CN112859587B - PID target tracking control method based on additional integrated module - Google Patents
PID target tracking control method based on additional integrated module Download PDFInfo
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Abstract
The invention provides a PID target tracking control method based on an additional integrated module. In the field of target tracking control, since a target always moves at a low intermediate frequency, the tracking accuracy of the low intermediate frequency is a problem of general attention of the system. The method comprises the steps of firstly identifying a controlled object on a photoelectric tracking experiment platform, then designing a PID controller based on an additional integrated module, solving the problem of parameter adjustment in the controller by adopting a multi-target optimization algorithm, and finally completing the tracking of a target after implementing the control method provided by the invention. The performance index representing the tracking accuracy of the photoelectric tracking system is known to be error suppression capability, and after comparing a PID controller based on an additional integrated module with a PID control method without adding the integrated module, the error suppression capability of the control method provided by the invention at low and medium frequencies is obviously superior to that of a PID, thereby achieving the effect of improving the tracking accuracy.
Description
Technical Field
The invention belongs to the field of tracking control of a photoelectric system, and particularly relates to a PID (proportion integration differentiation) controller based on an additional integrated module, which is used for target tracking. The additional integrated module is added into the traditional PID controller to control the voltage signal of the motor, so that the error suppression capability of the system is effectively improved, and the tracking precision of the photoelectric tracking system is fully improved.
Background
The photoelectric tracking system consists of a main control system, a servo system, an image system, a signal transmission and equal division system, and the servo system drives the motor to rotate according to the output signal of the controller and the voltage after receiving the deviation signal of the image sensor, so that the tracking error is reduced. The design of the controller in the servo system is therefore an important factor affecting the tracking accuracy. In most cases, the system is always designed as a type-I system, that is, the open-loop transfer function of the system only contains one integral element, and at the moment, the system has a certain low-frequency error suppression capability. However, the tracking capabilities of this type of system are somewhat inadequate when performing fast object tracking tasks. Therefore, the document PID-I controller of charged coupled tracking loop for fast-steering mirror [ J ]. Optical Engineering,2011,50(4):043002. the PID-I controller is proposed to enable the system to have two integration links, thereby improving the non-static-error degree of the system; in addition, the adjustment parameters of the controller are considered from an amplitude margin and a phase margin, namely the amplitude margin is larger than or equal to 6dB, and the phase margin is larger than or equal to 45 degrees, so that the error suppression effect of 10dB improvement compared with the first-type system under the sampling frequency of 2KHz is obtained. However, the document does not consider the problem that the stability is reduced due to the phase lag because the system type is improved. Based on this, the document "A comprehensive performance improvement control method by fractional order control" [ J ]. IEEE Photonics Journal,2018,10(5):1-11. the controller is subjected to fractional order exploration, namely the type of the system is between one type and two types, but not integral multiple of the number of integral links; the controller has the advantage of higher error rejection than the one-type system, but has less phase lag than the two-type system, so the method adopts a compromise method to improve the tracking accuracy of the system. From the basic theory of signal and information processing, it can be seen that any complex signal is compounded by a plurality of sine waves with different frequencies and different sizes. From the control theory, a higher-type control loop has the capability of suppressing higher-order tracking errors, so that a high-type system always belongs to a research hotspot in order to reduce the tracking errors of the system as much as possible. Meanwhile, the disadvantage of the high-type loop is an unstable phenomenon caused by phase lag, and parameter adjustment work of the controller is still important in order to better apply the advantages of the control algorithm.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in order to improve the tracking precision of a tracking system, the invention provides a PID target tracking control method based on an additional integrated module. The method adds an integrated module on the basis of the original PID controller, and aims to improve the type of a control loop to three types, thereby improving the tracking accuracy of a tracking system. Meanwhile, the problem of parameter adjustment of the controller based on the multi-target optimization algorithm NSGA-II is also solved.
