An Iterative Feedforward Tuning Algorithm for Linear Servo Systems

Abstract

The present application provides an iterative feedforward tuning algorithm for a linear servo system, comprising the following steps: constructing a feedforward controller structure; setting each feedback gain coefficient of the feedback controller, obtaining reference trajectory parameters, selecting the moment when the gain coefficient of the feedback controller changes, and then presetting the integral gain change function of the feedback controller; the integral gain change function is used to dynamically adjust the integral gain coefficient of the feedback controller according to the reference trajectory parameters and the moment when the gain coefficient changes during operation of the linear servo system; obtaining the motor displacement tracking error in real time and projecting it into the subspace spanned by each basis function vector of the feedforward controller structure to obtain the velocity error component, the acceleration error component, and the nonlinear error component; based on these error components, using the least squares method to update each feedforward gain coefficient until the motor displacement tracking error approaches zero. The iterative feedforward tuning algorithm of the present application is more efficient and accurate in compensating for the motor displacement tracking error.

Description

Technical Field

[0001] The present application relates to the field of motor control technology, and in particular to an iterative feedforward tuning algorithm for a linear servo system. Background Art

[0002] Linear servo systems are widely used in modern industry, such as automated production lines and CNC machine tools. Precise motor position control is crucial in these applications, and motor tracking error can severely impact system performance and product quality. Feedforward control effectively compensates for the servo system's dynamic tracking error and is widely used in motion scenarios with stringent tracking requirements. The quality of the feedforward controller coefficient tuning directly impacts the compensation effectiveness of the feedforward control, and therefore the dynamic tracking error of the linear servo system.

[0003] Iterative feedforward tuning (IFFT) involves constructing a deterministic feedforward controller structure (basis function vectors) and designing the iterative update rate of the controller coefficients. Existing approaches to improving IFFT efficiency and accuracy typically focus on designing the iterative update rate, often using complex iterative update rates. However, complex iterative algorithms consume more memory and have limited scalability. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, the present application aims to provide an iterative feedforward tuning algorithm for a linear servo system, comprising the following steps:

[0005] Constructing a feedforward controller structure, the feedforward controller structure including a velocity basis function vector, an acceleration basis function vector, and a nonlinear friction basis function vector; wherein each basis function vector has a corresponding feedforward gain coefficient;

[0006] Setting each feedback gain coefficient of the feedback controller; the feedback gain coefficient includes a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient;

[0007] Acquiring reference trajectory parameters to select a gain coefficient change moment of the feedback controller and thereby presetting an integral gain change function of the feedback controller; the reference trajectory parameters include at least a motor reference speed; the integral gain change function is used to dynamically adjust the integral gain coefficient of the feedback controller according to the reference trajectory parameters and the gain coefficient change moment during operation of the linear servo system;

[0008] Controlling the motor operation under the action of a variable gain feedback controller corresponding to the integral gain variation function, and obtaining the motor displacement tracking error in real time;

[0009] Linearly projecting the motor displacement tracking error obtained in real time into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain a velocity error component, an acceleration error component, and a nonlinear error component;

[0010] According to the velocity error component, the acceleration error component, and the nonlinear error component, the feedforward gain coefficients are updated using a least squares method until the motor displacement tracking error approaches zero.

[0011] According to the technical solution provided in the embodiment of the present application, the construction of the feedforward controller structure specifically includes the following steps:

[0012] Acquire multiple influencing parameters that affect the displacement tracking error of the motor in the linear servo system; the influencing parameters include at least a first influencing parameter associated with the motor operating speed, a second influencing parameter associated with the motor operating acceleration, and a third influencing parameter associated with nonlinear friction between mechanical components in the linear servo system;

[0013] The velocity basis function vector is constructed based on the first influencing parameter, the acceleration basis function vector is constructed based on the second influencing parameter, and the nonlinear friction basis function vector is constructed based on the third influencing parameter;

[0014] The velocity basis function vector, the acceleration basis function vector and the nonlinear friction basis function vector are combined to obtain a feedforward controller structure.

