CN112462610B - Multistage multi-order hysteresis correction network control method for photoelectric tracking system - Google Patents
Multistage multi-order hysteresis correction network control method for photoelectric tracking system Download PDFInfo
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Abstract
The invention discloses a multistage and multistage lag correction network control method of a photoelectric tracking system, which adopts a multistage and multistage lag correction network arranged according to a specific rule to realize high-precision tracking and automatic setting of control parameters in a working frequency band of the photoelectric tracking system under the conditions of not changing the frame of the existing control system and not influencing the relative stability of the system. Compared with the existing photoelectric tracking control system, the method improves the tracking precision, weakens the contradiction between the tracking precision and the stability in the current photoelectric tracking system, and solves the problems of unclear design basis and parameter setting of designers in the design.
Description
Technical Field
The invention relates to the field of control of photoelectric tracking systems, in particular to a multistage and multistage hysteresis correction network control method for a photoelectric tracking system, which is suitable for a high-precision photoelectric tracking system which has higher requirements on tracking precision and stability margin and can be quickly realized without design personnel having rich control system design experience.
Background
In the fields of photoelectric measurement, laser communication, astronomical observation and the like, a photoelectric system plays an important role as an execution mechanism for quickly and accurately finding and tracking a target. In recent years, with the increase of detection distance and the enhancement of rapidity and maneuverability of tracking targets, higher requirements are put on the tracking accuracy of a photoelectric tracking system, and challenges are brought to corresponding photoelectric tracking control technologies. In order to achieve the above object, the photoelectric tracking control system needs to have a stronger tracking error suppression capability.
From the perspective of control system design, the most effective method for improving the error suppression capability of the photoelectric tracking system is to improve the control bandwidth of the system or increase the gain within the bandwidth. The bandwidth increase range is limited by factors such as the mechanical characteristics of the system and the data transmission delay, and the cost increase caused by bandwidth increase is high. Increasing the gain within the system bandwidth is a design idea preferred by the designers of general control systems, and the most direct method is to increase the number of system integrators. On the premise of unchanged bandwidth, the more the number of integrators is, the larger the low-frequency gain of the system is, and the stronger the suppression capability of the tracking error is. For example, tang Tao et al, PID-I type controller proposed in "PID-I controller of charged coupled device-based tracking loop for fast-maintaining mixer" in 2011, improves the error suppression capability in the low-frequency band in the photovoltaic system by adding two integrators; the dynamic high-type control of the Changchun optical machine in the servo system of the electro-optic theodolite also realizes the high tracking precision of the electro-optic system by adding a plurality of integrators. However, these methods have not been widely used in engineering, and the most important reason is that the phase loss caused by the integrator is unavoidable, and the phase loss causes the stability margin of the system to be greatly reduced and even causes instability phenomenon in some cases, so that the engineering application of these methods is limited. The lead-lag calibration method, for example, published in 2009 in Automatica under the heading "Synthesis of phase-lead/lag modulators with complete information on gain and phase indexes", can simulate an integral operator in a certain frequency band to improve the gain of the system, but also brings about phase loss in a certain frequency band. When the effective gain is reduced due to nonlinear phenomena such as system drive protection and integral saturation, the controller not only reduces the tracking precision, but also risks phase margin reduction and even system instability. Because the inherent contradiction relationship exists between the system gain represented by the integral operator and the stability margin represented by the system phase, the design of the controller with high tracking accuracy and high stability margin in the traditional feedback closed loop structure becomes a difficult point.
