CN113985736A - Smith predictor control method and device based on least square - Google Patents

Smith predictor control method and device based on least square Download PDF

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CN113985736A
CN113985736A CN202111250068.1A CN202111250068A CN113985736A CN 113985736 A CN113985736 A CN 113985736A CN 202111250068 A CN202111250068 A CN 202111250068A CN 113985736 A CN113985736 A CN 113985736A
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smith predictor
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罗勇
郭珊珊
赵雨萱
贺伟
赵兴强
丁宇
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses a Smith predictor control method based on least square and a device thereof, belonging to the field of target tracking control of a photoelectric tracking system, aiming at the problem that the traditional Smith predictor control method in the photoelectric tracking system can only improve the control performance of the system by separating time lag and cannot directly compensate the time lag to cause the limited improvement of tracking precision.

Description

Smith predictor control method and device based on least square
Technical Field
The invention belongs to the field of target tracking control of photoelectric tracking systems, and particularly relates to a Smith predictor control method and a Smith predictor control device based on least square.
Background
In the photoelectric tracking system, a control module calculates corresponding control quantity based on a visual axis deviation value extracted by a CCD image sensor so as to drive a frame to rotate, and the tracking of a maneuvering target is completed. In order to obtain a sharp image, a long processing time is usually required, resulting in a low sampling rate of the system with a non-negligible time lag. The time lag may limit the tracking bandwidth of the system, causing degradation in control performance, thereby affecting the boresight tracking accuracy. In order to compensate the influence of time lag on the control performance, a time lag compensation method called a Smith predictor widely applied to the industrial control field is introduced into the photoelectric tracking control field, the Smith predictor performs advanced feedback by using model output without time lag to approximately separate the time lag from a closed loop so as to reduce the influence of the time lag on the stability of the system and further improve the control performance of the system by improving gain. In the document Improved Smith predictor control for fast maintaining minor system (Iop Conference Series: Earth & Environmental Science,2017), a controlled object model is modified by using a fiber-optic gyroscope, and a closed-loop model is used as the controlled object model, so that the control performance of the Smith predictor under the condition of parameter perturbation is Improved, but the performance improvement effect of the system is still limited by time lag mismatch and time lag outside the closed loop. The document "Stabilization Control System with Fiber-Optical gyroscopic Based on Modified Smith Predictor Control Scheme" constructs an improved Smith Predictor with disturbance observation performance in a speed closed loop, so that the influence of speed loop time lag on Control performance can be reduced, and the inertial stability of a visual axis can be improved at the same time, but the method does not directly compensate time lag, and the time lag separated out of the closed loop still causes the deviation between output and input, so that the improvement of the Tracking precision of the System is limited; aiming at the problems, a structure for predicting and extrapolating the track signal at the past moment by a least square method is provided, and the signal time lag is directly compensated on the basis of the separation time lag, so that the tracking precision of the system is further improved.
Disclosure of Invention
Aiming at the fact that the traditional Smith predictor method can only improve the control performance by separating the time lag of a closed-loop system and does not directly compensate the time lag, the method proposes that on the basis of the traditional Smith predictor, the track signal of the past moment extracted by the Smith predictor structure is extrapolated and predicted based on the least square method, the signal time lag is directly compensated, and the tracking performance of the system can be further improved.
In order to achieve the purpose of the invention, the invention provides an improved Smith predictor control method based on least square prediction, which comprises the following specific implementation steps:
step (1): the optical fiber gyroscope is arranged on the photoelectric tracking platform of the fast reflecting mirror and used for respectively sensing the moving speed of two shafts of the platform in an inertial space, the CCD image sensor is arranged on the tracking equipment, and target miss distance information with time lag is output.
Step (2): high-precision speed object model of platform acquired by frequency response tester
Figure BDA0003322322970000021
It is a real object model GvAn approximation of;
and (3): obtaining a speed controlled object model
Figure BDA0003322322970000022
On the basis of (2), designing a speed controller CvRealizing speed closed loop; design position controller C on outer ring of CCD positionpAnd position closed loop is realized, so that double closed loop control of speed and position is established.
And (4): the classical Smith predictor structure is constructed at the position loop: adding a negative feedback integral link 1/s at a position controller to construct a rapid position loop; passing CCD miss distance and speed given signal through position object model
Figure BDA0003322322970000023
The outputs of which are superimposed to obtain an intermediate signal r as input to the fast position loop, at which time the gain of the position controller can be increased to increase the gainThe bandwidth is increased.