[0015] According to the technical solution provided in the embodiment of the present application, setting each feedback gain coefficient of the feedback controller specifically includes the following steps:

[0016] According to Routh criterion, a first stability condition of the linear servo system when the integral gain coefficient is zero and a second stability condition of the linear servo system when the integral gain coefficient is not zero are obtained;

[0017] The feedback gain coefficients of the feedback controller are set according to the first stability condition and the second stability condition.

[0018] According to the technical solution provided in the embodiment of the present application, obtaining the reference trajectory parameters to select the gain coefficient change moment of the feedback controller and then presetting the integral gain change function of the feedback controller specifically includes the following steps:

[0019] Selecting a critical speed according to the reference trajectory parameters;

[0020] The integral gain coefficient when the running speed of the motor is greater than or equal to the critical speed is set to 0, the DC gain of the feedback controller is adjusted to a finite value, the integral gain coefficient when the running speed of the motor is less than the critical speed is limited to a first value, the DC gain of the feedback controller is adjusted to infinity, and thus the integral gain change function is obtained.

[0021] According to the technical solution provided in the embodiment of the present application, the integral gain change function is

[0022] Where, sech(x)=2 / (e αx +e -αx ), k i is the integral gain coefficient, α is the factor that determines k i The parameter of the rate of change, t1 is the command time for the linear servo system to start running. t5 is the command time for the next running start. t2(v r =ε) and t3(v r =ε) is the gain coefficient change moment, γ is the first value, and ε is the critical speed.

[0023] According to the technical solution provided in the embodiment of the present application, the linear projection of the motor displacement tracking error obtained in real time into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain the velocity error component, the acceleration error component, and the nonlinear error component specifically includes the following steps:

[0024] The motor is controlled to run according to the reference trajectory. Under the action of the variable gain feedback controller, when the critical speed is less than or equal to the first preset threshold, the expression of the motor displacement tracking error is obtained. The expression of the motor displacement tracking error is:

[0025] Where K = [K v, ,K a ,K f ] is the feedforward gain coefficient matrix, K v is the feedforward gain coefficient corresponding to the velocity basis function vector, K a is the feedforward gain coefficient corresponding to the acceleration basis function vector, K f is the feedforward gain coefficient corresponding to the nonlinear friction basis function vector, M=[k d +b,m,c] T is the system model parameter matrix, b and c are the viscous damping coefficient and Coulomb friction coefficient of the friction force on the motor, m is the total mass of the motor and load, k d is the differential gain coefficient, is each basis function, including velocity basis function vector, acceleration basis function vector and nonlinear friction basis function vector, k p is the proportional gain coefficient;

[0026] The motor displacement tracking error is linearly represented by a basis function so that the velocity feedforward gain coefficient, the acceleration feedforward gain coefficient, and the nonlinear friction feedforward gain coefficient are linearly decoupled, thereby obtaining the velocity error component, acceleration error component, and nonlinear error component in the motor displacement tracking error.

[0027] According to the technical solution provided in the embodiment of the present application, the linear projection of the motor displacement tracking error into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain the velocity error component, the acceleration error component, and the nonlinear error component specifically includes the following steps:

[0028] The motor displacement tracking error is linearly projected into the subspace spanned by the basis function vectors of the feedforward controller structure, the projection of the motor displacement tracking error on the velocity basis function vector is taken as the velocity error component, the projection of the motor displacement tracking error on the acceleration basis function vector is taken as the acceleration error component, and the projection of the motor displacement tracking error on the nonlinear friction basis function vector is taken as the nonlinear error component.

[0029] According to the technical solution provided in the embodiment of the present application, the feedforward gain coefficients are updated using the least squares method according to the velocity error component, the acceleration error component, and the nonlinear error component until the motor displacement tracking error approaches zero, specifically comprising the following steps:

[0030] Get the motor displacement tracking error E under the j-th motor operation j , the motor displacement tracking error E j The corresponding feedforward gain matrix composed of the feedforward gain coefficients is K j ;

[0031] The motor displacement tracking error E j As the input of the iterative feedforward tuning algorithm, and under the action of the variable gain feedback controller corresponding to the integral gain change function to control the motor operation, the feedforward gain coefficient iterative update rate based on the least squares method is obtained under the j+1th motor operation feedforward gain matrix K j+1 ;

[0032] Iterate the above steps until the motor displacement tracking error E j Tends to zero.

