CN103777523B - Aircraft multiloop model bunch Composite PID robust Controller Design method - Google Patents
Aircraft multiloop model bunch Composite PID robust Controller Design method Download PDFInfo
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Abstract
The invention provides a kind of aircraft multiloop model bunch Composite PID robust Controller Design method, the method directly determines to obtain by frequency sweep flight test the model cluster that amplitude-frequency in whole envelope and phase-frequency characteristic form under given differing heights, Mach number condition; Directly determine that open-loop cut-off frequency is interval according to the amplitude versus frequency characte in flight envelope; Directly determine with the phase margin corresponding to cutoff frequency interval interval according to the phase-frequency characteristic in flight envelope; By adding multistage PID controller and the phase margin index in aircraft whole envelope and the identification Method in System Discrimination determine multistage PID robust controller sum of series parameter value; Magnitude margin index in the full flight envelope of aircraft
Description
Technical Field
The invention relates to a design method of an aircraft controller, in particular to a design method of a composite PID robust controller of an aircraft multi-loop model cluster, and belongs to the fields of measurement and control technology, flight mechanics and the like.
Background
The control of the take-off and landing process of the aircraft plays an important role in flight safety; because the flying speed of the aircraft is greatly changed in the taking-off and landing processes, the aircraft can also face a strong nonlinear problem even according to a longitudinal model; on the other hand, the control rudder of the aircraft has the phenomena of saturation, dead zone and the like; from the consideration of flight safety, when the system flies at ultra-low altitude (such as take-off/landing of an airplane), the controller must ensure that the system has certain stability margin, no overshoot and stability, so that the design of the ultra-low altitude flight controller is very complex, and the design of controlling the airplane cannot be directly applied by the existing control theory.
In the design of modern practical flight controllers, a small part of the design is designed by adopting a state space method, and most of the design is still designed by adopting a modern frequency method represented by a classical frequency domain method represented by PID and an inverse Nyquist array method. The modern control theory is characterized by a state space method, takes analytic calculation as a main means, and takes performance index realization as the optimal modern control theory, then a series of controller design methods such as an optimal control method, a model reference control method, an adaptive control method, a dynamic inverse control method, a feedback linearization method, a direct nonlinear optimization control, a variable gain control method, a neural network control method, a fuzzy control method, a robust control method and a multi-method combination control are developed, the published academic papers are in ten thousand, for example, 2011 GhasemiA designs a reentry aircraft controlled by an adaptive fuzzy sliding mode (GhasemiA, MoradiM, menhajmb.adaptivefuzzyingtoncontropresscontrolledesigne low-liftretryvehicle [ J ] journal of aeronautic engineering, sliding mode, 25(2): 210), and int3 year baoticebaotirebalance designs a nonlinear aircraft for a fuzzy pilot system, fuzzy pilot system engineering, and intelligent vehicle model system for unmanned aerial vehicle (mobile vehicle navigation system). 2013,24(3):499- & 509), many studies only stay in the idealized simulation study stage; the design has three problems that (1) because the ultra-low altitude operation stability test of the aircraft can not be carried out, an accurate mathematical model of a controlled object is difficult to obtain; (2) for evaluating important performance indexes of a flight control system such as stability margin specified by military standards, a state space method can not be expressed in an obvious form like a classical frequency method; (3) the controller structure is too complex, no constraints of actual controllers and flight states are considered, and the designed controller is not physically realizable.
The university scholark systematically and creatively researches how to popularize the frequency domain method into the design of a multivariable system, utilizes the concept of the advantage of the diagonal matrix to convert the multivariable problem into the design problem of a univariate system of a classical method which is well known by people, and then sequentially presents the methods of a Mayne sequence regression method, a MacFarlane characteristic trajectory method, an Owens parallel vector expansion method and the like. Especially when the computer aided design program with graphic display terminal is used, the experience and intelligence of the designer can be fully exerted to design the controller which not only meets the quality requirement, but also is physically realizable and has simple structure; the multivariate frequency method is improved and researched at home and abroad (a multivariate frequency domain design method of a high and high altitude, Rocheng, Shenhui, Huidewen and flexible satellite attitude decoupling controller, aerospace science news, 2007, Vol.28(2), pp 442-447; Lithocarpus, Charpy, Tiaoling cloud, Tilt turning hypersonic cruise aircraft multivariate frequency domain method decoupling design, rocket and guidance science news, 2011, Vol.31(3) and pp 25-28), but the design method can consider that the conservatism is too large when the system is uncertain, and cannot obtain reasonable design results under the condition that the aircraft is restricted by a control rudder.
