Servo press control method based on input and output feedback linearization

Abstract

The invention belongs to the field of power electronics and motor control, and particularly relates to a servo press control method based on input and output feedback linearization, which is used for performing dynamic model modeling on a servo press and adopting a nonlinear system control method based on input and output feedback linearization. A dynamic model with an affine nonlinear system is converted into a linear dynamic model, a generalized predictive control algorithm is adopted as a control strategy of the whole system, the control model adopts a controlled autoregressive integral moving average process model, accurate track control over the servo press is completed through a linear control method, the control precision is remarkably improved, and the control precision is improved. And the device is suitable for servo presses with various transmission structures.

Description

Technical Field

[0001] The invention belongs to the field of power electronics and motor control, and specifically relates to a servo press control method based on input-output feedback linearization. Background Art

[0002] The motor control method in traditional servo presses is mainly cascaded field-oriented control. The traditional cascaded field-oriented control uses position loop PI, speed loop PI, current loop PI, plus coordinate transformation matrix and SVPWM for control. Therefore, the traditional servo press control method has the following problems:

[0003] (1) The moment of inertia in the servo press model is a typical nonlinear problem, which will affect the adjustment response of the PI parameters to the system;

[0004] (2) If we rely solely on kinematic relationships without considering the transmission of force and acceleration, and only consider the corresponding relationship of position, the trajectory tracking control accuracy of the system will deteriorate. Summary of the invention

[0005] In order to solve the deficiencies of the prior art, the present invention provides a servo press control method based on input-output feedback linearization.

[0006] The present invention is achieved through the following technical solutions:

[0007] A servo press control method based on input-output feedback linearization, characterized in that it includes the following steps:

[0008] Step 1: Use the Lagrange equation to establish the dynamic equation of the servo press.

[0009] Step 2: Express the dynamic equation of the servo press obtained in step 1 as an affine nonlinear system of differential homeomorphic transformation, gradually differentiate the output function y until the input u appears, design the state feedback v to eliminate the nonlinear term, and calculate the nonlinear state feedback expression of the system.

[0010] Step 3: Use the generalized predictive control algorithm as the control strategy for the entire system. The control model adopts the controlled autoregressive integral moving average process model. Using the Diophantine equation, the state feedback v of the generalized predictive control algorithm is obtained.

[0011] Step 4: Substitute the state feedback v obtained in step 3 into the nonlinear state feedback expression of the system in step 2 to obtain u. Divide u by the reduction ratio of the reducer to obtain the motor given torque T. e * , through the motor given torque T e * The given current of the motor at the k+1th moment is calculated.

[0012] Step 5: Calculate the feedback value of the quadrature-axis current at the k+1th moment and the feedback value of the direct-axis current at the k+1th moment according to the stator voltage equation.

[0013] Step 6: Substitute the given current of the motor at the k+1th moment, the feedback value of the quadrature-axis current at the k+1th moment, and the feedback value of the direct-axis current at the k+1th moment into the model-predicted current control first-order value function, and apply the voltage vector that obtains the minimum value of the model-predicted current control first-order value function to the power module to output a PWM wave to control the motor operation.

[0014] As a preferred option:

[0015] In the step 1,

[0016] The dynamic equation of the servo press is established using the Lagrange equation:

[0017]

[0018] Among them, τ c is the crank load torque; M(θ c ) is the inertia coefficient; N(θ c ) is the eccentricity coefficient of the press; is the crank feedback angular acceleration; is the crank feedback angular velocity.

[0019] The step 2 specifically includes the following steps:

[0020] The dynamic equation of the servo press can be transformed into:

[0021]

[0022] Then, formula (35) is expressed as the affine nonlinear system of differential homeomorphism transformation as follows:

[0023]

[0024] y=h (36),

[0025] in, h=[x1](40);u=[τ c ] (42); where f and g are smooth vector fields on the second-order system; h is a smooth scalar function on the second-order system;

[0026] The output function y is gradually differentiated until the input u appears.

