CN112947310B - Rotary servo motor track precompensation method and device based on prediction model - Google Patents

Rotary servo motor track precompensation method and device based on prediction model Download PDF

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CN112947310B
CN112947310B CN202110116092.XA CN202110116092A CN112947310B CN 112947310 B CN112947310 B CN 112947310B CN 202110116092 A CN202110116092 A CN 202110116092A CN 112947310 B CN112947310 B CN 112947310B
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汪泽
胡楚雄
朱煜
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Tsinghua University
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Abstract

A rotary servo motor track precompensation method and device based on a prediction model belong to the technical field of rotary motor motion control. The method utilizes a prediction model and disturbance observation to predict the closed-loop track tracking control effect of the rotating motor, and designs a track precompensation link according to the prediction model and the disturbance observation so as to correct position errors to realize good track tracking control performance. The track precompensation method comprises a linear prediction model containing generalized disturbance observation and a track precompensation link based on the prediction model. According to the method, the track tracking control state of the rotary motor closed-loop control system at the future moment is effectively predicted according to the known model information, the optimal track precompensation quantity is determined by utilizing the prediction information, and the track tracking performance can be improved on the premise of not changing the structure of the closed-loop controller.

Description

Rotary servo motor track pre-compensation method and device based on prediction model
Technical Field
The invention relates to a servo motor motion control method, in particular to a rotary motor track precompensation method and a rotary motor track precompensation device based on a prediction model.
Background
The rotary servo motor converts the voltage signal into torque and rotating speed to drive a control object, and compared with the traditional motor, the rotary servo motor has the advantages of high response speed, high tracking/positioning precision, easiness in precise control and the like. However, a series of problems such as tracking control lag caused by insufficient rigidity of a tracking motion controller and a track tracking control error caused by external disturbance are inevitably faced in the track tracking motion control process of the rotary servo motor. The existing commercial servo tracking controller and the controller are packaged by a relatively closed bottom layer control algorithm so as to ensure the stability and the motion control precision of basic closed-loop control. Under the condition, a user is difficult to correct and optimize the bottom layer motion control algorithm according to the specific requirements of the actual motion control scene, so that the motion control precision of the servo motor cannot be further improved by changing the structure and the control parameters of the motion controller.
Different from the sealing property of a bottom layer control algorithm, the controller with higher integration level can not modify the structure and parameters of the bottom layer controller and can not meet the requirement of two-axis cooperative control. However, the servo control system basically leaves a corresponding interface for the user to input the desired command for the motor at the position input position. Theoretically, for a closed-loop linear system, the track tracking precision can be improved in a track precompensation mode under the condition that the structure and parameters of a closed-loop controller are not changed. In other words, the client only needs to properly modify and compensate the original expected input trajectory, so that the actual output of the motor motion system with tracking lag is closer to the original expected input, and the improvement of the trajectory tracking control precision is indirectly realized.
However, until now, there has been no better solution.
Disclosure of Invention
The invention aims to provide a rotary servo motor track precompensation method based on a prediction model, which provides a proper track compensation amount determination mode through the prediction model of a closed-loop motion control system and the compensation of disturbance so as to solve the problems, and the rotary servo motor track precompensation method has stronger anti-jamming capability and good track tracking precision. The main idea of the rotary servo motor track precompensation method based on the prediction model is as follows: on the basis that a rotary motor closed-loop servo motion control system can realize basically stable closed-loop track tracking control, a system output state linear prediction model is determined in a closed-loop system identification mode; then determining an iterative formula of a generalized disturbance estimation value according to the deviation between the actual value of the output measured by the encoder at the current moment (namely the k moment) and the current moment output value predicted by the prediction model at the previous moment; and then determining future N under the influence of the disturbance by using the estimated value of the disturbancepTime of day (i.e., k + N)pTime of day) state prediction; finally, determining future N by utilizing a mode of multiple iterationscTime of day (i.e., k + N)cTime of day). The compensation is placed in a register, through NcAfter the moment, the compensation quantity is overlapped with the original expected track input, and the overlapped result is used as the expected input instruction of the system and is input into a closed-loop servo motion control system to realizeAnd pre-compensating the track.