In summary, the existing control method cannot design a stable low-altitude flight controller with small overshoot according to the stability margin index in the full-flight envelope when the aircraft model changes.
Disclosure of Invention
In order to overcome the technical defects that the prior method can not design a stable margin index meeting the stability index in a full flight envelope under the condition that the model change of an aircraft in the full flight envelope is large, the overshoot is small, and a stable low-altitude flight controller is stable, the invention provides a method for designing a composite PID robust controller of an aircraft multi-loop model cluster, which directly determines and obtains a model cluster formed by amplitude-frequency and phase-frequency characteristics in the full envelope through a sweep frequency flight test under the conditions of different given heights and Mach numbers; directly determining an open-loop cut-off frequency interval according to the amplitude-frequency characteristic in the flight envelope; directly determining a phase margin interval corresponding to the cut-off frequency interval according to the phase frequency characteristic in the flight envelope; determining the grade and parameter values of a multi-stage PID robust controller by adding the multi-stage PID controller, and determining a phase margin index in a full envelope of the aircraft and a model identification method in system identification; amplitude margin index in full flight envelope of aircraftCarrying out controller effect verification under the condition of given decibel number; a robust controller which is consistent with the full-flight envelope and has small overshoot and is stable in low-altitude flight is designed from the concepts of phase margin and amplitude margin.
The technical scheme adopted by the invention for solving the technical problems is as follows: a design method of a composite PID robust controller of an aircraft multi-loop model cluster is characterized by comprising the following steps:
step 1, under the conditions of different given altitudes and Mach numbers, directly obtaining amplitude-frequency and phase-frequency characteristics in a full envelope of an aircraft allowed to fly through a sweep frequency flight test to form a model cluster between an operating control surface and the flight altitude in the full envelope of the aircraft, and obtaining the flutter frequency of the aircraft by crossing the flight envelope to obtain an open-loop transfer function model cluster matrix between the corresponding operating control surface and the flight altitude of the aircraft, wherein the open-loop transfer function model cluster matrix is as follows:
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is a positive integer and is a non-zero integer,is an independent variable of the laplacian transform,is the flying height of the aircraft,is a Mach number of the component (A),in order to be an uncertain vector,is composed ofA single-mode square matrix is adopted,is composed ofA polynomial diagonal matrix of the form,is composed ofA single-mode square matrix is adopted,in order to be a polynomial expression,is a positive integer;
selecting
The conditions are satisfied:
and
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is composed ofA single-mode square matrix is adopted,is composed ofA polynomial diagonal matrix of the form,is composed ofTo (1) aLine and firstThe elements of the column are, in turn,is composed ofTo (1) aLine and firstThe elements of the column are, in turn,,is composed ofA single-mode square matrix is adopted,in order to be a polynomial expression,is a phase angle mathematical sign;
the controller of the aircraft multi-circuit system is set as follows:
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is composed ofA diagonal matrix;is composed ofTo (1) aLine and firstThe elements of the column are, in turn,；
step 2, the controller，The design process of (2) is as follows:
(1) order toThe specific expression form is as follows:
wherein
、
In order to be a polynomial expression,for the commonly used laplace-changed variable in the transfer function,respectively the altitude and the mach number,is the delay time of the pitch loop,to followThe gain of the variation is varied in such a way that,is a polynomialMiddle followThe cluster of coefficients that are varied is,is a polynomialMiddle followThe cluster of coefficients that are varied is,is an uncertainty in the model;
(2) judging at the uncertain part of the known modelThe method for directly determining the open-loop cut-off frequency interval according to the amplitude-frequency characteristic in the flight envelope comprises the following steps:
fromNamely, it isIs approximately asObtaining the open-loop cut-off frequencyMaximum value of solutionAnd minimum valueOpen loop cut-off frequencyThe interval is;