The technical scheme adopted by the invention for solving the technical problems is as follows: a PID target tracking control method based on an additional integrated module comprises the following specific steps:
step (1), installing an image sensor (CCD) on a tracking platform, and testing the position characteristics of a controlled object by a Dynamic Signal Analyzer (DSA), thereby obtaining a position object model G p (s)；
Step (2) at the acquisition positionControlled object model G p On the basis of(s), a Proportional-Integral-Derivative (PID) controller C is designed P (s), wherein the proportional link exists to reduce the tracking error of the system, and the integral link exists to improve the no-static-error degree of the system; the differential link exists to improve the dynamic performance of the system;
step (3) in the designed PID controller C P Adding an additional integrated module C on the basis of(s) a (s) forming a PID controller C based on the additional integrated module m (s) wherein the module C is integrated a (s) the purpose is to upgrade the type of system to three, thus upgrading the system to be free of slack;
step (4) aiming at PID controller C based on additional integrated module m The undetermined parameters of(s) are obtained by optimizing a multi-target optimizing Algorithm, namely a Non-poor ordering Genetic Algorithm (NSGA-II), wherein the performance indexes are as follows: system bandwidth, system error rejection ratio and stability margin interval;
step (5), designing a PID controller C based on an additional integrated module m (s), the tracking method is applied to an actual system to generate a voltage signal to control a motor, so that the target is tracked; after comparing with the PID control method without adding an integrated module, the effect of improving the tracking precision is achieved.
By utilizing the five steps, the target can be tracked through the PID controller based on the additional integrated module. Firstly, the image sensor detects a system tracking error signal, secondly, the error signal is input into the position controller to obtain a voltage signal, and the motor is controlled, so that the tracking platform rotates, the tracking error is gradually reduced, and the tracking task is completed. Finally, by comparison, the tracking accuracy of the control method provided by the invention at low and medium frequency (target motion frequency band) is obviously superior to that of PID, and the effect of improving the tracking accuracy is achieved.
Compared with the prior art, the invention has the following advantages:
(1) compared with the traditional one-type loop control method, the tracking controller provided by the invention has higher tracking precision and has the advantage of tracking a faster target;
(2) compared with the common control method for improving the tracking precision, such as sensor signal fusion, an error observer and the like, the tracking controller provided by the invention does not need to introduce an additional control loop or sensor;
(3) compared with the traditional method for adjusting the parameters of the controller by using the numerical values, the method provided by the invention fully considers the principle of conservation of system performance, considers the problems from the perspective of multi-performance indexes, and is more comprehensive;
(4) the invention has low cost and small calculation amount, fully utilizes the conditions of the system and does not add extra cost, space, load and power consumption to the system.
Drawings
FIG. 1 is a control block diagram of the present invention;
FIG. 2 is a physical schematic of the platform drive motor and load;
FIG. 3 is a diagram of a system position model fit;
FIG. 4 is a closed loop Bode diagram of the system position;
the system of fig. 5 uses pure PID versus Bode plot for error rejection based on additional integration module PID.
Detailed Description
Embodiments of the present invention are described below with reference to the drawings. The following examples are only illustrative of the present invention, and the scope of the present invention shall include the full contents defined by the claims; and the claims of the present invention can be realized in their entirety by those skilled in the art from the following examples.
The invention relates to a PID target tracking control method based on an additional integrated module, which specifically comprises the following steps:
(1) the control block diagram of the present invention is shown in fig. 1. The block diagram uses the output signal y to perform a tracking function on the input signal r. Wherein G(s) is a position controlled object measured by the image sensor, C(s) is a controller for outputting a voltage signal u, e is a tracking error detected by the image sensor, F(s) is an open-loop transfer function, and T(s) is a closed-loop transfer function.
Taking the tracking process of the photoelectric tracking experiment platform driven by the voice coil motor in a single direction as an example, the model is simplified and analyzed, as shown in fig. 2. The circuit balance principle can be used as follows:
wherein U is a Is the armature voltage of the voice coil motor, K b Is the motor back emf coefficient, θ a Being the deflection angle of the platform, R a Is the motor armature loop resistance, I a Is the motor armature loop current, L a Is the motor armature loop inductance, and t is time.
The motor moment balance equation can be obtained:
wherein C is m Is the force coefficient of the voice coil motor, I a For the motor armature loop current, d is the distance from the elastic support to the center of the voice coil motor, J is the load moment of inertia of the platform, and theta a Angle of deflection of the platform, f m Is the mechanical damping coefficient of the platform, K is the elastic support elastic coefficient, and t is the time.