The fractional order correction method is a novel control strategy for making a compromise between the number of integrators and phase loss, gain increase in the whole bandwidth range is obtained by losing a small part of phases in a full frequency band in a balanced manner, and the control effect similar to that of a half integrator is realized. Although the number of effective integrators is reduced, the tracking accuracy is slightly reduced compared with a multi-integrator system, the phase loss is small, the system is balanced, and the stability of the system is not reduced due to the change of the effective gain. For example, in the article "a comprehensive performance improvement control method by fractional order control", a control method of fractional order correction is adopted in the middle and low frequency band of the fast-reflection mirror operation, which proves the feasibility of the fractional order correction for improving the tracking accuracy without changing the stability margin of the system. Although there are many conclusions theoretically, some application achievements are obtained under certain limiting conditions, however, as the development of fractional order element devices with the characteristic of 'half integrator' has not been a major breakthrough so far, the corrector with the characteristic of fractional order correction cannot be directly obtained on a digital computer, and the wide implementation of the theoretical method becomes a bottleneck in engineering application. However, if the frequency response characteristic of the theoretical fractional order corrector is regarded as the additive effect of a plurality of "one integrator" and "zero integrator", the effect of the fractional order correction can be approximated to some extent. One simple way to achieve the additive effect is to cascade a plurality of lead-lag correctors under a certain law, but this law has not been clear until now nor has it been able to directly guide engineering implementation.
By combining the analysis, the feasibility of simulating fractional order correction characteristics of a plurality of lag correctors is fully utilized, and the calibration network configuration method, parameter setting and the like in the lag correctors are designed by determining the cascade rules of the lag correctors and the relation between the cascade rules and the tracking accuracy and stability of the system, so that a simple multistage and multistage lag correction network control strategy is realized, and the tracking accuracy of the photoelectric tracking system is improved. The invention is an effective means for solving the contradiction between tracking precision and stability in the current photoelectric tracking system, and has good application prospect.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the photoelectric tracking system needs to meet the requirements of tracking precision and stability margin of a full working frequency band at the same time. However, there is an inherent contradiction between the tracking accuracy and the stability margin, and the existing feedback control method does not have the capability of adjusting the contradiction.
The technical scheme adopted by the invention is as follows: a multistage and multistage hysteresis correction network control method for a photoelectric tracking system comprises the following two parts: the device comprises a performance setting module 1 and a parameter setting module 2.
The transfer function characteristic of the controlled photoelectric tracking system is obtained by means of system identification and the like, and is an input condition of the performance setting module 1. The maximum bandwidth and the transmission time delay condition of the system are determined according to the transfer function identification result of the photoelectric tracking system, and appropriate performance parameters can be designed on the basis. In the performance setting module 1, a set of feasible tracking performance parameters including the relative order of the controller, the working frequency range, the order and the number of stages of the hysteresis correction network are automatically set according to the transfer function characteristics and the mechanical characteristics of the controlled object.
A designer can set three performance parameters of expected phase margin of a photoelectric tracking system, a correction frequency band of a multistage multi-order lag correction network and fitting precision of the multistage multi-order lag correction network to a fractional order operator, the phase margin of the photoelectric tracking system is expressed by relative order parameters, the correction frequency band of the multistage multi-order lag correction network is expressed by a working frequency band range, the fitting precision of the multistage multi-order lag correction network to the fractional order operator is expressed by the order and the order of the lag correction network, the structure and the parameters of the correction network are directly output through a normalized flow by internal software calculation, the output parameters are directly related to the tracking performance of the photoelectric tracking system, the method does not need the designer to have professional correction network design experience, and can even directly adopt preset values to carry out one-click operation, so that the embarrassment of design according to fuzziness in a general correction network design is avoided.
At the same time, the three sets of parameters required by the system may also be manually modified by the control system designer. The specific meanings and boundary ranges of the individual parameters are explained in detail in the description of the embodiments. After the performance parameter setting is completed, the parameter setting module 2 automatically calculates the structure and controller parameters of the multistage multi-stage hysteresis correction network by using the performance parameters, and provides the design and parameter setting results of the correction network.
