CN108170155B - Passive fault-tolerant control method of three-degree-of-freedom helicopter - Google Patents

Passive fault-tolerant control method of three-degree-of-freedom helicopter Download PDF

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CN108170155B
CN108170155B CN201810033159.1A CN201810033159A CN108170155B CN 108170155 B CN108170155 B CN 108170155B CN 201810033159 A CN201810033159 A CN 201810033159A CN 108170155 B CN108170155 B CN 108170155B
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angle
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CN108170155A (en
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周东华
杨其伟
卢晓
钟麦英
王友清
王建东
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Shandong University of Science and Technology
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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
    • 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
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft

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Abstract

The invention relates to the field of aircraft control, in particular to a passive fault-tolerant control method of a three-degree-of-freedom helicopter, which comprises the following steps of S101: establishing a dynamic model of the three-degree-of-freedom helicopter: the method includes the following steps that pitching, lifting and course movement of the helicopter are simulated and respectively correspond to three angles: a pitch angle, a lifting angle and a course angle are used for establishing a dynamic equation of the three-degree-of-freedom helicopter; s102: a passive fault-tolerant control scheme: the helicopter runs, the running values of the lifting angle and the course angle are given, the given values of the lifting angle and the course angle are obtained through calculation, the given value of the pitch angle is obtained through calculation, and then S103 and S103 are executed: designing a passive fault-tolerant controller: when the motor fails, the motor is adjusted to enable the helicopter to be in a limited time; and then obtaining passive fault-tolerant input values of the lifting angle and the course angle, calculating to obtain a passive fault-tolerant input value of the pitch angle, and controlling to ensure that the three-degree-of-freedom helicopter can normally run when no fault exists and eliminate the influence of the fault on the accuracy of the flight position when the fault occurs.

Description

Passive fault-tolerant control method of three-degree-of-freedom helicopter
Technical Field
The invention relates to the field of aircraft control, in particular to a passive fault-tolerant control method of a three-degree-of-freedom helicopter.
Background
In recent years, helicopters are widely applied in various fields, and compared with fixed-wing aircrafts, the helicopters have the remarkable characteristics of vertical take-off and landing, hovering, front-back flying, left-right flying and the like, so that the helicopters are widely applied in various fields of military use, civil use and the like, for example, when 5.12 Wenchuan extra-large earthquakes occur, rescue workers cannot quickly reach disaster areas due to blockage of roads, and at this time, the helicopter, particularly a heavy helicopter, has great advantages.
The helicopter is a typical complex system, a flight control system of the helicopter has the characteristics of strong coupling, nonlinearity, multiple input and multiple output and the like, once a fault occurs, serious consequences are easily caused, and therefore a controller of the helicopter has good fault tolerance.
Based on the above situation, in order to meet the requirements of practical application, a control method considering that the helicopter can still well complete the flight task when the actuator fails is urgently needed, so that the safe operation of the helicopter is ensured.
Disclosure of Invention
In order to solve the above problems, the present invention provides a passive fault-tolerant control method for a three-degree-of-freedom helicopter, which has the following specific technical scheme:
a passive fault-tolerant control method of a three-degree-of-freedom helicopter, wherein the helicopter comprises two driving motors, and the method comprises the following steps:
s101: establishing a dynamic model of the three-degree-of-freedom helicopter: the method is characterized by simulating pitching, lifting and course movement of the helicopter, wherein the pitching, the lifting and the course movement respectively correspond to three angles: establishing a dynamic equation of the three-degree-of-freedom helicopter by using a pitch angle p, a lifting angle xi and a course angle lambda;
s102: a passive fault-tolerant control scheme: helicopter running, setting up lifting angle xidAnd course angle lambdadIs given, thereby calculating the pitch angle pdThen, S103 is executed,
s103: designing a passive fault-tolerant controller: when the motor fails, the motor is adjusted to enable the helicopter to be xi → xi in a limited timed、p→pd(ii) a Then obtaining passive fault-tolerant input values u of the rising angle xi and the heading angle lambda1And calculating the passive fault-tolerant input value u of the pitch angle2Then control is made so that p → pd。
Optimally, in step S101, two thrusts F generated by the two motorsf、FbThe thrust generated is approximately proportional to the voltage applied thereto, and KfConstant thrust produced by the motorThe thrust is as follows:
Figure BDA0001547112950000021
optimally, in step S101, the control inputs of the two motors are:
Figure BDA0001547112950000022
optimally, in step S103, the control voltages of the two motors are:
Figure BDA0001547112950000023
optimally, the kinetic equation in step S101 is: ,
Figure BDA0001547112950000024
Figure BDA0001547112950000025
Figure BDA0001547112950000026
wherein L ishIs the distance between each motor and the pitch axis; j. the design is a squarepIs the moment of inertia of the pitch axis,
Figure BDA0001547112950000027
wherein M ishIs the mass of the helicopter body; l isaIs the distance from the course axis to the helicopter body; t isgIs the equivalent gravitational moment of the pitch axis, Tg＝MhgLa-MwgLw；JeIs the moment of inertia of the lifting shaft,
Figure BDA0001547112950000028
Lwis the distance from the course axis to the balance mass, MwIs the mass of the counterbalance; j. the design is a squaretIs the moment of inertia of the heading axis,
Figure BDA0001547112950000029
optimally, in step S102, the input equation when the actuator fails is:
Figure BDA00015471129500000210
wherein
Figure BDA00015471129500000211
Optimally, in step S102, the dynamic model of the helicopter when the actuator fails is:
Figure BDA00015471129500000212
optimally, in step S102, the pitch angle is obtained as follows:
first, two virtual inputs are introduced
Figure BDA0001547112950000031
w2＝ulcosξsinp
Controllable input u can be obtained1：
Figure BDA0001547112950000032
Wherein
Figure BDA0001547112950000033
Because of the limitations of the mechanical structure,
Figure BDA0001547112950000034
the denominator of (c) cosp > 0, so u is represented by a numerator1Symbol of (a) w1d、w2dRespectively as w1、w2Control signal of (2) can be obtained
Figure BDA0001547112950000035
In the same way, design u2So that p → pd
Optimally, according to the calculation of the previous step, defining the error e as:
Figure BDA0001547112950000036
wherein p isdFrom the last step of the process, the process is carried out,
the tracking error rate is then:
Figure BDA0001547112950000037
defining the slip form surface as:
Figure BDA0001547112950000038
where β > 0 is a constant to be designed, m and n are positive odd numbers, ξ, p, λ,
the available control laws are:
Figure BDA0001547112950000039
wherein 1 < m/n < 2, η > 0,
Figure BDA00015471129500000310
lf，*＞0，*＝ξ，p，λ。
aiming at the defects of the conventional passive fault-tolerant control method, the invention provides the passive fault-tolerant control method of the three-degree-of-freedom helicopter, which effectively meets the actual application requirements, can ensure the normal operation of the three-degree-of-freedom helicopter when no fault exists, and can eliminate the influence of the fault on the accuracy of the flight position when the fault occurs.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
FIG. 1 is a pictorial view of a three-degree-of-freedom helicopter in accordance with an embodiment of the present invention;
FIG. 2 is a simplified block diagram of a three degree of freedom helicopter of one embodiment provided by the present invention;
fig. 3 is a graph of actual and given lift angle versus time according to one embodiment of the present invention.
Fig. 4 is a graph of actual and given pitch angle versus time according to one embodiment of the present invention.
FIG. 5 is a graph of actual and given heading angle versus time, in accordance with one embodiment of the present invention. .
Detailed Description
The technical solution of the present invention will be further described in detail with reference to the accompanying drawings and examples.
Example (b):
the following detailed description of the embodiments of the present invention will be provided with reference to the drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented. It should be noted that, as long as there is no conflict, the embodiments and the features of the embodiments of the present invention may be combined with each other, and the technical solutions formed are within the scope of the present invention.
Additionally, the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer-executable instructions, and while a logical order is illustrated in the flowcharts, in some cases, the steps illustrated or described may be performed in an order different than here.
Aiming at the problems in the prior art, the invention provides a passive fault-tolerant control method of a three-degree-of-freedom helicopter, which comprises the following steps:
step S101, establishing a dynamic model of the three-degree-of-freedom helicopter
The three-degree-of-freedom double-rotor helicopter semi-physical simulation platform is shown in figure 1, a universal joint is arranged at the joint of a base and a frame arm, the universal joint enables the frame arm to freely move around a lifting shaft and a course shaft, one end of the frame arm is a helicopter body and consists of a cross beam suspended at the front end of the frame arm and two propellers arranged on the cross beam, the two propellers are respectively driven by two direct current motors, the shafts of the two motors are parallel, and the thrust is perpendicular to the cross beam. The other end of the frame arm is provided with a balance block which is used for reducing the energy of the motor required by the helicopter body when the helicopter body hovers, so that the helicopter body can be lifted under the drive of a smaller voltage by the motor. Rely on two motors to drive the screw and rotate and produce lift, the every single move (pitch), lift (elevation), the course (travel) motion of simulation helicopter corresponds three angle respectively: pitch angle p, lift angle xi, course angle lambda
Due to the limitation of a mechanical structure, the ranges of the pitch angle and the lifting angle are respectively-45 deg and p are less than or equal to +45deg and-27.5 deg and ξ are less than or equal to +30 deg.