[0027]

[0028] Design status feedback v:

[0029]

[0030] Among them, β0, β1, and β2 are configuration parameters;

[0031]

[0032] The nonlinear state feedback expression of the system is obtained:

[0033]

[0034] in,

[0035] The step three specifically includes the following steps:

[0036] The formula (53) of the state feedback v can be transformed to:

[0037]

[0038] After linearization, the system equation (55) is transformed by Lagrange, and the transfer function is obtained as follows:

[0039]

[0040] By sampling and holding it with a sampling period T, the discrete transfer function can be obtained from formula (56):

[0041]

[0042] in, B(z -1 )=b1z -1 +b2z -2 (62); A(z -1 )=1+a1z -1 +a2z -2 (63); a1, a2, b1, b2 are all constants; T s Indicates the control cycle;

[0043] The control model adopts a controlled autoregressive integrated moving average process model, and the expression of the controlled autoregressive integrated moving average process model is:

[0044]

[0045] Among them, ξ represents the mean is zero and the variance is σ 2 white noise; y(k) represents θ c The value at time k; Δ = 1-z -1; v(k-1) represents the v value at time k-1; C(z -1 )=1;

[0046] The Diophantine equation can be used to obtain the predicted value of the system output at the leading time j. The following Diophantine equation is selected:

[0047] 1=E j (z -1 )A(z -1 )Δ+z -j F j (z -1 )(65),

[0048] Among them, E j (z -1 ) and F j (z -1 ) is represented by A(z -1 ) is the only polynomial determined by the prediction length j; z -j represents a lag of j periods in the discrete domain;

[0049] In order to separately represent the input control information before time k and after time k, the following Diophantine equation is selected:

[0050] E j (z -1 )B(z -1 )=L j (z -1 )+z -j H j (z -1 ) (66),

[0051] Among them, L j (z -1 ) and H j (z -1 ) is represented by E j (z -1 )B(z -1 ) uniquely determined polynomial;

[0052] Using formula (64) and Diophantine equations (65) and (66), we can obtain the following formula:

[0053] y(k+j)=L j (z -1 )Δv(k+j-1)+H j (z -1 )Δv(k-1)+F j (z -1 )y(k) (67),

[0054] Among them, y(k+j) represents the y value at the jth moment ahead; v(k+j-1) represents the v value at the j-1th moment ahead; v(k-1) represents the v value at the k-1th moment;

[0055] The expression of the quadratic value function J of generalized predictive control is:

[0056]

[0057] Among them, N0 represents the first step prediction length of the system, N0 = 1; N1 represents the system prediction length; N u represents the input control length; λ represents the weight factor; y * Indicates the desired system output target value;

[0058] Substitute formula (67) into formula (68), and let N1 = 1, j = 1, We can get formula (69):

[0059]

[0060] Where f = H j (z -1 )Δv(k-1)+F j (z -1 )y(k)(70); the T in the upper right corner means transposition;

[0061] Taking the minimum value from formula (69), we can further obtain the calculation formula of state feedback v:

[0062] v(k)=v(k-1)+(L j T L j +λ) -1 L j T (y * -f) (71),

[0063] Among them, v(k) represents the value of v at time k.

[0064] The specific steps of step five are:

[0065] The stator voltage equation is:

[0066]

[0067] in:

[0068] ψ d =L d i d +ψ f (76),

[0069] ψq =L q i q (77),

[0070] Above, V d is the direct-axis voltage; V q is the quadrature axis voltage; i d is the direct axis current; i q is the quadrature axis current; R is the stator resistance; ω e is the electrical angular velocity; ψ d is the direct-axis stator flux; ψ q is the quadrature-axis stator flux; ψ f is the permanent magnet flux; L d is the direct-axis inductance; L q is the quadrature-axis inductance;

[0071] According to the stator voltage equation, using Euler's forward approximation rule, the current value at the kth moment can be calculated to obtain the current value at the k+1th moment:

[0072]

[0073] Among them, i q (k) is the feedback value of the quadrature-axis current at the kth moment; i q (k+1) is the feedback value of the quadrature axis current at the k+1th moment; i d (k) is the feedback value of the direct axis current at the kth moment; i d (k+1) is the feedback value of the direct-axis current at the k+1th moment; T s is the control period; V d (k) is the direct-axis voltage at the kth moment; V q (k) is the quadrature axis voltage at the kth moment.

