CN112015196A - Attitude control system amplitude limiting value design method, storage medium and server - Google Patents

Attitude control system amplitude limiting value design method, storage medium and server Download PDF

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CN112015196A
CN112015196A CN202011127940.9A CN202011127940A CN112015196A CN 112015196 A CN112015196 A CN 112015196A CN 202011127940 A CN202011127940 A CN 202011127940A CN 112015196 A CN112015196 A CN 112015196A
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control system
amplitude limiting
attitude control
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朱凯
钟友武
赵卫娟
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Landspace Technology Co Ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/244—Spacecraft control systems
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/244—Spacecraft control systems
    • B64G1/245—Attitude control algorithms for spacecraft attitude control

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Abstract

The invention provides an attitude control system amplitude limiting value design method, a storage medium and a server. The method is used for solving the optimization problem with LMI constraint and providing the amplitude limiting value design method of the proportional control item and the differential control item when the control is limited. By adopting the amplitude limiting values of the proportional term and the differential term in the optimized control law, the stability of the control system under the conditions of larger uncertainty and strong interference can be improved, and the robustness of the control system under the limited control is improved; the defects that the amplitude constraint of the feedback quantity is adjusted according to engineering experience or a target practice simulation result, theoretical basis is lacked, time is consumed for iteration, and the solving efficiency is obviously improved.

Description

Attitude control system amplitude limiting value design method, storage medium and server
Technical Field
The invention relates to the technical field of aerospace, in particular to an aircraft control technology, and specifically relates to an attitude control system amplitude limiting value design method, a storage medium and a server.
Background
In actual engineering, the deflection range of an aircraft servo mechanism is restricted, a flight control system is a nonlinear system, and the stability of the flight control system is related to the flight state, the amplitude limit of a servo deflection angle, the amplitude limit processing of each feedback item in a control law and the like.
When the saturation problem of the control quantity is not considered, the robustness and the performance of the control system can be considered at the same time, and the control gains of the proportional term and the differential term are selected preferentially; however, when the aircraft is subjected to a large external disturbance or the dynamic model has a large uncertainty, in order to improve the robustness of the control system, improve the stability of the control system and avoid control saturation as much as possible, according to engineering experience, 60% -70% of the maximum deflection angle of the servo mechanism is generally used as the amplitude limiting value of the differential term in the control law, and 30% -40% of the maximum deflection angle of the servo mechanism is used as the amplitude limiting value of the proportional term in the control law. Usually, amplitude constraints of various feedback quantities in the control law are repeatedly adjusted and determined according to engineering experience or a target practice simulation result, certain theoretical basis is lacked, and the iterative design process is time-consuming.
Disclosure of Invention
The invention aims to solve the problem of amplitude limiting value design of a proportional term and a differential term in a control law of an aircraft attitude control system under the condition of limited control.
One aspect of the invention provides an attitude control system amplitude limiting value design method, which comprises the following steps:
establishing a dynamic model of the single attitude control channel of the aircraft around the centroid in a small disturbance manner;
designing a control law and control parameters of the aircraft attitude control channel based on a PD control structure;
based on the control law, establishing a feedback term and a posture control system nested saturation limited model with limited control quantity, wherein the feedback term comprises a differential feedback term and a proportional feedback term;
converting the design problem of the amplitude limiting value of a feedback item in a control law into an optimization problem of an attraction domain of a control system with input subjected to nested saturation constraint;
and solving the amplitude limiting value of the feedback item by solving the optimal attraction domain of the control system with the input constrained by nested saturation.
Further, a stability margin test sub-algorithm is adopted to design control parameters in the control law.
Further, the method for establishing the attitude control system nested saturation limited model with limited feedback items and controlled variables comprises the following steps:
constructing a saturation function with a limiting value of 1;
expressing the control quantity by a product of a maximum amplitude limit and a saturation function, wherein the feedback term which is also expressed by the product of the maximum amplitude limit and the saturation function is nested;
substituting the control quantity into the aircraft single attitude control channel small disturbance dynamic model around the centroid to obtain an attitude control system nested saturation limited model with limited feedback items and control quantity.