[0033] According to the technical solution provided in the embodiment of the present application, the motor displacement tracking error is related to the reference trajectory and the nonlinear friction force.

[0034] Compared with the prior art, the beneficial effects of the present application are as follows: starting from the linear decoupling perspective of the feedforward gain, the present application first constructs a feedforward controller with a three-dimensional structure of "speed + acceleration + nonlinear friction", taking into account the main factors affecting the motor displacement tracking error (reference trajectory and nonlinear friction); secondly, the linear decoupling of the feedforward gain is achieved based on the variable gain feedback controller. Without relying on an overly complex iterative update algorithm, the present application rationally constructs the feedforward controller structure and optimizes the synergy between the feedback controller and the feedforward controller, linearly projects the motor displacement tracking error into the subspace spanned by the basis function vectors of the feedforward controller structure, obtains the velocity, acceleration and nonlinear error components, realizes the linear decoupling of the feedforward gain, and then uses the least squares method to update the feedforward gain coefficient, which can more efficiently and accurately achieve compensation for the motor displacement tracking error. It reduces the computational burden and memory usage brought by the complex iterative algorithm, improves the efficiency and accuracy of the iterative feedforward tuning, and thus minimizes the motor displacement tracking error caused by the reference trajectory and nonlinear friction. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flowchart of the steps of an iterative feedforward tuning algorithm for a linear servo system provided in an embodiment of the present application;

[0036] Figure 2 A diagram illustrating the execution process of an iterative feedforward tuning algorithm for a linear servo system provided in an embodiment of the present application;

[0037] Figure 3 This is a control program structure diagram in the permanent magnet linear motor servo motion control platform provided in an embodiment of the present application;

[0038] Figure 4 A graph showing the position, velocity, and acceleration of a reference displacement trajectory provided in an embodiment of the present application. DETAILED DESCRIPTION

[0039] The present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the relevant invention and are not intended to limit the invention. It should also be noted that, for ease of description, only portions relevant to the invention are shown in the accompanying drawings.

[0040] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0041] Example 1

[0042] As mentioned in the background technology, in order to solve the problems in the prior art, this application proposes an iterative feedforward tuning algorithm for a linear servo system. Figure 1 and Figure 2 As shown, the following steps are included:

[0043] S1. Constructing a feedforward controller structure, wherein the feedforward controller structure includes a velocity basis function vector, an acceleration basis function vector, and a nonlinear friction basis function vector; wherein each basis function vector has a corresponding feedforward gain coefficient;

[0044] S2. Setting each feedback gain coefficient of the feedback controller; the feedback gain coefficient includes a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient;

[0045] S3. Obtaining reference trajectory parameters to select a gain coefficient change moment of the feedback controller, and then presetting an integral gain change function of the feedback controller; the reference trajectory parameters include at least a motor reference speed; the integral gain change function is used to dynamically adjust the integral gain coefficient of the feedback controller according to the reference trajectory parameters and the gain coefficient change moment when the linear servo system is running;

[0046] S4, controlling the motor operation under the action of the variable gain feedback controller corresponding to the integral gain variation function, and obtaining the motor displacement tracking error in real time;

[0047] S5. Linearly projecting the motor displacement tracking error obtained in real time into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain a velocity error component, an acceleration error component, and a nonlinear error component;

[0048] S6. Update each of the feedforward gain coefficients using a least squares method according to the velocity error component, the acceleration error component, and the nonlinear error component until the motor displacement tracking error approaches zero.

[0049] In a preferred embodiment, the constructing of the feedforward controller structure specifically includes the following steps:

[0050] Acquire multiple influencing parameters that affect the displacement tracking error of the motor in the linear servo system; the influencing parameters include at least a first influencing parameter associated with the motor operating speed, a second influencing parameter associated with the motor operating acceleration, and a third influencing parameter associated with nonlinear friction between mechanical components in the linear servo system;

[0051] The velocity basis function vector is constructed based on the first influencing parameter, the acceleration basis function vector is constructed based on the second influencing parameter, and the nonlinear friction basis function vector is constructed based on the third influencing parameter;

[0052] The velocity basis function vector, the acceleration basis function vector and the nonlinear friction basis function vector are combined to obtain a feedforward controller structure.