And (5): a least square prediction link is added in front of a fast position ring structure of a classic Smith predictor, and a least square algorithm is applied to predict and extrapolate an intermediate signal r to estimate a target track at the current moment as the input of the fast position ring.
In the step (1), the fiber-optic gyroscope has high precision, high sampling rate and small lag time which can be ignored; the CCD image sensor has low sampling rate and non-negligible lag time.
Speed controller C of step (3)vAnd designing by adopting a pole-zero object method so that the compensated open-loop object becomes a type 1 system. The transfer function of the velocity loop is high due to the high bandwidth of the velocity loop
Figure BDA0003322322970000024
Can be viewed as an ideal transfer model 1. The positional object model is thus approximated as
Figure BDA0003322322970000025
Wherein tau ismFor the model of the system time lag τ obtained by identification, the position controller C is nowpCan be designed as a proportional controller.
In step (4), the transfer function of the intermediate signal r is as follows:
Figure BDA0003322322970000026
where R is the target given signal, typically τ ≈ τmIf < 1, R is approximately equal to R.e within the control bandwidth range-τsThe intermediate signal r is a target track signal at a past time within the bandwidth.
And (5) fitting the latest historical track points by using a least square algorithm to obtain an optimal fitting model, replacing the oldest track point when a new track point is received, then re-fitting to update fitted model parameters, and then extrapolating and calculating the target track at the current moment according to the lag time of the CCD to be used as the input of a quick position ring in the Smith predictor structure.
Compared with the prior art, the invention has the following advantages:
(1) the method deduces and analyzes the Smith structure, can separate time lag and has the function of extracting the target track at the past moment.
(2) Compared with the existing Smith predictor method, the method has the function of separating time lag, has the capability of directly compensating the time lag through least square track prediction, and can remarkably improve the low-frequency tracking capability of the system.
(3) The invention has clear thought, simple structure and easy realization in engineering.
Drawings
FIG. 1 is a control block diagram of an improved Smith predictor control method based on least squares prediction in accordance with the present invention;
FIG. 2 is a time domain plot of the target reference signal, the intermediate signal r, and the least squares prediction signal at different frequencies of the present invention;
fig. 3 is a graph comparing the error suppression capability of the present invention with respect to a dual closed loop of velocity position, and a dual closed loop with the addition of a conventional Smith predictor.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
Fig. 1 is a control block diagram of a method for controlling an improved Smith predictor based on least square prediction, which includes a speed loop, a position loop and a Smith predictor including an additional least square prediction link Q; a least square prediction link is added in the structure of the traditional Smith predictor, so that the system time lag can be separated from a closed loop, the time lag can be directly compensated, and the influence of the time lag on the tracking precision can be compensated to the maximum extent theoretically. The concrete implementation steps of the device for realizing the time lag compensation are as follows:
step (1): the optical fiber gyroscope is arranged on the photoelectric tracking platform of the fast reflecting mirror and used for respectively sensing the moving speed of two shafts of the platform in an inertial space, the CCD image sensor is arranged on the tracking equipment, and target miss distance information with time lag is output.
Step (2): high-precision speed object model of platform acquired by frequency response tester
Figure BDA0003322322970000031
Model (model)
Figure BDA0003322322970000032
Is a real object model GvThe approximation of (2) is convenient for designing a high-bandwidth speed inner ring, and a speed object model is as follows:
Figure BDA0003322322970000033
wherein the content of the first and second substances,
Figure BDA0003322322970000034
is the natural oscillation frequency, xi is the damping coefficient, TeIs an electrical time constant. Adjustment of platform baud curves using spectrometer measurements
Figure BDA0003322322970000035
And the parameters enable the fitting curve to be basically superposed with the measured curve, so that the platform high-precision model is obtained.