Further, the saturation function with the clipping value of 1 is expressed as:
Figure 826201DEST_PATH_IMAGE001
。
therefore, the method for designing the amplitude limiting value of the attitude control system provided by the invention provides a method for designing the nested amplitude limiting of the control quantity by utilizing the optimization control theory of the control limited system aiming at the problem of stable control of the aircraft attitude control system under the condition of control limitation, namely, a control limited model of the attitude control system is established, the problem of amplitude limiting value design of a proportional term and a differential term in a control law is converted into the problem of attraction domain optimization of the control system subjected to nested saturation constraint, and the method for designing the amplitude limiting value of the proportional control term and the differential control term under the condition of control limitation is provided by solving the problem of optimization with LMI constraint.
Compared with the prior art, the amplitude limiting value design method provided by the invention adopts the amplitude limiting values of the proportional term and the differential term in the optimized control law, improves the stability of the control system under the condition of larger uncertainty and strong interference, and improves the robustness of the control system under the condition of limited control; the method avoids the defects that when the amplitude constraint of the feedback quantity is adjusted according to engineering experience or a target practice simulation result, theoretical basis is lacked and time-consuming iteration is needed, and remarkably improves the solving efficiency.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description, serve to explain the principles of the invention.
Fig. 1 is a flow chart of an attitude control system amplitude limit value design method according to an exemplary embodiment.
Detailed Description
Reference will now be made in detail to exemplary embodiments of the present invention, examples of which are not to be construed as limiting the invention but are to be construed as more particularly describing certain aspects, features and embodiments of the invention, which are susceptible to various modifications and alternative forms by those skilled in the art without departing from the scope or spirit of the invention.
A flow diagram of an attitude control system clipping value design method according to an exemplary embodiment is given in fig. 1. As shown in fig. 1, the method comprises the steps of:
s101: establishing a dynamic model of the single attitude control channel of the aircraft around the centroid in a small disturbance manner;
s102: designing a control law and control parameters of the aircraft attitude control channel based on a PD control structure;
s103: based on the control law, establishing a feedback term and a posture control system nested saturation limited model with limited control quantity, wherein the feedback term comprises a differential feedback term and a proportional feedback term;
s104: converting the design problem of the amplitude limiting value of a feedback item in a control law into an optimization problem of an attraction domain of a control system with input subjected to nested saturation constraint;
s105: and solving the amplitude limiting value of the feedback item by solving the optimal attraction domain of the control system with the input constrained by nested saturation.
Preferably, in step S102, a stability margin test sub-algorithm is used to design the control parameters in the control law.
Preferably, the method for establishing the attitude control system nested saturation limited model with the limited feedback items and the limited control quantity in step S103 specifically includes the following steps:
constructing a saturation function with a limiting value of 1;
expressing the control quantity by a product of a maximum amplitude limit and a saturation function, wherein the feedback term which is also expressed by the product of the maximum amplitude limit and the saturation function is nested;
substituting the control quantity into the aircraft single attitude control channel small disturbance dynamic model around the centroid to obtain an attitude control system nested saturation limited model with limited feedback items and control quantity.
Preferably, the saturation function with the clipping value of 1 is expressed as:
Figure 478899DEST_PATH_IMAGE001
。
the method of the present disclosure is further illustrated by the application example below.