In order to achieve the purpose, the invention provides the following technical scheme:
a rotary servo motor track precompensation method based on a prediction model comprises the following steps:
establishing a closed-loop transfer function of the rotating motor according to system identification, establishing a prediction model of the actual position output at the k +1 moment according to the actual position output and the expected position input from the k-2 moment to the k moment and a disturbance amount predicted value at the k moment by using the transfer function,
wherein the disturbance quantity predicted value at the k moment is estimated according to a vector difference between an actual position output at the k moment and a predicted position output at the k moment predicted by the prediction model, and the disturbance quantity predicted value at the k-1 moment, wherein the disturbance quantity predicted value at the 0 moment is 0;
predicting k + N at time k using the prediction modelpPredicted position output of time, where NpIs a prediction domain;
at time k, according to the sum of k + NpDesired position input at time and predicted k + NpThe ratio of the difference of the predicted position output at the time to the gain factor to obtain k + NcFinal trajectory compensation amount of time, wherein Nc≤Np-1；
According to the k + NcFinal track compensation and k + N of timecAnd the input phases of the expected positions at the moment are superposed and input into a closed-loop servo motion control system to control the rotation servo motor to operate.
The invention also provides a rotary servo motor track precompensation device based on the prediction model, which comprises the following components:
the prediction model building module is used for building a closed-loop transfer function of the rotating electrical machine according to system identification, building a prediction model for the actual position output at the moment k +1 according to the actual position output and the expected position input from the moment k-2 to the moment k and the disturbance quantity predicted value at the moment k by using the transfer function,
wherein the disturbance quantity predicted value at the k moment is estimated according to a vector difference between an actual position output at the k moment and a predicted position output at the k moment predicted by the prediction model, and the disturbance quantity predicted value at the k-1 moment, wherein the disturbance quantity predicted value at the 0 moment is 0;
a prediction domain prediction module for predicting k + N at time k using the prediction modelpPredicted position output of time, where NpIs a prediction domain;
a track compensation amount obtaining module for obtaining the compensation amount at the k moment according to the k + NpDesired position input at time and predicted k + NpThe ratio of the difference of the predicted position output at the time to the gain factor to obtain k + NcFinal amount of track compensation at time, where Nc≤Np-1；
A superposition input module for obtaining the k + NcFinal track compensation amount and k + N of timecAnd the input phases of the expected positions at the moment are superposed and input into a closed-loop servo motion control system to control the rotation servo motor to operate.
The invention has the following advantages and prominent technical effects: accurately predicting the output state of the motor at the future moment in the running process of the motor; good disturbance rejection capability; the effect of accurate compensation for track tracking errors; the improvement of the tracking control effect can be realized without changing the structure and parameters of a bottom controller of a servo motion control system.
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FIG. 1 is a block flow diagram of a method for trajectory precompensation based on a prediction model.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings and examples of the present invention, and it is apparent that the described embodiment is a specific embodiment, but not all embodiments, of the present invention for trajectory tracking control of a rotary servo motor. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In the present embodiment, N is setp＝2,N c1, withThe volume compensation amount is determined as follows:
according to system identification, establishing a closed-loop transfer function of the rotating motor:
Figure BDA0002920707330000031
wherein K is KaktrgFor equivalent gain parameter, k, of a closed-loop control system of a rotating electrical machinea、kt、rgThe parameters are respectively the gain of a driver current amplifier, the ratio of motor torque current and the motor transmission ratio, P, Y are respectively the actual position output and the expected position input of the motor, s is an operator of Laplace transform, J, B is respectively the equivalent mass and the friction damping coefficient of the rotating motor, and the parameters can be obtained by measurement or system identification in the practical application process. k is a radical ofp、ki、kdThe proportional, integral and differential parameters of the closed-loop PID controller can be determined according to the specific condition of the closed-loop servo controller;
as shown in FIG. 1, u is the voltage signal output by the PID controller, which is input to the driver kaI is the driver output current signal which is input to motor ktT is torque output by the motor, disturbance gammadOn the output of the motor. ω is the rotational angular velocity of the motor shaft, and θ is the rotational angular velocity of the motor shaft.
Figure BDA0002920707330000032
Represents the pair k + NpThe predicted value of the state at the moment,
Figure BDA0002920707330000033
for the delay step, future N determined by multiple iterations according to the state predicted valuecTime of day (i.e., k + N)cTime of day) of the track compensation amount signal is input into a register to store NcAnd outputting the corresponding track compensation amount when the corresponding time is reached.