The method relates a large number of network parameters in a multistage multi-order lag correction network with three expected performance parameters, only three performance parameters are needed to be input, poles and zeros with a fixed multiplying power relation are configured in a working frequency band according to a configuration formula, meanwhile, the maximum gain coefficient which can be borne by the system is automatically calculated, finally, the multistage multi-order lag correction network which is smooth enough in amplitude and phase and accurate enough in fitting of a fractional order integration system is formed, and the requirements of a photoelectric tracking system on tracking accuracy and stability margin are met; the calculation software is used for automatically calculating and outputting all correction network parameters, so that the workload of designers is greatly reduced, and the problems of design difficulty and design rule non-uniformity caused by the unclear relation among a complex structure, parameter design and system performance in a general correction network are solved.
The control system implementing personnel can directly put the correction network parameters into corresponding software codes, and then the multistage and multistage hysteresis correction network can be realized in the computer.
Compared with the prior system, the invention has the following advantages:
1. under the traditional feedback control framework, the invention improves the tracking precision of the photoelectric tracking system and simultaneously weakens the contradiction between the tracking precision and the stability margin. Compared with the traditional single integrator system, the invention can provide higher in-bandwidth tracking capability under the same bandwidth condition; compared with a multi-integrator system, the method is insensitive to gain change, has high enough stability margin, and does not need to bear the risk of stability damage caused by various reasons in the system operation process. On the comprehensive capability of the system, the invention has better system tracking performance;
2. the modules of the invention adopt automatic setting and calculating methods, can automatically design the multistage and multistage hysteresis correction network and output corresponding network parameters in the whole process after the identification result of the controlled system is obtained, can automatically obtain the design result without the operation of professional persons in the whole process, and is very convenient for engineering realization. Meanwhile, in order to further improve the design freedom of designers, a way for manually setting related parameters is provided in the performance setting module (module 1), and the system performance requirements can be conveniently and individually designed.
Drawings
FIG. 1 is a block diagram of a multi-stage multi-order lag correction network control system for a photoelectric tracking system in accordance with the present invention;
FIG. 2 is a diagram of the distribution of the zero-poles and the amplitude and phase response of the multi-stage and multi-stage lag correction network according to the present invention;
FIG. 3 is a block diagram of the control design and implementation process of the multi-stage hysteresis correction network of the present invention.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings.
In the photoelectric tracking system, a mode that a plurality of lag correctors are cascaded and overlapped under a certain rule is adopted, smooth control gain improvement and phase loss in a working frequency range are realized, and a certain system stability margin requirement is met while the tracking precision of the photoelectric tracking system is effectively improved.
The invention aims at a photoelectric tracking system, which can be regarded as a single-input single-output linear constant system in the working frequency band and can be represented by a transfer function G(s), wherein r (t) is a tracked input signal, and y (t) is an actual tracking position of the photoelectric tracking system. Because the delay effect caused by signal sampling and transmission always exists in the system operation process, the controlled system discussed in the invention should be added with a time delay link e -τs The total controlled object of the photoelectric tracking system is G(s) e -τs As shown in fig. 1. On the basis of the determination of the controlled object, the designer first designs a basic corrector C 0 (s) which functions to correct the open loop characteristic of the system to a transfer characteristic of approximately 1. However, since there is always a time lag in the controlled object and the basis corrector cannot compensate for it, the general basisThe basic corrector is designed to be C 0 (s)≈G -1 (s) of the reaction mixture. The controlled object added with the basic corrector can be approximately regarded as a pure time delay link e -τs . The multistage, multistage hysteretic correction network proposed by the present invention is represented in fig. 1 as a block β(s) in the basic corrector C 0 And(s) further adding a correction link. Thus, the correction controller of the photoelectric tracking system is a set of a base corrector and a multistage, multistage hysteretic correction network C(s) = β(s) C 0 (s)。
The open-loop transfer function of the photoelectric tracking system comprising the basic controller and the multistage multi-order hysteresis correction network is as follows:
F(s)＝β(s)C 0 (s)G(s)e -τs ≈β(s)e -τs (1)
if β(s) is a standard integral system, β(s) = K/s is satisfied N Then it is extremely easy to calculate to obtain when at least p is satisfied m Under the condition of rad phase margin, if the maximum open loop bandwidth of the system is omega c Then the maximum gain of β(s) is:
the maximum order N of the system should satisfy:
as can be seen from equation (2), if the bandwidth of the system is not changed, and it is desired to increase the gain to obtain higher tracking accuracy, it is necessary to increase the value of the integration order N, but when N is limited to an integer, it is very difficult for the inequality (3) to have an equal sign. On the other hand, if β(s) is not a pure integral element but a complex element formed by multiple sets of poles-zero, the analysis of the bandwidth, phase, etc. becomes very complex. Therefore, the invention assumes the amplitude and phase performance of the multistage and multistage hysteresis correction network beta(s) on the frequency domain and the fractional standard integral transfer function K/s α The same, namely:
β(s)≈K/s α (4)
the limitation of the fractional order is 0 < alpha < 2, so that the system is not a non-causal system with the numerator higher than the denominator, and the system cannot be stable due to the phase loss of the system caused by the over-high integral order. The slope of the amplitude-frequency curve of the multistage hysteresis correction network beta(s) is about-20 alpha dB/dec, and the phase is about-pi alpha/2 rad. Obviously, when alpha is larger than 1, the amplitude of the low frequency band of the correction network is higher than that of a common first-order integral correction system, and the closed-loop tracking precision of the correction network is higher than that of the common first-order integral correction system according to the rule of high amplitude and high precision. Meanwhile, alpha is a rational number smaller than 2, the phase in the working range of the system can not drop minus pi all the time, which ensures that the system has enough phase margin all the time, and scholars have proved theoretically that (4) has excellent gain robustness, and the change of the system gain can not change the stability of the system, so the robust stability and the tracking precision of the system are ensured. The fractional order α is then defined as the relative order of the system. The larger the relative order α, the higher the system tracking accuracy, but at the same time the lower the stability margin.
As a non-strict equation, K/s in equation (4) α Is a fractional order integral transfer function. Limited by current fractional order element technology, this transfer function has not been directly implemented. However, the present invention is inspired by the fact that the broken line formed by a plurality of groups of lead-lag correctors can simulate the transfer characteristic of the fractional order, and a group of frequency points omega from low to high is selected in the working frequency band 1 、ω 2 、ω 3 、ω 4 …ω 2n Adding a pole, a zero, a pole, a zero … to the frequency points to form a series-connected pole-zero combination, and adding an integrator to form a multi-stage lag correction network beta(s) similar to fractional order integration. Frequency range [ omega ] with zero pole 1 ,ω 2n ]I.e. the frequency band range parameter in the performance setting module (module 1). The distribution of the zero poles, the amplitude frequency and the phase frequency curve of beta(s) in the frequency domain are shown in fig. 2. When the number of the lag correctors added in a certain frequency band is increased, the amplitude frequency and the phase frequency curve of the lag correctors are increasedThe line is smoother and smoother, the fitting effect on the fractional order integral system is better and better, but the complexity of system implementation is higher and higher. Suppose that each frequency ω i M superposed zeros or poles are arranged on the network, n independent lag correctors with non-superposed frequencies are arranged in beta(s), 2nm pole zeros and an integrator are arranged in beta(s), the number of stages of the formed multistage and multistage lag correction network is n, the order is m, and the form is as follows:
in order to enable the performance of the n-level m-order hysteresis correction network in the working frequency range to meet the formula (4) as much as possible and reduce the complex work of independently designing 2nm pole zeros in the formula (5), the invention provides the following design conditions:
1) Defining a constant c as the frequency multiple relation of the upper and lower bounds of the frequency band range in the whole multistage multi-order lag correction network, namely:
2) Each independent lag corrector zero has a fixed multiple e with respect to the pole frequency, and between each two adjacent independent lag correctors, the pole has a fixed multiple d with respect to the zero frequency, i.e. for any i =1,2,.. N, there are:
by the above assumptions, the constants e, d and their determined intermediate frequency points ω i The zero pole of the multi-stage and multi-stage hysteresis correction network does not need to be manually distributed for obtaining, but is determined by the set relative order alpha and the operating frequency range multiple c. The relationship is as follows:
ω 2n the frequency point of the last zero point of the whole multistage hysteresis correction network is a frequency point which does not affect the bandwidth and the phase margin of the system, and the cut-off frequency of the correction network is not higher than 0.1 time of the frequency of the open-loop bandwidth, namely omega 2n ≤0.1ω c 。
In summary, the design and implementation of the multi-stage and multi-stage hysteresis correction network includes two modules executed sequentially: the performance setting module 1 and the parameter setting module 2 are sequentially executed in the implementation process.
