CN111522241A - Active fault-tolerant control method and device based on fixed time observer - Google Patents

Active fault-tolerant control method and device based on fixed time observer Download PDF

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CN111522241A
CN111522241A CN202010381563.5A CN202010381563A CN111522241A CN 111522241 A CN111522241 A CN 111522241A CN 202010381563 A CN202010381563 A CN 202010381563A CN 111522241 A CN111522241 A CN 111522241A
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control system
observer
fault
rotorcraft
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CN111522241B (en
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邱剑彬
王桐
王雨佳
樊渊
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Harbin Institute of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses an active fault-tolerant control method and device based on a fixed time observer, which are applied to the fault-tolerant control of a rotor type aircraft, and the method comprises the following steps: establishing a mathematical model of a rotary wing type aircraft attitude control system; establishing a fixed-time sliding-mode observer according to a mathematical model of a rotary wing type aircraft attitude control system; establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system and a fixed time sliding mode observer; controlling the rotor type aircraft by using a fault-tolerant controller; the invention has the advantages that: the system stability is strong, and the modeling error is small.

Description

Active fault-tolerant control method and device based on fixed time observer
Technical Field
The invention relates to the technical field of fault-tolerant control of rotary wing type aircrafts, in particular to an active fault-tolerant control method and device based on a fixed time observer.
Background
Compared with a fixed-wing aircraft, the rotary-wing aircraft has the advantages of being capable of vertically taking off and landing and hovering in the air while having a high flying speed. In recent years, as the related technology of the unmanned rotary wing type aircraft is mature day by day, the unmanned rotary wing type aircraft is widely applied in various industries. For example, military monitoring and investigation tasks, rescue tasks in fire and earthquake, etc.; meanwhile, the method is also one of important tools and means for Mars detection.
The rotary wing type aircraft can efficiently and accurately complete tasks and is highly dependent on an internal flight control system. However, due to the complex working environment, the external atmospheric conditions and the activities of other objects can generate certain disturbances on the aircraft, which affects the control performance of the aircraft. Meanwhile, the high-intensity operation inevitably causes abrasion of machine body parts and damage of an actuator and a sensor. Therefore, the research on fault-tolerant control methods for rotor-type aircrafts is particularly important to ensure the efficient completion of the control tasks thereof.
Chinese patent publication No. CN110502027A discloses a four-rotor unmanned aerial vehicle attitude fault-tolerant control method based on a self-adaptive terminal sliding mode, and in order to solve a time-varying fault, firstly, mathematical models of a position subsystem and an attitude subsystem of a four-rotor unmanned aerial vehicle are established, and an error function of the position subsystem is defined. Then, under the condition that the attitude subsystem pitch angle takes place the time-varying trouble, application unmanned aerial vehicle attitude angle error is calmed to zero, realizes the fault-tolerant of self-adaptation, but this patent application system control's stability does not solve.
Chinese patent publication No. CN105353615B discloses an active fault-tolerant control method of a four-rotor aircraft based on a sliding-mode observer, which designs the sliding-mode observer, performs linear transformation on a system, reconstructs an actuator fault based on the idea of equivalent error injection, adds compensation control in sliding-mode control by utilizing a reconstructed estimated value of the actuator fault, and finally forms a complete active fault-tolerant controller. According to the method, the sliding-mode observer is designed to reconstruct and estimate the fault, the online adjustment of the gain of the controller can be realized, the control law is optimal, the control precision and the response speed of the flight of the four-rotor aircraft are effectively improved, and the design basis of the fault-tolerant controller can be provided for the complex four-rotor aircraft with the actuator fault. The invention can realize the online adjustment of the gain of the controller, so that the provided control law is optimal. However, the actual mathematical model of the four-rotor aircraft is highly nonlinear and strongly coupled, and the fault-tolerant control scheme adopts a linear model, so that the modeling error is large; in addition, the problem of jitter of sliding mode control is not solved, so that the system stability is poor.
Disclosure of Invention
The invention aims to solve the technical problems of poor system stability and large modeling error of the control method of the rotor type aircraft in the prior art.
The invention solves the technical problems through the following technical means: an active fault-tolerant control method based on a fixed time observer is applied to fault-tolerant control of a rotor type aircraft, and comprises the following steps:
the method comprises the following steps: establishing a mathematical model of the attitude control system of the rotary wing aircraft according to the control input dynamic value of the control system, the nonlinear dynamic value of the control system and the sum of the comprehensive disturbance quantities;
step two: establishing a fixed-time sliding mode observer according to an input dynamic value, a nonlinear dynamic value, an error variable and a state quantity of the sliding mode observer in a mathematical model of the attitude control system of the rotor type aircraft;
step three: establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system, a fixed time sliding mode observer and a tracking error;
step four: and controlling the rotor type aircraft by using a fault-tolerant controller.