Discretizing the obtained closed-loop transfer function, establishing a difference equation of the system, andfrom this, the following equivalent parameter α is calculated1，α2，α3，β1，β2，β3：
Figure BDA0002920707330000041
Wherein T issFor discrete control of the sampling period of the system, T in this embodiments＝0.2ms；
Obtaining a relationship between the predicted state and the known reference trajectory:
p(k+1)＝α1p(k)+α2p(k-1)+α3p(k-2)+β1y(k)+β2y(k-1)+β3y(k-2)
the known reference trajectory refers to the known actual position output and the known desired position input from time k-2 to time k,
where k represents the current time in discrete motion control, p (k) represents the actual position output at time k, i.e., the measured value of the encoder at time k, and y (k) represents the desired position input at time k, i.e., the position command input into the closed-loop system at time k;
the following relation is established:
Figure BDA0002920707330000042
wherein x (k) ═ p (k), p (k-1), p (k-2)]T，yr(k)＝[y(k),y(k-1),y(k-2)]TVector representations of actual position output and expected position input at adjacent times, respectively; y isp(k) P (k) is the actual position output at time k, γd(k) The sum of all equivalent external disturbances at the moment k can be obtained by a disturbance observer, and the following are provided:
Figure BDA0002920707330000043
wherein β ═ β1,β2,β3]And let α ═ α1,α2,α3]。
From the above, a prediction model of the predicted actual position output vector is obtained:
Figure BDA0002920707330000044
wherein
Figure BDA0002920707330000045
The predicted value is output for the actual position at the time k +1 at the time k;
Figure BDA0002920707330000046
the predicted disturbance amount of the external disturbance at the time k may be obtained through the calculation result in the subsequent S6.
Obtaining a disturbance quantity predicted value of disturbance
Figure BDA0002920707330000047
Figure BDA0002920707330000048
Wherein
Figure BDA0002920707330000049
A vector difference between a true value (encoder measurement value) output for the actual position at time k and an estimated value (the estimated value is calculated by the formula in S5 at time k-1), and
Figure BDA00029207073300000410
setting the prediction field to Np2 and determines k + N according to steps S5-S6pState vector prediction at time:
Figure BDA0002920707330000051
Figure BDA0002920707330000052
setting control field N c1, satisfies Nc≤Np-1; calculating a gain coefficient δ:
Figure BDA0002920707330000053
at the moment k, calculating a first partial track compensation amount y at the moment k +1 according to a known statec1(k +1) is:
Figure BDA0002920707330000054
wherein
Figure BDA0002920707330000055
Calculating k +1 moment, and comparing the tracking error vector with the first partial track compensation amount yc1(k +1) performing multiple iterative summations as final track compensation quantity
Figure BDA0002920707330000056
Figure BDA0002920707330000057
Wherein e (k) ═ yr(k)-x(k)＝[e(k),e(k-1),e(k-2)]TIs a tracking error vector;
Figure BDA0002920707330000058
representing the error accumulated by n iterations, wherein i is the ith iteration and n is the iteration number;
where e (k) is the vector difference between the actual position output and the desired position input at time k.
The invention also provides a rotary motor track pre-compensation device based on the prediction model, which can be installed in electronic equipment. The electronic device may include a processor, a memory, and may further include a computer program stored in the memory and executable on the processor. Wherein the memory comprises at least one type of readable storage medium including flash memory, removable hard disks, multimedia cards, card-type memory (e.g., SD or DX memory, etc.), magnetic memory, magnetic disks, optical disks, etc. The processor is a control core of the electronic device, connects various components of the entire electronic device using various interfaces and lines, and executes various functions of the electronic device and processes data by running or executing programs or modules stored in the memory and calling data stored in the memory.
According to the realized function, the rotary motor track pre-compensation device based on the prediction model can comprise a prediction model construction module, a prediction domain prediction module, a track compensation quantity obtaining module and a superposition input module. The module of the present invention refers to a series of computer program segments that can be executed by a processor of an electronic device and can perform a fixed function, and is stored in a memory of the electronic device.