Example 1
The attitude control law design of a pitching channel of an aircraft is taken as an example. The design method of the clipping value of the clipping item comprises the following steps:
1. establishing a small deviation dynamic model of the longitudinal motion around the mass center of a certain aircraft as follows:
Figure 114280DEST_PATH_IMAGE002
wherein the content of the first and second substances,
Figure 536034DEST_PATH_IMAGE003
，
Figure 598668DEST_PATH_IMAGE004
，
Figure 738662DEST_PATH_IMAGE005
，
Figure 443313DEST_PATH_IMAGE006
，
Figure 719573DEST_PATH_IMAGE007
，
Figure 953108DEST_PATH_IMAGE008
the number of increments is represented as such,
Figure 580399DEST_PATH_IMAGE009
the angle of attack is shown as an indication,
Figure 292003DEST_PATH_IMAGE010
the pitch angle rate is expressed in terms of,
Figure 953928DEST_PATH_IMAGE011
a pitch channel control quantity is represented and,
Figure 358365DEST_PATH_IMAGE012
the thrust force is indicated by the expression,
Figure 207372DEST_PATH_IMAGE013
the derivative of lift to angle of attack is represented,
Figure 988246DEST_PATH_IMAGE014
representing a lift force pair
Figure 239099DEST_PATH_IMAGE015
The derivative of (a) of (b),
Figure 814437DEST_PATH_IMAGE016
the mass of the aircraft is represented and,
Figure 416320DEST_PATH_IMAGE017
which represents the acceleration of the force of gravity,
Figure 735306DEST_PATH_IMAGE018
the angle of inclination of the trajectory is shown,
Figure 840665DEST_PATH_IMAGE019
representing the moment of inertia of the aircraft about the z-axis of the arrow system,
Figure 586904DEST_PATH_IMAGE020
the speed of the aircraft is indicated and,
Figure 410503DEST_PATH_IMAGE021
the derivative of the pitching moment with respect to the angle of attack is represented,
Figure 798759DEST_PATH_IMAGE022
the derivative of the pitch moment with respect to the pitch angle rate is represented,
Figure 758625DEST_PATH_IMAGE023
representing a pitch moment pair
Figure 675766DEST_PATH_IMAGE024
The derivative of (c).
2. By adopting a PD control structure, the pitch channel control law is designed as follows:
Figure 986661DEST_PATH_IMAGE025
determining control parameters by using stability margin test sub-algorithm
Figure 913029DEST_PATH_IMAGE026
And
Figure 727401DEST_PATH_IMAGE027
。
3. according to the maximum deflection angle of the servomechanism
Figure 346601DEST_PATH_IMAGE028
Constraining the control quantity of the pitch channel
Figure 144793DEST_PATH_IMAGE029
The constraint of the differential term is
Figure 609272DEST_PATH_IMAGE030
，
Figure 543730DEST_PATH_IMAGE031
Are design parameters. Considering the constraint on the controlled variable, the controlled variable is
Figure 68253DEST_PATH_IMAGE032
Expressed as:
Figure 88161DEST_PATH_IMAGE033
wherein the content of the first and second substances,
Figure 356332DEST_PATH_IMAGE034
。
order to
Figure 145296DEST_PATH_IMAGE035
，
Figure 840720DEST_PATH_IMAGE036
The pitch channel small deviation dynamics model can be represented as the following nested saturation-limited model:
Figure 347924DEST_PATH_IMAGE037
wherein the content of the first and second substances,
Figure 419785DEST_PATH_IMAGE038
，
Figure 63256DEST_PATH_IMAGE039
，
Figure 929581DEST_PATH_IMAGE040
，
Figure 924082DEST_PATH_IMAGE041
，
Figure 534055DEST_PATH_IMAGE042
。
4. the design problem of the amplitude limiting value of a differential feedback term in a control law is converted into an attraction domain optimization problem of a control system with the input subject to nested saturation constraint.
Figure 563191DEST_PATH_IMAGE043
Figure 334838DEST_PATH_IMAGE044
Wherein the content of the first and second substances,
Figure 82214DEST_PATH_IMAGE045
for a given positive definite matrix, positive definite matrix
Figure 230299DEST_PATH_IMAGE046
、
Figure 113941DEST_PATH_IMAGE047
、
Figure 56489DEST_PATH_IMAGE048
To optimize the variables.