[0053] In a preferred embodiment, setting each feedback gain coefficient of the feedback controller specifically includes the following steps:

[0054] According to Routh criterion, a first stability condition of the linear servo system when the integral gain coefficient is zero and a second stability condition of the linear servo system when the integral gain coefficient is not zero are obtained;

[0055] The feedback gain coefficients of the feedback controller are set according to the first stability condition and the second stability condition.

[0056] In a preferred embodiment, the step of obtaining reference trajectory parameters to select a gain coefficient change moment of the feedback controller and then presetting an integral gain change function of the feedback controller specifically includes the following steps:

[0057] Selecting a critical speed according to the reference trajectory parameters;

[0058] The integral gain coefficient when the running speed of the motor is greater than or equal to the critical speed is set to 0, the DC gain of the feedback controller is adjusted to a finite value, the integral gain coefficient when the running speed of the motor is less than the critical speed is limited to a first value, the DC gain of the feedback controller is adjusted to infinity, and thus the integral gain change function is obtained.

[0059] In a preferred embodiment, the integral gain variation function is:

[0060] Where, sech(x)=2 / (e αx +e -αx ), k i is the integral gain coefficient, α is the factor that determines k i The parameter of the rate of change, t1 is the command time for the linear servo system to start running. t5 is the command time for the next running start. t2(v r =ε) and t3(v r =ε) is the gain coefficient change moment, γ is the first value, and ε is the critical speed.

[0061] In a preferred embodiment, linearly projecting the motor displacement tracking error acquired in real time into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain a velocity error component, an acceleration error component, and a nonlinear error component specifically includes the following steps:

[0062] The motor is controlled to run according to the reference trajectory. Under the action of the variable gain feedback controller, when the critical speed is less than or equal to the first preset threshold, the expression of the motor displacement tracking error is obtained. The expression of the motor displacement tracking error is:

[0063] Where K = [K v ,K a ,K f ] T is the feedforward gain coefficient matrix, K v is the feedforward gain coefficient corresponding to the velocity basis function vector, K a k a is the feedforward gain coefficient corresponding to the acceleration basis function vector, K f is the feedforward gain coefficient corresponding to the nonlinear friction basis function vector, M=[k d +b,m,c] T is the system model parameter matrix, b and c are the viscous damping coefficient and Coulomb friction coefficient of the friction force on the motor, m is the total mass of the motor and load, k d is the differential gain coefficient, is each basis function, including velocity basis function vector, acceleration basis function vector and nonlinear friction basis function vector, k p is the proportional gain coefficient;

[0064] The motor displacement tracking error is linearly represented by a basis function so that the velocity feedforward gain coefficient, the acceleration feedforward gain coefficient, and the nonlinear friction feedforward gain coefficient are linearly decoupled, thereby obtaining a velocity error component, an acceleration error component, and a nonlinear error component.

[0065] The critical speed being less than or equal to the first preset threshold value means approaching zero. The critical speed set in the experiment is 1e-5 (m / s).

[0066] In a preferred embodiment, linearly projecting the motor displacement tracking error into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain a velocity error component, an acceleration error component, and a nonlinear error component specifically includes the following steps:

[0067] The motor displacement tracking error is linearly projected into the subspace spanned by the basis function vectors of the feedforward controller structure, the projection of the motor displacement tracking error on the velocity basis function vector is taken as the velocity error component, the projection of the motor displacement tracking error on the acceleration basis function vector is taken as the acceleration error component, and the projection of the motor displacement tracking error on the nonlinear friction basis function vector is taken as the nonlinear error component.