In the present embodiment, the functions of the modules are as follows:
the prediction model building module is used for building a closed-loop transfer function of the rotating electrical machine according to system identification, building a prediction model for the actual position output at the moment k +1 according to the actual position output and the expected position input from the moment k-2 to the moment k and the disturbance quantity predicted value at the moment k by using the transfer function,
wherein the disturbance quantity predicted value at the k moment is estimated according to a vector difference between an actual position output at the k moment and a predicted position output at the k moment predicted by the prediction model, and the disturbance quantity predicted value at the k-1 moment, wherein the disturbance quantity predicted value at the 0 moment is 0;
prediction domainA prediction module for predicting k + N at time k using the prediction modelpPredicted position output of time, where NpIs a prediction domain;
a track compensation amount obtaining module for obtaining the compensation amount at the k moment according to the k + NpDesired position input at time and predicted k + NpThe ratio of the difference of the predicted position output at the time to the gain factor to obtain k + NcFinal trajectory compensation amount of time, wherein Nc≤Np-1；
A superposition input module for obtaining the k + NcFinal track compensation amount and k + N of timecAnd the input phases of the expected positions at the moment are superposed and input into a closed-loop servo motion control system to control the rotation servo motor to operate.
Further, the prediction model building module comprises:
the equivalent parameter obtaining unit is used for establishing a closed-loop transfer function of the rotating electrical machine according to system identification, and establishing a prediction model for the actual position output at the moment k +1 according to the actual position output and the expected position input from the moment k-2 to the moment k and the disturbance quantity predicted value at the moment k by utilizing the transfer function, and comprises the following steps:
the rotating machine closed loop transfer function is:
Figure BDA0002920707330000061
wherein K is equivalent gain parameter of the closed-loop control system of the rotating electrical machine, P, Y is actual position output and expected position input of the electrical machine respectively, s is an operator of Laplace transform, J, B is equivalent mass and friction damping coefficient of the rotating electrical machine respectively, and K isp、ki、kdRespectively are proportional, integral and differential parameters of a closed-loop PID controller;
establishing the equivalent parameter alpha1，α2，α3，β1，β2，β3：
Figure BDA0002920707330000062
Wherein T issA sampling period for a discrete control system;
the prediction model construction unit is used for establishing the relationship between the expected position input and the actual position output at the adjacent moment by using the equivalent parameters:
p(k+1)＝α1p(k)+α2p(k-1)+α3p(k-2)+β1y(k)+β2y(k-1)+β3y(k-2)
where k represents time, p (k) represents the actual position output at time k, and y (k) represents the desired position input at time k;
obtaining a relation between the actual position output at the moment k +1 and the sum of the actual position output at the moments k-2 to k, the expected position input and all equivalent external disturbances at the moment k:
Figure BDA0002920707330000071
wherein x (k) ═ p (k), p (k-1), p (k-2)]T，yr(k)＝[y(k),y(k-1),y(k-2)]TVector representations of actual position output and desired position input for adjacent time instants, respectively; y isp(k) P (k) is the actual position output at time k, γd(k) Is the sum of all equivalent external disturbances at time k, and has:
Figure BDA0002920707330000072
wherein β ═ β1,β2,β3]And let α ═ α1,α2,α3]；
A prediction model is derived for the predicted position output at time k + 1:
Figure BDA0002920707330000073
wherein
Figure BDA0002920707330000074
For the predicted position output at time k for time k +1,
Figure BDA0002920707330000075
and predicting the disturbance quantity of the external disturbance at the k moment.
Further, the prediction model construction module comprises a disturbance quantity prediction unit for estimating a disturbance quantity predicted value at the time k according to a vector difference between an actual position output at the time k and a predicted position output at the time k predicted by the prediction model and the disturbance quantity predicted value at the time k-1
Figure BDA0002920707330000076
The method comprises the following steps:
Figure BDA0002920707330000077
wherein
Figure BDA0002920707330000078
A vector difference between an actual position output for time k and a predicted position output for time k predicted by the prediction model, an
Figure BDA0002920707330000079
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The above description is only one embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent change and modification of the parameters and structures of the above embodiments according to the technical spirit of the present invention are still within the scope of the present invention.

Claims (9)

1. A rotary servo motor track precompensation method based on a prediction model is characterized by comprising the following steps:
establishing a closed-loop transfer function of the rotary servo motor according to system identification, establishing a prediction model for the actual position output at the moment k +1 according to the actual position output and the expected position input from the moment k-2 to the moment k and the predicted value of the disturbance quantity at the moment k by using the transfer function,
the disturbance quantity predicted value at the k moment is estimated according to a vector difference between the actual position output at the k moment and the predicted position output at the k moment predicted by the prediction model, and the disturbance quantity predicted value at the k-1 moment, wherein the disturbance quantity predicted value at the 0 moment is 0;
predicting k + N at time k using the prediction modelpPredicted position output of time, where NpIs a prediction domain;
at time k, according to the sum of k + NpDesired position input at time and predicted k + NpThe ratio of the difference of the predicted position output at the time to the gain factor to obtain k + NcFinal trajectory compensation amount of time, wherein Nc≤Np-1；
According to the k + NcFinal track compensation amount and k + N of timecAnd the input phases of the expected positions at the moment are superposed and input into a closed-loop servo motion control system to control the rotation servo motor to operate.