Two thrusts F generated by two motorsf、FbThree postures of the helicopter are controlled, indicating that the system is an under-actuated system. Because the helicopter is driven by two motors to generate lift force, the generated thrust is approximately proportional to the voltage applied on the helicopter, and K is setfIs a constant of thrust, the thrust generated by the motor is
Figure BDA0001547112950000051
In the modeling process of the three-degree-of-freedom helicopter control system, a ground coordinate system is adopted to analyze the stress and moment conditions of the system, fig. 2 is a simplified schematic diagram of a semi-physical simulation platform of the three-degree-of-freedom helicopter, in order to simplify the modeling process and the modeling result, in the process of establishing a mathematical model of a control system of the three-degree-of-freedom helicopter, some secondary factors need to be ignored, and some limitations and assumptions are added:
1. the mechanical part of the helicopter system is a rigid body which cannot generate elastic deformation;
2. the delay of digital signals and analog signals in system transmission is not considered, namely the helicopter control system is a non-delay system;
3. neglecting the inertia of the motor, the voltage and the torque of the direct current brushless motor keep a linear proportional relation;
4. air resistance during flight at low speed, motion friction of three rotating shafts and a gyro effect generated by rotation of a rotor wing are ignored.
According to the simplified model schematic diagram shown in fig. 3, in the established ground coordinate system, kinetic equations on three rotating axes can be respectively established:
Figure BDA0001547112950000052
Figure BDA0001547112950000053
Figure BDA0001547112950000054
wherein L ishIs the distance between each motor and the pitch axis; j. the design is a squarepIs the moment of inertia of the pitch axis,
Figure BDA0001547112950000055
wherein M ishIs the mass of the helicopter body; l isaIs the distance from the course axis to the helicopter body; t isgIs the equivalent gravitational moment of the pitch axis, Tg＝MhgLa-MwgLw；JeIs the moment of inertia of the lifting shaft,
Figure BDA0001547112950000056
Lwis the distance from the course axis to the balance mass, MwIs the mass of the counterbalance; j. the design is a squaretIs the moment of inertia of the heading axis,
Figure BDA0001547112950000057
wherein the two control inputs are
Figure BDA0001547112950000058
The control voltages of the front motor and the rear motor can be obtained from (15) and (17)
Figure BDA0001547112950000059
Step S102, passive fault-tolerant control scheme
Respectively change xid、pdAnd λdAs specified pitch, altitude and heading. The goal of the control scheme is to design u1And u2So that xi → xi within a finite timed、p→pdAnd λ → λd
Assuming that the control energy missing from the actuator is constant when the actuator fails, ffAnd fbRespectively representing the control energy missing from the front and rear actuators. Thus, the input equation of the actuator failure can be obtained as
Figure BDA0001547112950000061
Wherein
Figure BDA0001547112950000062
The dynamic model of the helicopter when the actuator fails can be obtained
Figure BDA0001547112950000063
The three-freedom-degree helicopter is an under-actuated system and has two control inputs (F)f、Fb) Three attitude angles (xi, p and lambda) need to be controlled, and two virtual inputs are introduced
Figure BDA0001547112950000064
Obtained from the formula (21)
Figure BDA0001547112950000065
Wherein
Figure BDA0001547112950000066
It should be noted that because of the mechanical limitations,
Figure BDA0001547112950000067
the denominator of (c) cosp > 0, so u is represented by a numerator1The symbol of (2).
Obtained from the formula (21)
Figure BDA0001547112950000068
Will omega1d、ω2dRespectively as omega1、ω2The control signal of (2) is obtained from the formula (23)
Figure BDA0001547112950000069
It is to be noted that p isdIs a control signal of p.
The whole passive fault-tolerant control scheme is divided into three parts:
1. design of omega1dAnd w2dSo that xi → xi when actuator failure occursdAnd p → pd
2. Will omega1dAnd w2dSubstitution into (22) and (24) respectively can yield u1And pd
3. Design u2So that p → pd
Step S103, designing a passive fault-tolerant controller
Defining a tracking error e as
Figure BDA0001547112950000071
Wherein p isdFrom type (24)
Then the tracking error rate is
Figure BDA0001547112950000072
Define a slip form surface of
Figure BDA0001547112950000073
Where β > 0 is a constant to be designed, and m and n are positive odd numbers, ξ, p, λ.