[0068] In a preferred embodiment, the updating of each feedforward gain coefficient using the least squares method according to the velocity error component, the acceleration error component, and the nonlinear error component until the motor displacement tracking error approaches zero specifically includes the following steps:

[0069] Get the motor displacement tracking error E under the j-th motor operation j , the motor displacement tracking error E j The corresponding feedforward gain matrix composed of the feedforward gain coefficients is K j ;

[0070] The motor displacement tracking error E j As the input of the iterative feedforward tuning algorithm, and under the action of the variable gain feedback controller corresponding to the integral gain change function to control the motor operation, the feedforward gain coefficient iterative update rate based on the least squares method is obtained under the j+1th motor operation feedforward gain matrix K j+1 ;

[0071] Iterate the above steps until the motor displacement tracking error E j Tends to zero.

[0072] Specifically, in the experimental order j, the jth motor displacement tracking error E output by the linear motor feedback module is obtained. j ; At this time, the j-th value of the feedforward gain matrix is ​​K j ;

[0073] The motor displacement tracking error E j As the input of the iterative feedforward tuning algorithm, the motor displacement tracking error E j It has a linear mapping relationship with the feedforward controller structure (basis function vector);

[0074] Motor displacement tracking error E j Perform linear projection to the space Ψ to obtain the projection vector of the tracking error, as shown in the following equation (1);

[0075]

[0076] Run the feedforward gain coefficient iterative update rate based on the least squares method to obtain the j+1th feedforward gain matrix K j+1 , as shown in the following formula (2) and formula (3);

[0077]

[0078] δ j =[0,0,0] T -λ j (3)

[0079] Where z is the left shift operator in the iteration domain and λ is the learning step matrix.

[0080] Under the repetitive trajectory of the linear servo system, the above steps are iteratively executed until the motor displacement tracking error E j The linear servo system accuracy requirement is met (i.e., close to zero), as shown in the following formula (4);

[0081]

[0082] In a preferred embodiment, the motor displacement tracking error is related to a reference trajectory and a nonlinear friction force.

[0083] Specifically, the dynamic equation of the linear servo system subject to nonlinear interference is established as shown in the following equation (5):

[0084]

[0085] Among them, x b is the motor output displacement; m is the total mass of the motor and load; f e is the electromagnetic thrust; T d is the nonlinear friction force on the motor, which mainly consists of viscous friction and Coulomb friction, as shown in the following formula (6):

[0086]

[0087] Where b and c are the viscous damping coefficient and Coulomb friction coefficient of the friction force acting on the motor. sgn() is the sign function, as shown in Equation (7).

[0088]

[0089] The frequency domain expressions of nonlinear friction force are shown in Equations (8) and (9):

[0090] T d (s,X b )=T v (s,X b )+T c (s,X b ) (8)

[0091]

[0092] Among them, X b is the frequency domain expression of the motor displacement, and Ξ(·) is the Laplace transform expression of the sign function sgn(·).

[0093] Linear motor output displacement x b With electromagnetic thrust fe The transfer function G p As shown in the following formula (10):

[0094]

[0095] where Λ(·) is the Laplace transform operator.

[0096] Specifically, the feedback controller in this application is a position loop feedback controller, which is a PI-D structure. The position loop feedback controller G c The expression is shown in the following formula (11):

[0097] G c1 =k p +k i / s,G c2 =k d s (11)

[0098] Among them, k p 、k i 、k d are the proportional gain coefficient, integral gain coefficient, and differential gain coefficient of the feedback controller.

[0099] In the position loop feedback controller G c Under the action, the motor output displacement x b The frequency domain expression is shown in equation (12):

[0100] X b =S(G c1 +F)X r +ST d (12)

[0101] Where F is the feedforward controller; X r is the frequency domain expression of the reference trajectory; S is the input disturbance sensitivity function, which is expressed as follows (13):

[0102]

[0103] The time domain expression of the motor displacement tracking error e is shown in the following equation (14):

[0104] e(t)=x r (t)-x b (t) (14)

[0105] Among them, x r Time domain expression of the reference trajectory.

[0106] According to formula (12), the frequency domain expression of the motor displacement tracking error e is shown in formula (15):

[0107]

[0108] That is, it can be obtained that the factors affecting the motor displacement tracking error mainly include the reference trajectory and nonlinear friction disturbance.