1. The performance setting module 1 presets a set of feasible parameters of the multistage and multistage hysteresis correction network, including relative order parameters, working frequency range parameters, and the order and the progression of the multistage and multistage hysteresis correction network, according to the design constraint conditions of a general photoelectric tracking control system.
The general servo system takes the phase margin as p m = pi/4, the predetermined relative order α is calculated to be obtained in order to make inequality (3) equal, without considering the time delay 0 =1.5. The working frequency range of the multi-level multi-order lag correction network is simultaneously defaulted to c 0 =100 octaves, so the initial frequency of the correction network is ω 1 ＝0.001ω c Termination frequency of ω 2n ＝0.1ω c . According to experience, in the frequency range, in order to simultaneously guarantee the smoothness of the multistage and multistage hysteresis correction network and the system implementation complexity, the stage number of the initially selected hysteresis correction network is 3, and the stage number is 1. The default performance parameter settings in the performance setting module 1 are as follows:
table 1 initial performance parameter setting table
The designer can follow the toolThe body requirements modify the parameters within the constraints of the performance parameters. The larger the relative order alpha is, the higher the accuracy of the system is, but the lower the stability margin of the system is, and meanwhile, the relative order must meet the stability requirement of the formula (3); at a cut-off frequency omega 2n The larger the working frequency range c under the condition of invariance, the wider the fitting frequency range of the fractional order integration system, but the higher the requirements on the number of stages and the order of the lag correction network. Generally speaking, the correction compensation within 100 octaves is enough to improve the tracking accuracy of the photoelectric tracking system in the low-frequency working range; the larger the order m and the order n are, the higher the accuracy of the beta(s) fitting fractional order integration system is, but the complexity of the controller implementation is brought to the system. The above parameters are selected as trade-offs.
2. The parameter setting module 2 is sequentially executed after the performance parameter module, wherein the correction network structure is given by formula (5); the correction of the network parameters is mainly performed by the derivation process for specific frequency points omega 1 、ω 2 、ω 3 、ω 4 …ω 2n And a gain parameter K. The following table is configured by the assumed conditions and parameter setting method in the performance setting module 1, and the specific gain and frequency points.
Table 2 table of correction network parameters
After the performance setting module 1 and the parameter setting module 2 are executed in sequence, the network beta(s) and each network parameter [ K, omega ] in the network beta(s) are corrected in a one-level and multi-level mode i ]I =1,2, … n. The parameters are added into a control correction network of the controlled object, namely, a multi-level multi-order hysteresis correction network is realized.