[0074] In step 6, the model predicts that the current control primary value function is:

[0075] g=|i q *(k+1)-i q (k+1)|+|i d *(k+1)-i d (k+1)| (82),

[0076] Among them, i d * (k+1) represents the given value of the direct-axis current at the k+1th moment, i d * (k+1)=0.

[0077] Beneficial effects of the present invention:

[0078] The present invention performs dynamic modeling on a servo press, adopts a nonlinear system control method of input-output feedback linearization, converts the dynamic model of an affine nonlinear system into a linear dynamic model, adopts a generalized predictive control algorithm as the control strategy of the entire system, and the control model adopts a controlled autoregressive integral sliding average process model. The precise trajectory control of the servo press is completed through a linear control method, and the control accuracy is significantly improved. The invention is suitable for servo presses of various transmission structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 This is a control algorithm block diagram of the present invention. DETAILED DESCRIPTION

[0080] Specific embodiments of the present invention are given below. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent changes made on the basis of the technical solution of this application fall within the protection scope of the present invention.

[0081] The technical solution for implementing the present invention is as follows:

[0082] Step 1: Use the Lagrange equation to establish the dynamic equation of the servo press.

[0083] The dynamic equation of the servo press is established using the Lagrange equation:

[0084]

[0085] Among them, τ c is the crank load torque; Γ is the Lagrangian 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;

[0086] The kinetic energy E of the crank-connecting rod mechanical structure in the above formula (2) is k The calculation is as follows:

[0087] E k =E c +E l +E s +E m (3)

[0088] Where 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 reducer; the expressions of each kinetic energy are:

[0089]

[0090]

[0091] in,

[0092] Among them, J p J is the moment of inertia of the servo press viewed from the crank side; c is the moment of inertia of the crank rotating around the central rotation point of the crank structure; J l is the moment of inertia of the connecting rod rotating around the center of mass of the slider; J g is the moment of inertia of the motor and reducer; v l is the velocity of the connecting rod midpoint; v s is the speed of the slider; ω m 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 reducer.

[0093] Substituting the above formulas (2)-(11) into formula (1), the dynamic equation of the servo press can be changed to the following equation:

[0094]

[0095] Among them, M(θ c ) is the inertia coefficient, i.e. the rotational inertia J of the servo press viewed from the crank side p ; N(θ c ) is the eccentricity coefficient of the press; is the crank feedback angular acceleration; M(θ c ) and N(θ c ) are:

[0096] M(θ c )=A1+A2+A3+A4+A5+A6+J g *n 2 (13)

[0097] N(θ c )=B1+B2+B3+B4+B5+B6+B7+B8+B9 (14),

[0098] in,

[0099] A1=J c(15),

[0100] A2=J l r 2 cos 2 (i c ) / B0 2 (16),

[0101] A3=2ar 2 sin 2 (i c ) (17),

[0102] A4=2br 3 sin 2 (i c )cos(θ c ) / B0 (18),

[0103] A5=2cr 4 sin 2 (i c )cos 2 (i c ) / B0 2 (19),

[0104] A6=m l r 2 / 4 (20),

[0105] B1=J l r 4 sin(θ c )cos 3 (i c ) / B0 4 (21),

[0106] B2=J l r 2 sin(θ c )cos(θ c ) / B0 2 (22),

[0107] B3=2ar 2 sin(θ c )cos(θ c ) (23),

[0108] B4=blr 3 sin(θ c )cos 2 (i c )*cos(F) / B0 2 (24),

[0109] B5=-br3 sin(θ c ) / B0 (25),

[0110] B6=2br 5 sin 3 (θ c )cos 2 (θ c ) / B0 3 (26),

[0111] B7=2clr 4 sin(θ c )cos 2 (θ c )cos(F) / B0 3 (27),

[0112] B8=-2cr 4 sin 3 (θ c )cos(θ c ) / B0 2 (28)

[0113] B9=2cr 6 sin 3 (θ c )cos 3 (θ c ) / B0 4 (29),

[0114] F = a sin (rs sin (θ c ) / l) (30),

[0115]

[0116] The above transformation processes are all obtained through transformation through common knowledge. Without the above description, those skilled in the art can obtain the above transformation based on common sense. This embodiment describes the transformation process more clearly, so the process is displayed in detail.