[0109] For a linear servo system with high response characteristics, the speed of the reference trajectory and the motor output speed are approximately equal, that is, sX b (s)≈sX r (s),Ξ(s,X b )≈Ξ(s,X r ). Therefore, the frequency domain expression of the motor displacement tracking error e is shown in the following equation (13):

[0110] E(s)=S[(k d +b)sX r (s)+ms 2 X r (s)+cΞ(s,X r )-FX r (s)] (13)

[0111] Iterative feedforward tuning uses basis functions to project the signal into the space spanned by the basis functions. The resulting parameterized feedforward controller F can eliminate the repetitive motor displacement tracking error caused by the reference trajectory and nonlinear friction during iterative tuning. Therefore, the constructed feedforward controller structure (basis function vector) is a three-dimensional structure of "velocity + acceleration + nonlinear friction," as shown in Equation (14).

[0112]

[0113] The parameterized feedforward controller output u ff The frequency domain expression of is shown in equation (15):

[0114]

[0115] Where, K=[K v ,K a ,K f ] T is the feedforward gain coefficient matrix, K v is the feedforward gain coefficient corresponding to the velocity basis function vector, K a is the feedforward gain coefficient corresponding to the acceleration basis function vector, K f is the feedforward gain coefficient corresponding to the nonlinear friction basis function vector.

[0116] Substituting equations (10) and (11) into equation (13), we can obtain the input disturbance sensitivity function: S The specific expansion is shown in the following formula (16):

[0117] (16)

[0118] Since the reference trajectory x r The main signal energy of is distributed in the low frequency band. According to different DC gains of the feedback controller, Equation (16) can be approximately expressed as shown in Equation (17):

[0119] (17)

[0120] Where, is the DC gain of the feedback controller. Finite value σ for k i The DC gain of the feedback controller when is 0 belongs to the set of positive real numbers.

[0121] When the motor running speed is greater than or equal to the critical speed (v r ≥ε), k i is 0, the DC gain of the feedback controller is adjusted to a finite value. The motor speed is less than the critical speed (v r <ε), k i The first value γ is used, and the DC gain of the feedback controller is adjusted to infinity. The gain change is determined by the motor reference speed v r The integral gain change function expression is shown in the following formula (18):

[0122]

[0123] Where, sech(x)=2 / (e ax +e -ax ), α determines k i The rate of change of t1 is the time when the linear servo system starts the movement. t5 is the time when the next movement starts. t2(v r =ε) and t3(v r =ε) is the moment when the integral gain of the feedback controller changes.

[0124] Therefore, by substituting equation (17) into equation (13), equation (13) can be organized as follows:

[0125]

[0126] Substituting equation (18) into equation (19), when the critical speed ε is small enough, equation (19) can be organized as shown in equation (20):

[0127]

[0128] Under the variable gain feedback control, the motor displacement tracking error and the basis function vectors of the feedforward controller structure are linearly mapped. The motor displacement tracking error can be linearly projected into the subspace spanned by the basis function vectors of the feedforward controller structure. At this point, the feedforward gain coefficient is linearly decoupled. The overall control block diagram is shown in the figure below. Figure 2 shown.

[0129] Example 2

[0130] In order to further illustrate the practical application effect of the present invention, this embodiment compares the traditional algorithm and further illustrates the superiority of the control method according to the present invention. Therefore, the comparison method includes the following steps:

[0131] On a permanent magnet linear motor servo motion platform (such as Figure 3 As shown, experiments were conducted on the iterative feedforward tuning algorithm of the linear servo system obtained by the design method shown in Example 1 and the iterative feedforward tuning algorithm of the linear servo system based on the traditional fixed gain feedback controller. The parameters of the permanent magnet synchronous linear motor used are as follows: mover mass m m =1.1Kg, electromagnetic thrust constant K T =28.6N / A, permanent magnet flux φ = 70.3m·Wb, winding phase resistance R = 4.33ohm, inductance L d =L q =19.7mH, the control program structure is as follows Figure 3 As shown;

[0132] In particular, the reference displacement trajectory is designed as an S-shaped (third-order) motion trajectory, and its position, velocity and acceleration curves are as follows Figure 4 The specific reference trajectory parameter settings are shown in Table 1 below.