In the formula,is a positive real number, and the number of the real numbers,as a variable in the frequency characteristic,for the purpose of the imaginary part representation,is the angular frequency;
(3) judging at the uncertain part of the known modelAnd then, according to the phase frequency characteristic in the flight envelope, calculating the maximum phase margin in the envelope:
and minimum phase margin within the envelope:
directly determining the frequency range corresponding to the cut-off frequency rangeThe phase margin interval of (a) is:；
wherein,is a positive real number;
(4) the transfer function of the candidate multi-stage PID controller is:
in the formula,Nis an integer, represents the number of stages of the multi-stage PID controller to be determined,、、 is a constant to be determined;
after the multi-stage PID controller is added,
fromNamely, it is
In order to obtain an open-loop cut-off frequencyMaximum value of solutionAnd minimum valueOpen loop cut-off frequencyThe interval is，
Phase margin indicator in aircraft full envelopeUnder given conditions, the phase margin of the system is added after the multi-stage PID controller is addedIt should satisfy:
namely, the following conditions are satisfied:
under the common constraint of the indexes and the maximum likelihood criterion or other criteria, the number of stages of the multi-stage PID controller can be determined according to the maximum likelihood method or the identification method in the identification of the system model structureNConstant of、、 ；
(5) Amplitude margin index within aircraft full envelopeIn the given case of decibels, the number of db,
fromNamely, it is
In obtaining the frequencyMaximum value of solutionAnd minimum value，The interval is，
And (3) judging:
namely, the following conditions are satisfied:
if the number of stages of the multi-stage PID controller is not met, the design of the flight controller is finished, and if the number of stages of the multi-stage PID controller is not met, the number of stages of the multi-stage PID controller is increased.
The invention has the beneficial effects that: based on the concepts of phase margin and amplitude margin, the parameters of the multi-stage PID robust controller are determined in the full-flight envelope according to the requirements of given phase margin and amplitude margin and a model identification method by adding the multi-stage PID controller, and the stable low-altitude flight robust controller which is in line with the full-flight envelope and has small overshoot is designed.
The present invention will be described in detail with reference to examples.
Detailed Description
Step 1, under the conditions of different heights and Mach numbers, linear sweep frequency signals are used:whereinAs an initial frequency,Is a cut-off frequency,、For sweeping time, or logarithmically swept signalsWhereinAs an initial frequency,Is a cut-off frequency,And T is sweep frequency time, the aircraft is excited, amplitude frequency and phase frequency characteristics in a flying full envelope are directly obtained through a sweep frequency flight test, a model cluster of an operation control surface and flight altitude in the aircraft full envelope is formed, flutter frequency of the aircraft can be obtained by crossing the flying envelope, and an open-loop transfer function model cluster matrix between the corresponding operation control surface and flight altitude of the aircraft is obtained as follows:
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is a positive integer and is a non-zero integer,is an independent variable of the laplacian transform,is the flying height of the aircraft,is a Mach number of the component (A),in order to be an uncertain vector,is composed ofA single-mode square matrix is adopted,is composed ofA polynomial diagonal matrix of the form,is composed ofA single-mode square matrix is adopted,in order to be a polynomial expression,is a positive integer;
selecting
The conditions are satisfied:
and
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is composed ofA single-mode square matrix is adopted,is composed ofA polynomial diagonal matrix of the form,is composed ofTo (1) aLine and firstThe elements of the column are, in turn,is composed ofTo (1) aLine and firstThe elements of the column are, in turn,,is composed ofA single-mode square matrix is adopted,in order to be a polynomial expression,is a phase angle mathematical sign;
the controller of the aircraft multi-circuit system is set as follows:
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is composed ofA diagonal matrix;is composed ofTo (1) aLine and firstThe elements of the column are, in turn,；
step 2, the controller，The design process of (2) is as follows:
(1) order toThe specific expression form is as follows:
wherein
、