[0117] Step 2: Express the dynamic equation of the servo press obtained in step 1 as an affine nonlinear system of differential homeomorphic transformation, gradually differentiate the output function y until the input u appears, design the state feedback v to eliminate the nonlinear term, and calculate the nonlinear state feedback expression of the system.

[0118] The dynamic equation (12) of the servo press obtained in step 1 can be transformed to:

[0119]

[0120] Then, formula (35) is expressed as the affine nonlinear system of differential homeomorphism transformation as follows:

[0121]

[0122] y=h (36),

[0123] in, h=[x1](40);u=[τ c ](41); Wherein the above f and g are smooth vector fields on the second-order system, and h is a smooth scalar function on the second-order system; the above formulas (41) and (40) show that the dimensions of the input u and the output y are equal, and both dimensions are equal to 1.

[0124] The basic idea of ​​differential homeomorphism transformation is to gradually differentiate the output function y until the input u appears, and then design the state feedback v to eliminate the nonlinear term. Based on the above process, the specific calculation process is as follows:

[0125] Define the Lie derivative of h with respect to f as follows:

[0126]

[0127] The above formula shows that h is the directional derivative along the vector f, and is also a smooth scalar function on the second-order system.

[0128] Similarly, higher-order Lie derivatives can be defined, and each order of Lie derivatives can be expressed recursively as follows:

[0129]

[0130] For the output function y, its relative degree r can be defined i ,satisfy:

[0131]

[0132] because So the relative degree r i =2.

[0133] According to formula (36), the zero-order derivative, first-order derivative, and second-order derivative of the output function y are:

[0134] The zeroth derivative of y:

[0135] The first derivative of y: because: therefore It has nothing to do with u, so we need to continue to find the second-order derivative of y.

[0136] The second derivative of y:

[0137] remember:

[0138]

[0139] Among them, β0, β1, and β2 are all configuration parameters and are positive numbers, which can configure the desired linearized system dynamics.

[0140] The nonlinear state feedback expression of the system can be obtained, that is, the mathematical expression between u and v:

[0141]

[0142] Step 3: Generalized predictive control.

[0143] Here, the generalized predictive control algorithm is used as the control strategy of the entire system. The optimal parameters are adjusted to obtain the state feedback v (calculation result v) of the generalized predictive control algorithm as follows:

[0144] Substituting formula (49), formula (50), formula (51) and formula (52) into formula (53), we can obtain:

[0145]

[0146] After linearization, the system equation (55) is transformed by Lagrange, and the transfer function is obtained as follows:

[0147]

[0148] By sampling and holding it with a sampling period T, the discrete transfer function can be obtained from formula (56):

[0149]

[0150] in, B(z -1 )=b1z -1 +b2z -2 (62); A(z -1 )=1+a1z -1 +a2z -2 (63); a1, a2, b1, b2 are all constants; T s Indicates the control period.

[0151] The control model adopts the controlled autoregressive integral moving average process model (CARIMA). This model has the characteristics of being able to describe non-stationary disturbances, making the system output steady-state error zero, and eliminating the deviation caused by step disturbances. The expression of the controlled autoregressive integral moving average process model is:

[0152]

[0153] Among them, ξ represents the mean is zero and the variance is σ 2 white noise; y(k) represents θ c The value at time k; Δ = 1-z -1 ; v(k-1) represents the v value at time k-1; C(z -1 )=1.