2. The rotary servo motor trajectory precompensation method based on a prediction model as claimed in claim 1, wherein said establishing a rotary servo motor closed-loop transfer function according to system identification, and using said transfer function to establish a prediction model for an actual position output at a time k +1 according to an actual position output and a desired position input at a time k-2 to k and a predicted value of a disturbance quantity at a time k, comprises:
the closed-loop transfer function of the rotary servo motor is as follows:
Figure FDA0003591844300000011
wherein K is equivalent gain parameter of the closed-loop control system of the rotary servo motor, P, Y is actual position output and expected position input of the motor respectively, s is an operator of Laplace transform, J, B is equivalent mass and friction damping coefficient of the rotary servo motor respectively, and Kp、ki、kdProportional, integral and differential parameters of a closed-loop PID controller are respectively;
establishing the equivalent parameter alpha1，α2，α3，β1，β2，β3：
Figure FDA0003591844300000012
Wherein T issA sampling period for a discrete control system;
establishing a relation between the expected position input and the actual position output at adjacent moments by using the equivalent parameters:
p(k+1)＝α1p(k)+α2p(k-1)+α3p(k-2)+β1y(k)+β2y(k-1)+β3y(k-2)
where k represents time, p (k) represents the actual position output at time k, and y (k) represents the desired position input at time k;
obtaining a relation between the actual position output at the moment k +1 and the sum of the actual position output at the moments k-2 to k, the expected position input and all equivalent external disturbances at the moment k:
Figure FDA0003591844300000021
wherein x (k) ═ p (k), p (k-1), p (k-2)]T，yr(k)＝[y(k),y(k-1),y(k-2)]TVector representations of actual position output and expected position input at adjacent times, respectively; y isp(k) P (k) is the actual position output at time k, γd(k) Is the sum of all equivalent external disturbances at time k, and has:
Figure FDA0003591844300000022
wherein beta is [ beta ]1,β2,β3]And let α ═ α1,α2,α3]；
A prediction model is derived for the predicted position output at time k + 1:
Figure FDA0003591844300000023
wherein
Figure FDA0003591844300000024
For the predicted position output at time k for time k +1,
Figure FDA0003591844300000025
and predicting the disturbance quantity of the external disturbance at the k moment.
3. The rotary servo motor trajectory precompensation method based on a predictive model according to claim 2,
estimating a disturbance amount predicted value at the k moment according to a vector difference between the actual position output at the k moment and the predicted position output at the k moment predicted by the prediction model and the disturbance amount predicted value at the k-1 moment
Figure FDA0003591844300000026
The method comprises the following steps:
Figure FDA0003591844300000027
wherein
Figure FDA0003591844300000028
Outputting and predicting the actual position at time kA difference in vector between predicted position outputs at time k predicted by the model, an
Figure FDA0003591844300000029
4. The rotary servo motor trajectory precompensation method based on a predictive model according to claim 3,
predicting k + N at time k by using the prediction modelpThe predicted position output at the time includes:
Figure FDA00035918443000000210
Figure FDA00035918443000000211
5. the rotary servo motor trajectory precompensation method based on a predictive model according to claim 2,
the gain factor δ is obtained as follows:
Figure FDA0003591844300000031
the subscript in the lower right corner represents the element in the corresponding position of the matrix in [ ].
6. The rotary servo motor trajectory precompensation method based on a predictive model according to claim 3,
at time k, according to the equation for k + NpDesired position input at time and predicted k + NpThe ratio of the difference of the predicted position output at the time to the gain factor to obtain k + NcThe final track compensation amount of the moment comprises:
at time k, k + N is obtainedcFirst partial trajectory compensation quantity y of timec1(k+Nc) Comprises the following steps:
Figure FDA0003591844300000032
wherein
Figure FDA0003591844300000033
Comparing the tracking error vector with the first partial track compensation amount yc1(k+Nc) Performing multiple iterative summations as k + NcFinal track compensation of time of day
Figure FDA0003591844300000034
The representation is as follows:
Figure FDA0003591844300000035
wherein e (k) ═ yr(k)-x(k)＝[e(k),e(k-1),e(k-2)]TIs a tracking error vector;
e (k) the vector difference between the actual position output and the desired position input for time k;
i is the ith iteration;
n is the number of iterations.