Claims (1)
1. A multistage and multistage hysteresis correction network control method for a photoelectric tracking system is characterized by comprising the following steps: the method comprises sequentially executing two modules: the system comprises a performance setting module (1) and a parameter setting module (2), wherein the performance setting module (1) sets expected frequency response characteristics of the photoelectric tracking system, a design range of a correction network and fitting accuracy, and the expected frequency response characteristics, the design range of the correction network and the fitting accuracy are respectively expressed by relative orders, working frequency bands and correction network order numbers; the parameter setting module (2) calculates the structure of the multistage multi-stage hysteresis correction network and all network parameters in the structure in software according to the designed performance parameter input, and automatically generates a calculation result of parameter setting, so that the multistage multi-stage hysteresis correction network meeting the tracking precision and stability margin performance requirements can be quickly and conveniently realized;
aiming at a photoelectric tracking system, the photoelectric tracking system can be regarded as a single-input single-output linear constant system in the working frequency band, and can be represented by a transfer function G(s), r (t) is a tracked input signal, y (t) is the actual tracking position of the photoelectric tracking system, and because the delay effect caused by signal sampling and transmission always exists in the operation process of the system, a time delay link e is added to a controlled system -τs The total controlled object of the photoelectric tracking system is G(s) e -τs On the basis of the determination of the controlled object, a basic corrector C is firstly designed 0 (s) which functions to correct the open loop characteristic of the system to a transfer characteristic of approximately 1, the base corrector being designed as C 0 (s)≈G -1 (s) the controlled object with the added basic corrector can be approximately regarded as a pure time delay element e -τs The multistage, multistage hysteretic correction network is represented by the module beta(s) in the basic corrector C 0 A correction link is further added on the basis of(s), and a correction controller of the photoelectric tracking system is a set C(s) = beta(s) C of a basic corrector and a multi-stage multi-order hysteresis correction network 0 (s)；
The open-loop transfer function of the photoelectric tracking system comprising the basic controller and the multistage multi-order hysteresis correction network is as follows:
F(s)＝β(s)C 0 (s)G(s)e -τs ≈β(s)e -τs (1)
if β(s) is a standard integral system, β(s) = K/s is satisfied N Then it is extremely easy to calculate to obtain when at least p is satisfied m Under the condition of rad phase margin, if the maximum open loop bandwidth of the system is omega c Then the maximum gain of β(s) is:
the maximum order N of the system should satisfy:
assuming the amplitude and phase performance of a multistage and multistage hysteresis correction network beta(s) on a frequency domain and a fractional order standard integral transfer function K/s α The same, namely:
β(s)≈K/s α (4)
wherein the fractional order α is defined as 0 < α < 2;
within the working frequency band, a group of frequency points omega from low to high is selected 1 、ω 2 、ω 3 、ω 4 …ω 2n Adding a pole, a zero, a pole, a zero … to the frequency points to form a series-connected pole-zero combination, and adding an integrator to form a multi-stage lag correction network beta(s) similar to fractional integration, wherein the frequency range [ omega ] of the zero pole is 1 ,ω 2n ]I.e. the frequency range parameter in the performance setting module (1), assuming each frequency omega i M superposed zeros or poles are arranged on the network, n independent lag correctors with non-superposed frequencies are arranged in beta(s), 2nm pole zeros and an integrator are arranged in beta(s), the number of stages of the formed multistage and multistage lag correction network is n, the order is m, and the form is as follows:
the design conditions are as follows:
1) Defining a constant c as the frequency multiple relation of the upper and lower bounds of the frequency band range in the whole multistage multi-order lag correction network, namely:
2) Each independent lag corrector zero has a fixed multiple relation e with the pole frequency, and the pole frequency and the zero frequency between every two adjacent independent lag correctors have a fixed multiple relation d, namely for any i =1,2, … n, the following components are provided:
by the above assumptions, the constants e, d and their determined intermediate frequency points ω i The zero-pole of the multistage multi-order lag correction network does not need to be manually distributed for obtaining, but is determined by the set relative order alpha and the working frequency range multiple c, and the relation is as follows:
ω 2n the frequency point of the last zero point of the whole multistage multi-order lag correction network is a frequency point which does not influence the bandwidth and the phase margin of a system, and the cut-off frequency of the correction network is not higher than 0.1 time of the frequency of the open-loop bandwidth, namely omega 2n ≤0.1ω c ；
In the implementation process, the performance setting module (1) and the parameter setting module (2) are executed in sequence.
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