And (3): obtaining a speed controlled object model
Figure BDA0003322322970000041
On the basis of (2), designing a speed controller CvRealizing speed closed loop; design position controller C on outer ring of CCD positionpAnd establishing speed and position double closed loop control. In the design process of each controller, in order to enable the compensated speed object to become a type 1 system, a zero-pole cancellation method is adopted, and a designed speed controller C is adoptedvThe model references are as follows:
Figure BDA0003322322970000042
wherein, KvFor the gain of the controllerThe anti-resonance link of the molecule is used for compensating resonance in the velocity object model, the double-integration link is used for compensating the differential link of the object and transforming the system into a first-order integration system, and the inertia link filters high-frequency noise. After the velocity is closed-loop, the object properties are improved, so the position object model is approximated as
Figure BDA0003322322970000043
Wherein tau ismFor the model of the system time lag τ obtained by identification, the position controller can be designed as Cp＝Kp。
And (4): the classical Smith predictor structure is constructed at the position loop: adding a negative feedback integral link 1/s at a position controller to construct a rapid position loop; passing CCD miss distance and speed given signal through position object model
Figure BDA0003322322970000044
The outputs of which are superimposed to obtain an intermediate signal r which is used as the input of the fast position loop, and at this time, the gain of the position controller can be increased to increase the bandwidth. Wherein the transfer function of the intermediate signal r is as follows:
Figure BDA0003322322970000045
where R is a given target signal, typically τ ≈ τmIf < 1, R is approximately equal to R.e within the control bandwidth range-τsThe intermediate signal r is a target track signal at a past time within the bandwidth.
And (5): a least square prediction link is added in front of a fast position loop structure of a classic Smith predictor, the latest historical track point is fitted by using a least square algorithm to obtain an optimal fitting model, the oldest track point is replaced when a new track point is received, fitting is conducted again to update fitting model parameters, a target track of the current moment is calculated by extrapolation according to the lag time of a CCD, the lag time contained in an intermediate signal r is compensated, the intermediate signal r is used as the input of the fast position loop in the Smith predictor structure, and the low-frequency target tracking capability of the system is improved.
The following describes the design process and experimental effect of the present invention in detail by taking a certain photoelectric tracking platform system as an example:
(1) the velocity transfer function model of the system obtained by frequency domain response fitting is as follows, because the fitting precision is high, the fitting model can be regarded as a real object in the design process.
Figure BDA0003322322970000046
(2) With the velocity model, the velocity controller is designed as follows:
Figure BDA0003322322970000051
(3) the sampling rate of the CCD image sensor is 50Hz, the time lag obtained by fitting is 0.02s, and the gain of the position controller with a pure double closed loop is designed to be Cp＝20。
(4) With the addition of the Smith controller, the gain of the position controller may be increased to Cp＝60。
(5) The least square algorithm adopts a linear quadratic polynomial as a fitting model, and comprises the following specific steps:
Figure BDA0003322322970000052
in the experiment, trajectory data of past 50 points are selected for fitting to obtain an optimal fitting model, an oldest trajectory point is replaced when a new trajectory point is received, fitting is performed again to update fitted model parameters, and a target trajectory at the current moment is calculated according to delay time extrapolation of a CCD and used as input of a quick position loop.
Fig. 2 is a time domain comparison of the target reference signal, the intermediate signal r and the least squares predicted trajectory signal at different frequencies. Under 1Hz, after least square prediction extrapolation, the lag of the intermediate signal r is well compensated, and the compensated track is almost overlapped with a target reference track signal; at 2Hz, least squares prediction can also be partially compensated, but the performance is degraded, causing distortion in the signal amplification. Therefore, the least square trajectory prediction method mainly focuses on low frequency bands.
Under the same experimental conditions, comparing error suppression residuals of a speed position double closed loop, adding a traditional Smith predictor and adding an improved Smith predictor control method, as shown in fig. 3, is a comparison graph of error suppression capability of the invention. Compared with a pure double closed-loop structure, the low-frequency error suppression capability of the system after the traditional Smith predictor is added is improved, but the error suppression capability is still limited, when the Smith predictor improved by least square prediction is used, the error suppression capability of the system below the low frequency is further obviously improved, and the low-frequency suppression effect aimed by the invention is particularly suitable for tracking the remote target with the signal mainly distributed at the low frequency.
Further, a Smith predictor control apparatus, comprising:
smith predictor: the Smith predictor is designed based on the mathematical model parameters of the controlled object obtained through calculation, and comprises a control error signal calculation unit and a parameter acquisition unit;
a Smith predictor parameter acquisition unit; collecting and processing the target reference signal and the intermediate signal and transmitting the processing result to the control error signal calculation unit;
a control error signal calculation unit which predicts and extrapolates a track signal at a past time by a least square method and directly compensates a signal time lag on the basis of a separation time lag to generate a control model;
a controller: the controller generates a control signal by using the control error signal and outputs the control signal to the controlled object to control the controlled object;
and (3) predicting and extrapolating the intermediate signal r by using a least square algorithm, estimating a target track at the current moment, taking the target track as the input of the rapid position loop, and outputting the target track to the controlled object to control the controlled object.