The control law of the design is
Figure BDA0001547112950000074
Wherein 1 < m/n < 2, η > 0,
Figure BDA0001547112950000075
lf，*＞0，*＝ξ，p，λ。
the following is a verification of a passive fault-tolerant control method of a three-degree-of-freedom helicopter, with the parameters of the passive fault-tolerant controller as shown in table 1
TABLE 1 parameters of Passive Fault tolerant controllers
Figure BDA0001547112950000076
The hardware parameters of the three-degree-of-freedom helicopter are shown in Table 2
TABLE 2 hardware parameters of three-DOF helicopter
Figure BDA0001547112950000077
Figure BDA0001547112950000081
Fig. 3-5 show that the passive fault-tolerant controller is designed to keep tracking the specified trajectory when the actuator fails at 40 s.
Aiming at the defects of the existing passive fault-tolerant control method, the invention provides a passive fault-tolerant control method of a three-degree-of-freedom helicopter, which effectively meets the requirements of practical application.
The above-mentioned embodiments are intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. A passive fault-tolerant control method of a three-degree-of-freedom helicopter is characterized by comprising the following steps: the helicopter comprises two drive motors, which comprise the following steps:
s101: establishing a dynamic model of the three-degree-of-freedom helicopter: the method includes the following steps that pitching, lifting and course movement of the helicopter are simulated and respectively correspond to three angles: establishing a dynamic equation of the three-degree-of-freedom helicopter by using a pitch angle p, a lifting angle xi and a course angle lambda;
in step S101, the dynamic models of the two motors are:
Figure FDA0002902681190000011
Figure FDA0002902681190000012
Figure FDA0002902681190000013
wherein L ishIs the distance between each motor and the pitch axis; j. the design is a squarepIs the moment of inertia of the pitch axis,
Figure FDA0002902681190000014
wherein M ishIs the mass of the helicopter body; l isaIs the distance from the course axis to the helicopter body; t isgIs the equivalent gravitational moment of the pitch axis, Tg＝MhgLa-MwgLw；JeIs the moment of inertia of the lifting shaft,
Figure FDA0002902681190000015
Lwis the distance from the course axis to the balance weight, MwIs the mass of the counterbalance; j. the design is a squaretIs the moment of inertia of the heading axis,
Figure FDA0002902681190000016
in which two thrust forces F generated by two motorsf、FbThe thrust generated is approximately proportional to the voltage applied thereto, and KfThe thrust constant is, the thrust generated by the motor is:
Figure FDA0002902681190000017
the control inputs to the two motors are:
Figure FDA0002902681190000018
the control voltages of the two motors are:
Figure FDA0002902681190000019
s102: a passive fault-tolerant control scheme: helicopter operation, given a lift angle xidAnd course angle lambdadCalculating to obtain given values of the lifting angle xi and the course angle lambda so as to obtain the pitch angle pdThen, S103 is executed,
s103: designing a passive fault-tolerant controller: when the motor fails, the motor is adjusted to enable the helicopter to be xi → xi in a limited timed、p→pd(ii) a Then obtaining passive fault-tolerant input values u of the rising angle xi and the heading angle lambda1And calculating the passive fault-tolerant input value u of the pitch angle2Then control is made so that p → pd；
In step S103, the input equation when the actuator fails is:
Figure FDA00029026811900000110
wherein
Figure FDA00029026811900000111
In step S102, the pitch angle is obtained as follows:
first, two virtual inputs are introduced
Figure FDA0002902681190000021
w2＝u1cosξsinp
Controllable input u can be obtained1：
Figure FDA0002902681190000022
Wherein
Figure FDA0002902681190000023
Because of the limitations of the mechanical structure,
Figure FDA0002902681190000024
the denominator of (c) cosp > 0, so u is represented by a numerator1Symbol of (a) w1d、w2dRespectively as w1、w2Control signal of (2) can be obtained
Figure FDA0002902681190000025
2. The passive fault-tolerant control method of a three-degree-of-freedom helicopter according to claim 1, characterized in that: in the step S103, the process proceeds,
defining the error e as:
Figure FDA0002902681190000026
the tracking error rate is then:
Figure FDA0002902681190000027
defining the slip form surface as:
Figure FDA0002902681190000028
wherein beta is*> 0 is a constant to be designed, m*And n*Is a positive odd number, (-) xi, p, lambda,
the available control laws are:
Figure FDA0002902681190000029
wherein 1 < m*/n*＜2，η*＞0，
Figure FDA00029026811900000210
lf，*＞0，*＝ξ，p，λ。
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