[0133] Table 1 Reference trajectory (S-shaped trajectory) parameters

[0134] <![CDATA[Displacement end point x max > <![CDATA[Maximum speed v max > <![CDATA[Maximum acceleration a max > <![CDATA[Jerk j max > 0.045(m) 0.2(m / s) <![CDATA[5(m / s 2 )]]> <![CDATA[250(m / s 3 )]]>

[0135] The experimental results show that the iterative feedforward tuning of the variable gain feedback controller based on this application requires 5 iterations, while the iterative feedforward tuning of the fixed gain feedback controller based on the traditional method requires 30 iterations. The iterative feedforward tuning results of the variable gain feedback controller based on this application are as follows: the maximum value of the motor displacement tracking error e max is 8.00 μm, and the motor displacement tracking error is non-zero RMS value e nrms The iterative feedforward tuning result of the fixed gain feedback controller is: the maximum value of the motor displacement tracking error e max The motor displacement tracking error is non-zero RMS value e nrmsCompared with the iterative feedforward tuning based on the fixed gain feedback controller, the iterative feedforward tuning based on the variable gain feedback controller in this application has an efficiency improvement of 75%, an accuracy improvement of 25%, and a motor displacement tracking steady-state error of 0.

[0136] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. The above is only the preferred implementation method of this application. It should be pointed out that due to the limitations of textual expression, there are objectively infinite specific structures. For ordinary technicians in this technical field, without departing from the principles of the present invention, they can also make several improvements, modifications or changes, and can also combine the above technical features in an appropriate manner; these improvements, modifications, changes or combinations, or the direct application of the inventive concept and technical solution to other occasions without improvement, should be regarded as the scope of protection of this application.

Claims

1. An iterative feedforward tuning algorithm for a linear servo system, characterized in that: The following steps are involved: Constructing a feedforward controller structure, the feedforward controller structure including a velocity basis function vector, an acceleration basis function vector, and a nonlinear friction basis function vector; wherein each basis function vector has a corresponding feedforward gain coefficient; Setting each feedback gain coefficient of the feedback controller; the feedback gain coefficient includes a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; Acquiring reference trajectory parameters to select a gain coefficient change moment of the feedback controller and thereby presetting an integral gain change function of the feedback controller; the reference trajectory parameters include at least a motor reference speed; the integral gain change function is used to dynamically adjust the integral gain coefficient of the feedback controller according to the reference trajectory parameters and the gain coefficient change moment during operation of the linear servo system; Controlling the motor operation under the action of a variable gain feedback controller corresponding to the integral gain variation function, and obtaining the motor displacement tracking error in real time; Linearly projecting the motor displacement tracking error obtained in real time into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain a velocity error component, an acceleration error component, and a nonlinear error component; According to the velocity error component, the acceleration error component, and the nonlinear error component, the feedforward gain coefficients are updated using a least squares method until the motor displacement tracking error approaches zero.

2. The iterative feedforward tuning algorithm for a linear servo system according to claim 1, wherein: The feedforward controller structure is constructed, specifically comprising the following steps: Acquire multiple influencing parameters that affect the displacement tracking error of the motor in the linear servo system; the influencing parameters include at least a first influencing parameter associated with the motor operating speed, a second influencing parameter associated with the motor operating acceleration, and a third influencing parameter associated with nonlinear friction between mechanical components in the linear servo system; The velocity basis function vector is constructed based on the first influencing parameter, the acceleration basis function vector is constructed based on the second influencing parameter, and the nonlinear friction basis function vector is constructed based on the third influencing parameter; The velocity basis function vector, the acceleration basis function vector and the nonlinear friction basis function vector are combined to obtain a feedforward controller structure.

3. The iterative feedforward tuning algorithm for a linear servo system according to claim 2, wherein: The setting of each feedback gain coefficient of the feedback controller specifically includes the following steps: According to Routh criterion, a first stability condition of the linear servo system when the integral gain coefficient is zero and a second stability condition of the linear servo system when the integral gain coefficient is not zero are obtained; The feedback gain coefficients of the feedback controller are set according to the first stability condition and the second stability condition.