5. Solving the optimization problem to obtain an optimized variable
Figure 760003DEST_PATH_IMAGE048
Thereby obtaining a slicing value of the differential term
Figure 977358DEST_PATH_IMAGE049
And further obtaining a control law:
Figure 715506DEST_PATH_IMAGE050
example two
The attitude control law design of a pitching channel of an aircraft is taken as an example. The design method of the clipping value of the clipping item comprises the following steps:
1. establishing a small deviation dynamic model of the longitudinal motion around the mass center of a certain aircraft as follows:
Figure 94535DEST_PATH_IMAGE002
wherein the content of the first and second substances,
Figure 550924DEST_PATH_IMAGE051
，
Figure 40812DEST_PATH_IMAGE052
，
Figure 633467DEST_PATH_IMAGE053
，
Figure 448976DEST_PATH_IMAGE054
，
Figure 861503DEST_PATH_IMAGE055
，
Figure 155081DEST_PATH_IMAGE008
the number of increments is represented as such,
Figure 867822DEST_PATH_IMAGE009
the angle of attack is shown as an indication,
Figure 588653DEST_PATH_IMAGE010
the pitch angle rate is expressed in terms of,
Figure 19635DEST_PATH_IMAGE011
a pitch channel control quantity is represented and,
Figure 851325DEST_PATH_IMAGE012
the thrust force is indicated by the expression,
Figure 152993DEST_PATH_IMAGE013
the derivative of lift to angle of attack is represented,
Figure 310305DEST_PATH_IMAGE014
representing a lift force pair
Figure 697424DEST_PATH_IMAGE015
The derivative of (a) of (b),
Figure 598384DEST_PATH_IMAGE016
the mass of the aircraft is represented and,
Figure 20138DEST_PATH_IMAGE017
which represents the acceleration of the force of gravity,
Figure 348351DEST_PATH_IMAGE018
the angle of inclination of the trajectory is shown,
Figure 222766DEST_PATH_IMAGE019
representing the moment of inertia of the aircraft about the z-axis of the arrow system,
Figure 396258DEST_PATH_IMAGE020
the speed of the aircraft is indicated and,
Figure 938098DEST_PATH_IMAGE021
the derivative of the pitching moment with respect to the angle of attack is represented,
Figure 171633DEST_PATH_IMAGE022
the derivative of the pitch moment with respect to the pitch angle rate is represented,
Figure 533345DEST_PATH_IMAGE023
representing pitching momentTo pair
Figure 776107DEST_PATH_IMAGE024
The derivative of (c).
2. By adopting a PD control structure, the pitch channel control law is designed as follows:
Figure 438033DEST_PATH_IMAGE025
determining control parameters by using stability margin test sub-algorithm
Figure 108048DEST_PATH_IMAGE026
And
Figure 957056DEST_PATH_IMAGE027
。
3. according to the maximum deflection angle of the servomechanism
Figure 737930DEST_PATH_IMAGE028
Constraining the control quantity of the pitch channel
Figure 254362DEST_PATH_IMAGE029
The constraint of the proportional term is
Figure 95279DEST_PATH_IMAGE056
，
Figure 166003DEST_PATH_IMAGE057
Are design parameters. Considering the constraint on the controlled variable, the controlled variable is
Figure 750568DEST_PATH_IMAGE058
Expressed as:
Figure 855927DEST_PATH_IMAGE059
wherein the content of the first and second substances,
Figure 602167DEST_PATH_IMAGE060
。
order to
Figure 691345DEST_PATH_IMAGE061
，
Figure 548443DEST_PATH_IMAGE062
The pitch channel small deviation dynamics model can be represented as the following nested saturation-limited model:
Figure 39467DEST_PATH_IMAGE063
wherein the content of the first and second substances,
Figure 956607DEST_PATH_IMAGE038
，
Figure 1924DEST_PATH_IMAGE039
，
Figure 928292DEST_PATH_IMAGE064
，
Figure 8243DEST_PATH_IMAGE065
，
Figure 361864DEST_PATH_IMAGE066
。
4. the design problem of the amplitude limiting value of a proportional feedback item in the control law is converted into an attraction domain optimization problem of a control system with nested saturation constraint input.