The circuit balance principle and the motor moment balance equation are combined to eliminate I a (t) and the driving input voltage U is obtained by Laplace change a And an output deflection angle theta a The transfer function of (c):
where s is the laplacian operator.
Therefore, the transfer model of the platform deflection angle and the input voltage is presented as an approximate third-order filter link. Since the numerator is constant, at a low frequency band, the input voltage and the output angle can be regarded as a proportional characteristic, which also indicates that the input voltage corresponds to the output angle position in a physical dimension. According to the polynomial theory, a third-order polynomial of a denominator always has a real number, so that a transfer function of a platform can be decomposed into series connection of a proportional link, an inertia link and a second-order oscillation link.
Wherein K is the coefficient of inertia element, T e Is an inertia coefficient of a first-order inertia link,
the second-order oscillation link natural frequency is obtained, xi is the second-order oscillation link damping ratio, and s is a Laplace operator.
(2) Fig. 3 shows a graph of the position transfer function Bode of the system obtained from the system sweeping the measured values. The solid line represents the measured curve, and the dotted line is the object obtained after identification according to the typical link.
After the object identification of fig. 3, the position loop PID controller is designed by using the zero-pole cancellation principle:
wherein the proportional link parameters
Differential link parameter
The undetermined parameter is an integral link parameter k i And T c 。
Controller molecule part
The second-order oscillation link in the denominator of the controlled position object is used for zero-pole cancellation and the inertia link
Is a low-pass filter, in order to ensure controlSystem ware C p Causality of(s) and at the same time for filtering out high frequency noise.
(3) Designing PID controller C based on additional integrated module m (s) driving the motor.
Integrated module C a (s) and PID controller C based on additional integrated module m (s) are respectively represented as:
wherein k, a and b respectively represent the proportional element and the coefficients of two first-order differential elements in the integrated module, and k c ＝kk i . Due to T c Is a low-pass filter which is always set near one-half sampling frequency point, the sampling frequency is 1 KHz, and T is set in the experiment c Set to 0.00032. The undetermined parameter is therefore k c ,a,b。
(4) Method for solving undetermined parameter k through NSGA-II multi-target optimization algorithm c ,a,b。
Wherein, the performance indexes are respectively:
wherein, J 1 ,J 2 ,J 3 Respectively representing the bandwidth, the error rejection ratio and the performance index of a stability margin interval, omega B Represents the frequency point, omega, corresponding to the amplitude value of-3 dB in the closed loop Bode diagram of the system 0 And ω c Respectively representing the initial frequency and the open-loop cut-off frequency, | E of the system m (j ω) | is the absolute value of the amplitude of the system frequency domain error suppression function in the Bode graph amplitude-frequency curve, and s ═ j ω; omega b And omega a Respectively represents two frequency points corresponding to the phase margin of 45 degrees in the open loop Bode graph phase-frequency curve of the system, and omega b ＞ω a . Selecting a set of parameters with the highest error suppression ratio, namely k, in the final optimization result c ＝5990,a＝1.2,b＝0.03。
(5) The closed loop characteristics were measured by applying the controller to the actual system, and a Bode plot of the closed loop position of the system is shown in fig. 4, which shows the tracking bandwidth around 5 hz.
(6) Pure PID controller C is adopted for comparison p (s) and PID controller C based on additional integrated module m Error suppression capability of(s), fig. 5 shows two systematic error suppression characteristics compared to Bode plots.
By comparison, it can be seen that the tracking error suppression curve is improved below 3.3 hz (low-if) by using the method of the present invention. Specifically, there is a boost effect of around 10dB at 1 hz. Because the target always moves at a low intermediate frequency, the method can effectively improve the tracking accuracy of the tracking system and has the potential of tracking a faster target.
And (4) completing the control method for realizing target tracking through the PID controller based on the additional integrated module by utilizing the six steps. The tracking accuracy of the tracking system is improved under the condition that a control loop is not added and an additional sensor is not introduced.
Parts of the invention not described in detail are well known in the art.
