia coefficients is obtained. crank torque Calculation formula: （35）， in, ; ; Give the crank an angle; Give the crank an angular velocity; Give the crank an angular acceleration; This represents the speed error coefficient, which is a constant. This represents the position error coefficient, which is a constant. Step 2: Utilize the rotational inertia of the servo press viewed from the motor side. Moment of inertia of the servo press viewed from the crank side The mathematical relationship between them yields the angle of the servo press following the crank feedback as viewed from the motor side. Changing moment of inertia The formula for calculation is: （36）， in, The reduction ratio of the reducer; the moment of inertia of the servo press viewed from the motor side. Crank feedback angle In constant flux; Step 3: Based on the stator voltage equation of the permanent magnet synchronous motor, and using Euler's forward approximation method, the first... Feedback value of direct-axis current at any time and the Feedback value of quadrature-axis current at any moment : （43）， （44）， in, For the first The feedback value of the quadrature-axis current at any given time; For the first The feedback value of the quadrature-axis current at any given time; For the first The feedback value of the direct-axis current at any given time; For the first The feedback value of the direct-axis current at any given time; To control the cycle; It is the first Direct-axis voltage at any given moment; It is the first The quadrature-axis voltage at any given moment; It is the stator resistance; It is electric angular velocity; It is a direct-axis inductor; It is a quadrature axis inductor; It is a permanent magnet flux chain; Step 4: Using the mechanical model equations of the permanent magnet synchronous motor and the angle of feedback of the servo press from the motor side as calculated in Step 2, Moment of inertia By combining a first-order low-pass filter algorithm, the motor load torque estimation value in the nonlinear inertia feedforward method based on the servo press is completed. Calculate using the estimated value of motor load torque. Replace the actual motor load torque value The estimated value of motor load torque With crank torque The corresponding values ​​on the motor side are added together to obtain the given torque of the motor. Then, based on the given value of the motor's quadrature-axis current... With the given torque of the motor The linear relationship is used to obtain the first motor. The given value of the quadrature-axis current at time t. The calculation formula is: （56）； in, It is the number of pole pairs of the motor; Step 5: In the control strategy In this case, the value function is set as follows: （57）， in, Indicates the first The given value of the direct-axis current at any given time; Substitute the eight voltage vectors of the three-phase two-level PWM inverter into the value function, and... The voltage vector that achieves the minimum value is defined as the optimal vector. The optimal vector is applied to the power module to output a PWM wave to control the motor operation.

2. The feedforward control method based on the nonlinear inertia system of a servo press according to claim 1, characterized in that: The servo press uses a crank-connecting rod transmission structure, the motor is a surface-mounted permanent magnet synchronous motor, and the driver is a three-phase two-level inverter.

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