7. A rotary servo motor track pre-compensation device based on a prediction model is characterized by comprising:
the prediction model building module is used for building a closed-loop transfer function of the rotary servo motor according to system identification, building a prediction model for the actual position output at the moment k +1 according to the actual position output and the expected position input from the moment k-2 to the moment k and the disturbance amount predicted value at the moment k by utilizing the transfer function,
wherein the disturbance quantity predicted value at the k moment is estimated according to a vector difference between an actual position output at the k moment and a predicted position output at the k moment predicted by the prediction model, and the disturbance quantity predicted value at the k-1 moment, wherein the disturbance quantity predicted value at the 0 moment is 0;
a prediction domain prediction module for predicting k + N at time k using the prediction modelpPredicted position output of time, where NpIs a prediction domain;
a track compensation amount obtaining module for obtaining the compensation amount at the k moment according to the k + NpDesired position input at time and predicted k + NpThe ratio of the difference of the predicted position output at the time to the gain factor to obtain k + NcFinal trajectory compensation amount of time, wherein Nc≤Np-1；
A superposition input module for obtaining the k + NcFinal track compensation amount and k + N of timecAnd the input phases of the expected positions at the moment are superposed and input into a closed-loop servo motion control system to control the rotation servo motor to operate.
8. The apparatus according to claim 7, wherein the prediction model construction module comprises:
the equivalent parameter obtaining unit is used for establishing a closed-loop transfer function of the rotary servo motor according to system identification, and establishing a prediction model for the actual position output at the moment k +1 according to the actual position output and the expected position input from the moment k-2 to the moment k and the disturbance amount predicted value at the moment k by utilizing the transfer function, and comprises the following steps:
the closed-loop transfer function of the rotary servo motor is as follows:
Figure FDA0003591844300000041
wherein K is equivalent gain parameter of the closed-loop control system of the rotary servo motor, P, Y is actual position output and expected position input of the motor respectively, s is operator of Laplace transform, J, B is equivalent mass and friction damping coefficient of the rotary servo motor respectively,kp、ki、kdrespectively are proportional, integral and differential parameters of a closed-loop PID controller;
establishing the equivalent parameter alpha1，α2，α3，β1，β2，β3：
Figure FDA0003591844300000042
Wherein T issA sampling period for a discrete control system;
the prediction model building unit is used for building the relation between the expected position input and the actual position output at the adjacent time by using the equivalent parameters:
p(k+1)＝α1p(k)+α2p(k-1)+α3p(k-2)+β1y(k)+β2y(k-1)+β3y(k-2)
where k represents time, p (k) represents the actual position output at time k, and y (k) represents the desired position input at time k;
obtaining a relation between the actual position output at the moment k +1 and the sum of the actual position output at the moments k-2 to k, the expected position input and all equivalent external disturbances at the moment k:
Figure FDA0003591844300000043
wherein x (k) ═ p (k), p (k-1), p (k-2)]T，yr(k)＝[y(k),y(k-1),y(k-2)]TVector representations of actual position output and expected position input at adjacent times, respectively; y isp(k) P (k) is the actual position output at time k, γd(k) Is the sum of all equivalent external disturbances at time k, and has:
Figure FDA0003591844300000051
wherein beta is [ beta ]1,β2,β3]And let α ═ α1,α2,α3]；
A prediction model is derived for the predicted position output at time k + 1:
Figure FDA0003591844300000052
wherein
Figure FDA0003591844300000053
For the predicted position output at time k for time k +1,
Figure FDA0003591844300000054
and predicting the disturbance quantity of the external disturbance at the k moment.
9. The apparatus according to claim 7, wherein the prediction model construction module comprises:
a disturbance amount prediction unit for estimating a disturbance amount prediction value at time k based on a vector difference between an actual position output at time k and a predicted position output at time k predicted by the prediction model, and a disturbance amount prediction value at time k-1
Figure FDA0003591844300000055
The method comprises the following steps:
Figure FDA0003591844300000056
wherein
Figure FDA0003591844300000057
A vector difference between an actual position output for time k and a predicted position output for time k predicted by the prediction model, and
Figure FDA0003591844300000058
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