[0154] The Diophantine equation can be used to obtain the predicted value of the system output at the leading time j. The following Diophantine equation is selected:

[0155] 1=E j (z -1 )A(z -1 )Δ+z -j F j (z -1 ) (65),

[0156] Among them, E j (z -1 ) and F j (z -1 ) is represented by A(z -1 ) is the only polynomial determined by the prediction length j; z -j represents a lag of j periods in the discrete domain.

[0157] In order to separately represent the input control information before time k and after time k, the following Diophantine equation is selected:

[0158] E j (z -1 )B(z -1 )=L j (z -1 )+z -j H j (z -1 ) (66),

[0159] Among them, L j (z -1 ) and H j (z -1 ) is represented by E j (z -1 )B(z -1 ) is a uniquely determined polynomial.

[0160] Using formula (64) and Diophantine equations (65) and (66), we can obtain the following formula:

[0161] y(k+j)=L j (z -1 )Δv(k+j-1)+Hj (z -1 )Δv(k-1)+F j (z -1 )y(k) (67),

[0162] Among them, y(k+j) represents the y value at the jth moment ahead; v(k+j-1) represents the v value at the j-1th moment ahead; v(k-1) represents the v value at the k-1th moment.

[0163] The expression of the quadratic value function J of generalized predictive control is:

[0164]

[0165] Among them, N0 represents the first step prediction length of the system, N0 = 1; N1 represents the system prediction length; N u represents the input control length; λ represents the weight factor; y * Indicates the desired system output target value.

[0166] Substitute formula (67) into formula (68), and let N1 = 1, j = 1, We can get formula (69):

[0167]

[0168] Where f = H j (z -1 )Δv(k-1)+F j (z -1 )y(k)(70); the T in the upper right corner means transpose.

[0169] Taking the minimum value of formula (69), we can further obtain the calculation formula of v:

[0170] v(k)=v(k-1)+(L j T L j +λ) -1 L j T (y * -f) (71),

[0171] Among them, v(k) represents the value of v at time k.

[0172] Step 4: Substitute the state feedback v obtained in step 3 into the nonlinear state feedback expression of the system in step 2 to obtain u. Divide u by the reduction ratio of the reducer to obtain the motor given torque T. e * , through the motor given torque T e *Further get the given current i of the motor at the k+1th moment q *(k+1).

[0173] Substitute the state feedback v obtained in step 3 into the nonlinear state feedback expression (54) of the system in step 2 to obtain u. Since u = τ c , then according to the calculation formula (54) of u, we can get τ c .

[0174] Motor given torque T e * The expression is:

[0175]

[0176] The given current i of the motor at the k+1th moment q *(k+1) is expressed as:

[0177]

[0178] Among them, ψ f is the permanent magnet flux; p is the number of motor pole pairs. By formula (73), the given current i of the motor at the k+1th moment can be calculated: q *(k+1).

[0179] Step 5: Calculate the feedback value of the quadrature-axis current at the k+1th moment and the feedback value of the direct-axis current at the k+1th moment according to the stator voltage equation.

[0180] The servo press of this embodiment adopts a crank-connecting rod transmission structure, the motor adopts a surface-mounted permanent magnet synchronous motor, and the driver adopts a three-phase two-level inverter.

[0181] The mathematical model of the surface-mounted permanent magnet synchronous motor in the rotating coordinate system, the stator voltage equation is:

[0182]

[0183] in:

[0184] ψ d =L d i d +ψ f (76),

[0185] ψ q =L q i q (77),

[0186] Above, V d is the direct-axis voltage; V q is the quadrature axis voltage; i d is the direct axis current; iq is the quadrature axis current; R is the stator resistance; ω e is the electrical angular velocity; ψ d is the direct-axis stator flux; ψ q is the quadrature-axis stator flux; ψ f is the permanent magnet flux; L d is the direct-axis inductance; L q is the quadrature-axis inductance.