4. The iterative feedforward tuning algorithm for a linear servo system according to claim 3, wherein: The obtaining of reference trajectory parameters to select the gain coefficient change moment of the feedback controller and then preset the integral gain change function of the feedback controller specifically includes the following steps: Selecting a critical speed according to the reference trajectory parameters; The integral gain coefficient when the running speed of the motor is greater than or equal to the critical speed is set to 0, the DC gain of the feedback controller is adjusted to a finite value, the integral gain coefficient when the running speed of the motor is less than the critical speed is limited to a first value, and the DC gain of the feedback controller is adjusted to infinity, thereby obtaining an integral gain change function.

5. The iterative feedforward tuning algorithm for a linear servo system according to claim 4, characterized in that: The integral gain variation function is: , in, , k i is the integral gain coefficient, α To decide k i The rate of change parameter, t 1 is the instruction time for the linear servo system to start running, t 5 is the instruction time for the next operation to start. t 2 ( v r = ε )and t 3 ( v r = ε ) is the gain coefficient change moment, γ is the first value, ε is the critical speed.

6. The iterative feedforward tuning algorithm for a linear servo system according to claim 5, characterized in that: The motor displacement tracking error obtained in real time is linearly projected into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain the velocity error component, the acceleration error component, and the nonlinear error component, specifically comprising the following steps: The motor is controlled to run according to the reference trajectory. Under the action of the variable gain feedback controller, when the critical speed is less than or equal to the first preset threshold, the expression of the motor displacement tracking error is obtained. The expression of the motor displacement tracking error is: ; in, K =[ K v , K a , K f ] T is the feedforward gain coefficient matrix, K v is the feedforward gain coefficient corresponding to the velocity basis function vector, K a is the feedforward gain coefficient corresponding to the acceleration basis function vector, K f is the feedforward gain coefficient corresponding to the nonlinear friction basis function vector, M =[ k d + b , m , c ] T is the system model parameter matrix, b 、 c are the viscous damping coefficient and Coulomb friction coefficient of the friction force on the motor, m is the total mass of the motor and load, k d is the differential gain coefficient, φ are the basis functions, including velocity basis function vector, acceleration basis function vector and nonlinear friction basis function vector, k p is the proportional gain coefficient; The motor displacement tracking error is linearly represented by a basis function so that the velocity feedforward gain coefficient, the acceleration feedforward gain coefficient, and the nonlinear friction feedforward gain coefficient are linearly decoupled, thereby obtaining the velocity error component, acceleration error component, and nonlinear error component in the motor displacement tracking error.

7. The iterative feedforward tuning algorithm for a linear servo system according to claim 1, wherein: The linear projection of the motor displacement tracking error into the subspace spanned by the basis function vectors of the feedforward controller structure to obtain a velocity error component, an acceleration error component, and a nonlinear error component specifically includes the following steps: The motor displacement tracking error is linearly projected into the subspace spanned by the basis function vectors of the feedforward controller structure, the projection of the motor displacement tracking error on the velocity basis function vector is taken as the velocity error component, the projection of the motor displacement tracking error on the acceleration basis function vector is taken as the acceleration error component, and the projection of the motor displacement tracking error on the nonlinear friction basis function vector is taken as the nonlinear error component.

8. The iterative feedforward tuning algorithm for a linear servo system according to claim 1, wherein: According to the velocity error component, the acceleration error component, and the nonlinear error component, the feedforward gain coefficients are updated using the least square method until the motor displacement tracking error approaches zero, specifically comprising the following steps: Get the j The motor displacement tracking error under the motor operation E j , the motor displacement tracking error E j The corresponding feedforward gain matrix composed of the feedforward gain coefficients is: K j ; The motor displacement tracking error E j As the input of the iterative feedforward tuning algorithm, and under the action of the variable gain feedback controller corresponding to the integral gain change function, the motor operation is controlled, and the feedforward gain coefficient iteration update rate based on the least squares method is obtained. j +1 feedforward gain matrix for motor operation K j+1 ; Iterate the above steps until the motor displacement tracking error E j Tends to zero.

9. The iterative feedforward tuning algorithm for a linear servo system according to claim 1, wherein: The motor displacement tracking error is related to the reference trajectory and the nonlinear friction force.

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