Further, a calculation execution apparatus for executing a Smith predictor control method.
Further, a storage medium, wherein the storage medium stores instructions for executing a Smith predictor control method.
The present invention is capable of various embodiments and modifications without departing from the spirit and scope of the invention in its broadest form. The above embodiments are intended to illustrate the present invention, and do not limit the scope of the present invention. That is, the scope of the present invention is shown by the scope of claims, not by the embodiments. Various modifications made within the scope of the claims and within the scope of the equivalent meaning to the claims are also considered to be within the scope of the present invention.

Claims (10)

1. A Smith predictor control method based on least square is characterized in that the control method applies a least square algorithm to predict and extrapolate an intermediate signal r, estimate a target track of the current moment and compensate signal time lag.
2. A least squares based Smith predictor control method as claimed in claim 1, wherein the control method comprises the steps of:
installing a fiber optic gyroscope on a quick reflection mirror photoelectric tracking platform, and installing a CCD image sensor on tracking equipment;
high-precision speed object model of platform acquired by frequency response tester
Figure FDA0003322322960000015
Obtaining a speed controlled object model
Figure FDA0003322322960000016
On the basis of (2), designing a speed controller CvRealizing speed closed loop; design position controller C on outer ring of CCD positionpRealizing position closed loop and establishing speed and position double closed loop control;
the classical Smith predictor structure is constructed at the position loop: adding a negative feedback integral link 1/s at a position controller to construct a rapid position loop; passing CCD miss distance and speed given signal through position object model
Figure FDA0003322322960000017
The outputs of the two are superposed to obtain a middle signal r which is used as the input of the fast position loop;
a least square prediction link is added in front of a fast position ring structure of a classic Smith predictor, and a least square algorithm is applied to predict and extrapolate an intermediate signal r to estimate a target track at the current moment as the input of the fast position ring.
3. A least squares based Smith predictor control method as claimed in claim 2 wherein said speed controller CvAnd designing by adopting a pole-zero object method so that the compensated open-loop object becomes a type 1 system.
4. A least squares based Smith predictor control method as claimed in claim 3 wherein the transfer function of the type 1 system is:
Figure FDA0003322322960000011
wherein, KvIn order to control the gain of the controller,
Figure FDA0003322322960000012
is the natural oscillation frequency, xi is the damping coefficient, T1Is the time constant of inertia.
5. A least squares based Smith predictor control method as claimed in claim 2 wherein the transfer function of the position object model is: is composed of
Figure FDA0003322322960000013
Wherein tau ismIs a model of the system time lag tau obtained by identification.
6. The method for controlling the Smith predictor based on the least square as claimed in claim 2, wherein a negative feedback integral link 1/s is added to the position controller to construct a rapid position loop; passing CCD miss distance and speed given signal through position object model
Figure FDA0003322322960000014
The outputs of which are superimposed to obtain an intermediate signal r as input to the fast position loop.
7. A least squares based Smith predictor control method as claimed in claim 6, wherein the transfer function of the intermediate signal r is:
Figure FDA0003322322960000021
where R is a given target signal, τ is the system time lag, τmFor time-lag models obtained by identification, CpFor position control, V is a closed loop transfer function of velocity.
8. A Smith predictor control apparatus, comprising:
smith predictor: the Smith predictor is designed based on the mathematical model parameters of the controlled object obtained through calculation, and comprises a control error signal calculation unit and a parameter acquisition unit;
a Smith predictor parameter acquisition unit; collecting and processing the target reference signal and the intermediate signal and transmitting the processing result to the control error signal calculation unit;
a control error signal calculation unit which predicts and extrapolates a track signal at a past time by a least square method and directly compensates a signal time lag on the basis of a separation time lag to generate a control model;
a controller: the controller generates a control signal by using the control error signal and outputs the control signal to the controlled object to control the controlled object;
and (3) predicting and extrapolating the intermediate signal r by using a least square algorithm, estimating a target track at the current moment, taking the target track as the input of the rapid position loop, and outputting the target track to the controlled object to control the controlled object.
9. A computation execution apparatus for executing a Smith predictor control method as set forth in claim 2.
10. A storage medium storing a Smith predictor control method as defined in claim 2.
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