In order to be a polynomial expression,for the commonly used laplace-changed variable in the transfer function,respectively the altitude and the mach number,is the delay time of the pitch loop,to followThe gain of the variation is varied in such a way that,is a polynomialMiddle followThe cluster of coefficients that are varied is,is a polynomialMiddle followThe cluster of coefficients that are varied is,is an uncertainty in the model;
(2) judging at the uncertain part of the known modelThe method for directly determining the open-loop cut-off frequency interval according to the amplitude-frequency characteristic in the flight envelope comprises the following steps:
fromNamely, it isIs approximately asObtaining the open-loop cut-off frequencyMaximum value of solutionAnd minimum valueOpen loop cut-off frequencyThe interval is;
In the formula,is a positive real number, and the number of the real numbers,as a variable in the frequency characteristic,for the purpose of the imaginary part representation,is the angular frequency;
(3) judging at the uncertain part of the known modelAnd then, according to the phase frequency characteristic in the flight envelope, calculating the maximum phase margin in the envelope:
and minimum phase margin within the envelope:
directly determining a phase margin interval corresponding to the cut-off frequency interval as follows:；
wherein,is a positive real number;
(4) the transfer function of the candidate multi-stage PID controller is:
in the formula,Nis an integer, represents the number of stages of the multi-stage PID controller to be determined,、、 is a constant to be determined;
after the multi-stage PID controller is added,
fromNamely, it is
In order to obtain an open-loop cut-off frequencyMaximum value of solutionAnd minimum valueOpen loop cut-off frequencyThe interval is，
Phase margin indicator in aircraft full envelopeUnder given conditions, the phase margin of the system is added after the multi-stage PID controller is addedIt should satisfy:
namely, the following conditions are satisfied:
under the common constraint of the indexes and the maximum likelihood criterion or other criteria, the number of stages of the multi-stage PID controller can be determined according to the maximum likelihood method or the identification method in the identification of the system model structureNConstant of、、 ；
(5) Amplitude margin index within aircraft full envelopeIn the given case of decibels, the number of db,
fromNamely, it is
In obtaining the frequencyMaximum value of solutionAnd minimum value，The interval is，
And (3) judging:
namely, the following conditions are satisfied:
if the number of stages of the multi-stage PID controller is not met, the design of the flight controller is finished, and if the number of stages of the multi-stage PID controller is not met, the number of stages of the multi-stage PID controller is increased.
Claims (1)
1. A design method of a composite PID robust controller of an aircraft multi-loop model cluster is characterized by comprising the following steps:
step 1, under the conditions of different given altitudes and Mach numbers, directly obtaining amplitude-frequency and phase-frequency characteristics in a full envelope of an aircraft allowed to fly through a sweep frequency flight test to form a model cluster between an operating control surface and the flight altitude in the full envelope of the aircraft, and obtaining the flutter frequency of the aircraft by crossing the flight envelope to obtain an open-loop transfer function model cluster matrix between the corresponding operating control surface and the flight altitude of the aircraft, wherein the open-loop transfer function model cluster matrix is as follows:
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is a positive integer and is a non-zero integer,is an independent variable of the laplacian transform,is the flying height of the aircraft,is a Mach number of the component (A),in order to be an uncertain vector,is composed ofA single-mode square matrix is adopted,is composed ofA polynomial diagonal matrix of the form,is composed ofA single-mode square matrix is adopted,in order to be a polynomial expression,is a positive integer;
selecting
The conditions are satisfied:
and
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is composed ofA single-mode square matrix is adopted,is composed ofA polynomial diagonal matrix of the form,is composed ofTo (1) aLine and firstThe elements of the column are, in turn,is composed ofTo (1) aLine and firstThe elements of the column are, in turn,,is composed ofA single-mode square matrix is adopted,in order to be a polynomial expression,is a phase angle mathematical sign;
the controller of the aircraft multi-circuit system is set as follows:
wherein,is composed ofThe method comprises the following steps of (1) square matrix,is composed ofA diagonal matrix;is composed ofTo (1) aLine and firstThe elements of the column are, in turn,；