[0187] According to the above stator voltage equation, using Euler's forward approximation rule, the current value at the kth moment can be calculated to get the current value at the k+1th moment:

[0188] Euler's forward approximation rule is:

[0189]

[0190] According to the stator voltage equation:

[0191]

[0192] Among them, i q (k) is the feedback value of the quadrature-axis current at the kth moment; i q (k+1) is the feedback value of the quadrature axis current at the k+1th moment; i d (k) is the feedback value of the direct axis current at the kth moment; i d (k+1) is the feedback value of the direct-axis current at the k+1th moment; T s is the control period; V d (k) is the direct-axis voltage at the kth moment; V q (k) is the quadrature axis voltage at the kth moment.

[0193] Step 6: Model prediction current control.

[0194] The current values ​​required by the model predicted current control primary value function g in the above-mentioned predictive current control have been calculated and directly introduced into the corresponding model predicted current control primary value function g, and the voltage vector corresponding to the minimum value of the model predicted current control primary value function g is applied to the power module output to control the motor rotation.

[0195] In the control strategy d * (k+1)=0, here i d * (k+1) represents the given value of the direct axis current at the k+1th time. The model-predicted current control primary value function g at the k+1th time can be obtained by optimizing the appropriate control rate. The model-predicted current control primary value function g is set to:

[0196] g=|i q*(k+1)-i q (k+1)|+|i d *(k+1)-i d (k+1)| (82),

[0197] In the value function q *(k+1),i q (k+1), i d (k+1) have been calculated through the above steps. Finally, the optimization step is to bring the eight voltage vectors of the three-phase two-level PWM (pulse width modulation) inverter into the value function respectively, and define the voltage vector with the minimum value of g as the optimal vector. The optimal vector acts on the power module to output the PWM wave to control the operation of the motor.

[0198] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A servo press control method based on input-output feedback linearization, characterized in that: The steps include: Step 1: Use Lagrange equation to establish the dynamic equation of servo press; Step 2: The dynamic equation of the servo press obtained in step 1 is expressed as an affine nonlinear system of differential homeomorphic transformation, and the output function y is gradually differentiated until the input u appears. The state feedback v is designed to eliminate the nonlinear term, and the nonlinear state feedback expression of the system is calculated; Step 3: Use the generalized predictive control algorithm as the control strategy for the entire system. The control model uses a controlled autoregressive integral moving average process model. Using the Diophantine equation, the state feedback v of the generalized predictive control algorithm is obtained. Step 4: Substitute the state feedback v obtained in step 3 into the nonlinear state feedback expression of the system in step 2 to obtain u. Divide u by the reduction ratio of the reducer to obtain the motor given torque T. e * , through the motor given torque T e * Calculate the given current of the motor at the k+1th moment; Step 5: Calculate the feedback value of the quadrature-axis current at the k+1th moment and the feedback value of the direct-axis current at the k+1th moment according to the stator voltage equation; Step 6: Substitute the given current of the motor at the k+1th moment, the feedback value of the quadrature-axis current at the k+1th moment, and the feedback value of the direct-axis current at the k+1th moment into the model-predicted current control first-order value function, and apply the voltage vector that obtains the minimum value of the model-predicted current control first-order value function to the power module to output a PWM wave to control the motor operation.

2. The servo press control method based on input-output feedback linearization according to claim 1 is characterized in that: In the step 1, The dynamic equation of the servo press is established using the Lagrange equation: Among them, τ c is the crank load torque; M(θ c ) is the inertia coefficient; N(θ c ) is the eccentricity coefficient of the press; is the crank feedback angular acceleration; is the crank feedback angular velocity.