Claims (4)
1. A PID target tracking control method based on an additional integrated module is characterized in that: the method comprises the following steps:
step (1), installing an image sensor on a tracking platform, and carrying out CCD: Charge-Coupled Device, measured by dynamic signal analyzer, DSA: a Dynamic Signal Analyzer for testing the position characteristics of the controlled object so as to obtain a position controlled object model G p (s)；
Step (2) of obtaining the controlled object model G at the position p On the basis of(s), a Proportional-Integral-Derivative (PID) controller C is designed P (s), wherein the proportional element is used for reducing the tracking error of the system, and the integral element is used for improving the no-static-error of the systemDegree; the differential link exists to improve the dynamic performance of the system;
step (3) in the designed PID controller C P Adding an additional integrated module C on the basis of(s) a (s) forming a PID controller C based on the additional integrated module m (s) wherein an integrated module C is added a (s) the purpose is to upgrade the type of system to three, thus upgrading the system to be free of slack;
for additional integrated modules C in step (3) a (s) and PID controller C based on additional integrated module m (s), the expression is as follows:
in the above formula, k, a and b are each C a (s) the coefficient of the proportional element, the two first order differential elements, and k c ＝kk i From a PID controller C based on an add-on integrated module m (s) expression, it can be seen that P (s) two integral operators, two first order differential links and a proportion link are introduced on the basis, wherein the integral link is used for improving the tracking precision of the tracking system, but 180-degree phase lag is introduced for the system, so that the two first order differential links are used for improving the phase of the system, and the phenomenon of system instability caused by too low open loop stability margin is avoided; the proportion link exists for finally adjusting the open loop gain of the open loop system;
step (4) aiming at PID controller C based on additional integrated module m The undetermined parameter(s) is obtained by optimizing a multi-target optimizing Algorithm, namely a Non-poor ordering Genetic Algorithm NSGA-II, a Non-Dominated sequencing Genetic Algorithm II, wherein the performance indexes are as follows: system bandwidth, system error rejection ratio and stability margin interval;
step (5),By designing PID controller C based on additional integrated module m (s), the tracking method is applied to an actual system to generate a voltage signal to control a motor, so that the target is tracked; after comparing with the PID control method without adding an integrated module, the effect of improving the tracking precision is achieved.
2. The PID target tracking control method based on the additional integration module as claimed in claim 1, wherein: when DSA is adopted to measure the controlled object in the step (1), the input signal is a sine sweep voltage signal, and the output signal is a position signal of an image sensor, so that a position controlled object model G is obtained p (s); secondly, offline identification is carried out on the actually measured curve, the type of the curve belonging to a typical link is preliminarily judged according to the trend of the curve, and then the size of parameters in the typical link is finely adjusted.
3. The PID target tracking control method based on the additional integrated module according to claim 1, wherein: the PID controller expression in the step (2) is as follows:
in the above formula, k p ,k i ,k d The coefficients of the proportional, integral and differential links, T c Is to make C P (s) satisfy causal inertial element coefficients, s being the frequency domain "laplacian" operator.
4. The PID target tracking control method based on the additional integration module as claimed in claim 1, wherein: in the step (4), because the performance of the system is conserved and each performance index of the actual system is sometimes mutually exclusive, based on the bandwidth and the error rejection ratio, the stability margin interval is used as a measure index for solving the controller parameter by the NSGA-II, and the performance index expression is as follows:
wherein, J 1 ,J 2 ,J 3 Respectively representing the performance indexes of bandwidth, error rejection ratio and stability margin interval, omega B Represents the frequency point, omega, corresponding to the amplitude value of-3 dB in the closed loop Bode diagram of the system 0 And ω c Respectively representing the initial frequency and the open-loop cut-off frequency, | E of the system m (j ω) | is the absolute value of the amplitude of the system frequency domain error suppression function in the Bode graph amplitude-frequency curve, and s ═ j ω; omega b And omega a Respectively represents two frequency points corresponding to the phase margin of 45 degrees in the open loop Bode graph phase-frequency curve of the system, and omega b >ω a ；
By utilizing the steps (1) to (5), the target can be tracked through a PID controller based on an additional integrated module, firstly, an image sensor detects a system tracking error signal, secondly, the error signal is input into the position controller to obtain a voltage signal, and a motor is controlled, so that a tracking platform rotates, the tracking error is gradually reduced, and a tracking task is completed; finally, by comparison, the tracking accuracy of the control method at low and medium frequencies, namely the target motion frequency band, is obviously superior to that of a PID (proportion integration differentiation), and the effect of improving the tracking accuracy is achieved.
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