step 2, the controller，The design process of (2) is as follows:
(1) order toThe specific expression form is as follows:
wherein
、
In order to be a polynomial expression,for the commonly used laplace-changed variable in the transfer function,respectively the altitude and the mach number,is the delay time of the pitch loop,to followThe gain of the variation is varied in such a way that,is a polynomialMiddle followThe cluster of coefficients that are varied is,is a polynomialMiddle followThe cluster of coefficients that are varied is,is an uncertainty in the model;
(2) judging at the uncertain part of the known modelThe method for directly determining the open-loop cut-off frequency interval according to the amplitude-frequency characteristic in the flight envelope comprises the following steps:
fromNamely, it isIs approximately asObtaining the open-loop cut-off frequencyMaximum value of solutionAnd minimum valueOpen loop cut-off frequencyThe interval is;
In the formula,is a positive real number, and the number of the real numbers,as a variable in the frequency characteristic,for the purpose of the imaginary part representation,is the angular frequency;
(3) judging at the uncertain part of the known modelAnd then, according to the phase frequency characteristic in the flight envelope, calculating the maximum phase margin in the envelope:
and minimum phase margin within the envelope:
directly determining a phase margin interval corresponding to the cut-off frequency interval as follows:；
wherein,is a positive real number;
(4) the transfer function of the candidate multi-stage PID controller is:
in the formula,Nis an integer, represents the number of stages of the multi-stage PID controller to be determined,、、 is a constant to be determined;
after the multi-stage PID controller is added,
fromNamely, it is
In order to obtain an open-loop cut-off frequencyMaximum value of solutionAnd minimum valueOpen loop cut-off frequencyInterval(s)Is composed of，
Phase margin indicator in aircraft full envelopeUnder given conditions, the phase margin of the system is added after the multi-stage PID controller is addedIt should satisfy:
namely, the following conditions are satisfied:
under the common constraint of the indexes and the maximum likelihood criterion or other criteria, the number of stages of the multi-stage PID controller can be determined according to the maximum likelihood method or the identification method in the identification of the system model structureNConstant of、、 ；
(5) Amplitude margin index within aircraft full envelopeIn the given case of decibels, the number of db,
fromNamely, it is
In obtaining the frequencyMaximum value of solutionAnd minimum value，The interval is，
And (3) judging:
namely, the following conditions are satisfied:
if the number of stages of the multi-stage PID controller is not met, the design of the flight controller is finished, and if the number of stages of the multi-stage PID controller is not met, the number of stages of the multi-stage PID controller is increased.
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| CN102081349A (en) * | 2011-01-27 | 2011-06-01 | 西北工业大学 | Flight test determination method of multi-input and multi-output equivalent pneumatic servo elastic robust stability |
| CN102081350A (en) * | 2011-01-27 | 2011-06-01 | 西北工业大学 | Method for determining equivalent aeroservoelasticity (ASE) robust stability of statically unstable aircraft through flight test |
| EP2520996A1 (en) * | 2011-05-05 | 2012-11-07 | The Boeing Company | Detection of imminent control instability |
| EP2623417A2 (en) * | 2012-02-06 | 2013-08-07 | Messier-Bugatti-Dowty | A method of managing a steering command for a steerable portion of aircraft landing gear |
| CN103587723A (en) * | 2013-11-07 | 2014-02-19 | 北京临近空间飞行器系统工程研究所 | Longitudinal on-line locus designing and tracking method for reentry initial segment analytic expression |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102081349A (en) * | 2011-01-27 | 2011-06-01 | 西北工业大学 | Flight test determination method of multi-input and multi-output equivalent pneumatic servo elastic robust stability |
| CN102081350A (en) * | 2011-01-27 | 2011-06-01 | 西北工业大学 | Method for determining equivalent aeroservoelasticity (ASE) robust stability of statically unstable aircraft through flight test |
| EP2520996A1 (en) * | 2011-05-05 | 2012-11-07 | The Boeing Company | Detection of imminent control instability |
| EP2623417A2 (en) * | 2012-02-06 | 2013-08-07 | Messier-Bugatti-Dowty | A method of managing a steering command for a steerable portion of aircraft landing gear |
| CN103587723A (en) * | 2013-11-07 | 2014-02-19 | 北京临近空间飞行器系统工程研究所 | Longitudinal on-line locus designing and tracking method for reentry initial segment analytic expression |
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