Figure 894476DEST_PATH_IMAGE067
Figure 358956DEST_PATH_IMAGE068
Wherein the content of the first and second substances,
Figure 558993DEST_PATH_IMAGE069
for a given positive definite matrix, positive definite matrix
Figure 817936DEST_PATH_IMAGE070
、
Figure 103424DEST_PATH_IMAGE071
、
Figure 371594DEST_PATH_IMAGE072
、
Figure 160559DEST_PATH_IMAGE073
To optimize the variables.
5. Solving the optimization problem to obtain an optimized variable
Figure 855982DEST_PATH_IMAGE073
To obtain the clipping value of the proportional term
Figure 628766DEST_PATH_IMAGE074
And further obtaining a control law:
Figure 435048DEST_PATH_IMAGE075
the embodiments of the present application described above may be implemented in various hardware, software code, or a combination of both. For example, the embodiments of the present application may also represent program codes for executing the above-described methods in a Digital Signal Processor (DSP). The present application may also relate to a variety of functions performed by a computer processor, digital signal processor, microprocessor, or Field Programmable Gate Array (FPGA). The processor described above may be configured in accordance with the present application to perform certain tasks by executing machine-readable software code or firmware code that defines certain methods disclosed herein. Software code or firmware code may be developed to represent different programming languages and different formats or forms. Different target platforms may also be represented to compile the software code. However, different code styles, types, and languages of software code and other types of configuration code for performing tasks according to the present application do not depart from the spirit and scope of the present application.
The foregoing is merely an illustrative embodiment of the present invention, and any equivalent changes and modifications made by those skilled in the art without departing from the spirit and principle of the present invention should fall within the protection scope of the present invention.

Claims (10)

1. A method for designing an amplitude limiting value of an attitude control system is characterized by comprising the following steps:
establishing a dynamic model of the single attitude control channel of the aircraft around the centroid in a small disturbance manner;
designing a control law and control parameters of the aircraft attitude control channel based on a PD control structure;
based on the control law, establishing a feedback term and a posture control system nested saturation limited model with limited control quantity, wherein the feedback term comprises a differential feedback term and a proportional feedback term;
converting the design problem of the amplitude limiting value of a feedback item in a control law into an optimization problem of an attraction domain of a control system with input subjected to nested saturation constraint;
and solving the amplitude limiting value of the feedback item by solving the optimal attraction domain of the control system with the input constrained by nested saturation.
2. The method for designing amplitude limiting values of an attitude control system according to claim 1, wherein a stability margin test sub-algorithm is adopted to design control parameters in the control law.
3. The method for designing the amplitude limiting value of the attitude control system according to claim 1, wherein the method for establishing the nested saturation-limited model of the attitude control system with the limitation of the feedback item and the control quantity comprises the following steps:
constructing a saturation function with a limiting value of 1;
expressing the control quantity by a product of a maximum amplitude limit and a saturation function, wherein the feedback term which is also expressed by the product of the maximum amplitude limit and the saturation function is nested;
substituting the control quantity into the aircraft single attitude control channel small disturbance dynamic model around the centroid to obtain an attitude control system nested saturation limited model with limited feedback items and control quantity.
4. The method for designing amplitude limiting value of an attitude control system according to claim 3, wherein the saturation function with the amplitude limiting value of 1 is represented as:
Figure 710850DEST_PATH_IMAGE001
。
5. the attitude control system amplitude limiting value design method according to claim 1, wherein the aircraft is a liquid rocket.
6. The method for designing amplitude limiting values of an attitude control system according to claim 5, wherein propellants used by the liquid rocket are a liquid oxygen propellant and a methane propellant.
7. The attitude control system amplitude limiting value design method according to claim 1, wherein the aircraft is a missile.
8. The method for designing the amplitude limiting value of the attitude control system according to claim 7, wherein the propellants adopted by the missile are a liquid oxygen propellant and a kerosene propellant.
9. A storage medium having stored thereon an executable program that, when called, executes an attitude control system limit value design method according to any one of claims 1 to 8.
10. A server, comprising a memory storing an executable program and a processor for invoking the executable program to perform an attitude control system clipping value design method according to any one of claims 1-4.
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