3. The servo press control method based on input-output feedback linearization according to claim 2 is characterized in that: The step 2 specifically includes the following steps: The dynamic equation of the servo press can be transformed into: Then, formula (35) is expressed as the affine nonlinear system of differential homeomorphism transformation as follows: y=h (36), in, h=[x1](40);u=[τ c ](41); Among them, f and g are smooth vector fields on the second-order system; h is a smooth scalar function on the second-order system; The output function y is gradually differentiated until the input u appears. Design status feedback v: Among them, β0, β1, and β2 are configuration parameters; The nonlinear state feedback expression of the system is obtained: in, 4. The servo press control method based on input-output feedback linearization according to claim 3 is characterized in that: The step three specifically includes the following steps: The formula (53) of the state feedback v can be transformed to: After linearization, the system equation (55) is transformed by Lagrange, and the transfer function is obtained as follows: By sampling and holding it with a sampling period T, the discrete transfer function can be obtained from formula (56): in, B(z -1 )=b1z -1 +b2z -2 (62); A(z -1 )=1+a1z -1 +a2z -2 (63); a1, a2, b1, b2 are all constants; T s Indicates the control cycle; The control model adopts a controlled autoregressive integrated moving average process model, and the expression of the controlled autoregressive integrated moving average process model is: Among them, ξ represents the mean is zero and the variance is σ 2 white noise; y(k) represents θ c The value at time k; Δ = 1-z -1 ; v(k-1) represents the v value at time k-1; C(z -1 )=1; The Diophantine equation can be used to obtain the predicted value of the system output at the leading time j. The following Diophantine equation is selected: 1=E j (With -1 )Until -1 )Δ+z -j F j (With -1 ) (65), Among them, E j (z -1 ) and F j (z -1 ) is represented by A(z -1 ) is the only polynomial determined by the prediction length j; z -j represents a lag of j periods in the discrete domain; In order to separately represent the input control information before time k and after time k, the following Diophantine equation is selected: E j (z -1 )B(z -1 )=L j (z -1 )+z -j H j (z -1 ) (66), Among them, L j (z -1 ) and H j (z -1 ) is represented by E j (z -1 )B(z -1 ) uniquely determined polynomial; Using formula (64) and Diophantine equations (65) and (66), we can obtain the following formula: y(k+j)=L j (z -1 )Δv(k+j-1)+H j (z -1 )Δv(k-1)+F j (z -1 )y(k) (67), Among them, y(k+j) represents the y value at the jth moment ahead; v(k+j-1) represents the v value at the j-1th moment ahead; v(k-1) represents the v value at the k-1th moment; The expression of the quadratic value function J of generalized predictive control is: Among them, N0 represents the first step prediction length of the system, N0 = 1; N1 represents the system prediction length; N u represents the input control length; λ represents the weight factor; y * Indicates the desired system output target value; Substitute formula (67) into formula (68), and let N1 = 1, j = 1, We can get formula (69): Where f = H j (z -1 )Δv(k-1)+F j (z -1 )y(k)(70); the T in the upper right corner means transposition; Taking the minimum value from formula (69), we can further obtain the calculation formula of state feedback v: v(k)=v(k-1)+(L j T L j +λ) -1 L j T (y * -f) (71), Among them, v(k) represents the value of v at time k.

5. The servo press control method based on input-output feedback linearization according to claim 4 is characterized in that: The specific steps of step five are: The stator voltage equation is: in: ψ d =L d I d +ψ f (76), ψ q =L q I q (77), Above, V d is the direct-axis voltage; V q is the quadrature axis voltage; i d is the direct axis current; i q is the quadrature axis current; R is the stator resistance; ω e is the electrical angular velocity; ψ d is the direct-axis stator flux; ψ q is the quadrature-axis stator flux; ψ f is the permanent magnet flux; L d is the direct-axis inductance; L q is the quadrature-axis inductance; According to the stator voltage equation, using Euler's forward approximation rule, the current value at the kth moment can be calculated to obtain the current value at the k+1th moment: Among them, i q (k) is the feedback value of the quadrature-axis current at the kth moment; i q (k+1) is the feedback value of the quadrature axis current at the k+1th moment; i d (k) is the feedback value of the direct axis current at the kth moment; i d (k+1) is the feedback value of the direct-axis current at the k+1th moment; T s is the control period; V d (k) is the direct-axis voltage at the kth moment; V q (k) is the quadrature axis voltage at the kth moment.

6. The servo press control method based on input-output feedback linearization according to claim 5 is characterized in that: In step 6, the model predicts that the current control primary value function is: g=|i q *(k+1)-i q (k+1)|+|i d *(k+1)-i d (k+1)| (82), Among them, i d * (k+1) represents the given value of the direct-axis current at the k+1th moment, i d * (k+1)=0.

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