The method comprises the steps of obtaining system fault information by using a fixed time sliding mode observer, designing a mathematical model of a rotor type aircraft attitude control system containing comprehensive disturbance, establishing a fault-tolerant controller according to the mathematical model of the rotor type aircraft attitude control system and the fixed time sliding mode observer, controlling the rotor type aircraft by using the fault-tolerant controller, considering factors such as tracking error and the comprehensive disturbance by using the fault-tolerant controller, having small modeling error, effectively processing faults of the system and having stability.
Preferably, the first step includes: using formulas
Figure BDA0002482293620000031
Figure BDA0002482293620000032
Establishing a mathematical model of a rotary wing type aircraft attitude control system;
wherein X represents a state variable of the control system; x1A first state quantity representing the control system,
Figure BDA0002482293620000033
representing the first derivative of a first state quantity of the control system, and X1＝[α，β]T，[]TRepresenting the transpose of the matrix, α representing the yaw angle of the rotorcraft, β representing the pitch angle of the rotorcraft;
X2a second state quantity representing the control system,
Figure BDA0002482293620000034
represents a first derivative of a second state quantity of the control system, and
Figure BDA0002482293620000035
representing the first derivative of the yaw angle of the rotorcraft,
Figure BDA0002482293620000036
representing the first derivative of the pitch angle of the rotorcraft;
f (X) represents a nonlinear dynamic value of the control system, and
Figure BDA0002482293620000037
m represents the effective mass of the aircraft, g represents the gravitational acceleration constant, LaRepresenting the length of the center of the rotorcraft from the front motor;
g (X) represents a control input dynamic value of the control system, and
Figure BDA0002482293620000038
Kfrepresenting the coefficient of moment generated by the motor, JαRepresenting the moment of inertia of the yaw axis, JβIndicating the pitch axisRotational inertia of LhRepresenting the length of the rear motor from the center of the rotorcraft;
u represents a matrix form of an input amount of the control system, and
Figure BDA0002482293620000041
Vfrepresenting the voltage, V, applied to the front motor of a rotorcraftbRepresenting the voltage applied to the rear motor of the rotorcraft;
Δ represents the integrated disturbance amount, and Δ ═ Δ f (x)) - (g (x)) + Δ g (x)) (ρi-1)U(t)+D(t),ρiFailure coefficient and p representing occurrence of actuator failure of rotorcrafti∈ [0, 1), Δ f (x) represents a first uncertainty value of the control system, Δ g (x) represents a second uncertainty value of the control system, u (t) represents a functional form of an input quantity of the control system, d (t) represents a functional form of an unknown external disturbance.
Preferably, the second step includes: using formulas
Figure BDA0002482293620000042
Figure BDA0002482293620000043
Establishing a fixed time sliding-mode observer, wherein ξ1Representing a first quantity of state of the sliding-mode observer, ξ2A first state quantity of the sliding mode observer is represented,
Figure BDA0002482293620000044
a first derivative of a first state quantity representing a sliding mode observer,
Figure BDA0002482293620000045
denotes the first derivative of the first state quantity of the sliding-mode observer, e denotes the error variable, and e is ξ1-X1And | | represents a euclidean distance symbol, p is a power exponent and p > 1, sign () represents a sign function, λ1Is a preset observer firstParameter, λ2Is a predetermined observer second parameter, λ3Is a predetermined observer third parameter, and λ1，λ2，λ3Are all constants greater than zero.
Preferably, the third step includes: using formulas
Figure BDA0002482293620000046
A fault tolerant controller is established in which, among other things,
Figure BDA0002482293620000047
is an estimate of the overall disturbance variable Delta, X2dTo control a second quantity of state X of the system2The reference signal of (a) is set,
Figure BDA0002482293620000048
for virtual control
Figure BDA0002482293620000049
An output through a differentiator;
Figure BDA00024822936200000410
is a preset second controller parameter, E2Is a second tracking error, and E2＝X2-X2d，
Figure BDA0002482293620000051
Is a first auxiliary function.
Preferably, the third step further comprises: using formulas
Figure BDA0002482293620000052
Obtaining a function
Figure BDA0002482293620000053
Wherein z represents the state variable of the differentiator, z1Expressed as a first state quantity of the differentiator, z2A second state quantity representing a differentiator, s (t) being an input to the differentiator and representing a perturbation parameterAnd > 0;
using formulas
Figure BDA0002482293620000054
A function sat (z) is obtained in which,bis a preset constant greater than zero;
using formulas
Figure BDA0002482293620000055
Figure BDA0002482293620000056
zout＝z2
A differentiator is established in which, among other things,
Figure BDA0002482293620000057
is the first derivative of the first state quantity of the differentiator,
Figure BDA0002482293620000058
is the first derivative of the second state quantity of the differentiator, zoutIs the output of the differentiator.
Preferably, the third step further comprises: using formulas
Figure BDA0002482293620000059
Constructing a first auxiliary function, wherein E1Is a first tracking error, and E1＝x1-x1d，X1dFor controlling a first quantity of state X of the system1The reference signal of (a);
Figure BDA00024822936200000510
is an auxiliary variable, and
Figure BDA00024822936200000511
is the first derivative of the auxiliary variable,
Figure BDA00024822936200000512
is a preset first controller parameter, wherein,
Figure BDA00024822936200000513
for controlling a first quantity of state X of the system1The first derivative of the reference signal.
The invention also provides an active fault-tolerant control device based on the fixed time observer, which is applied to the fault-tolerant control of the rotor type aircraft, and the device comprises:
the model establishing module is used for establishing a mathematical model of the attitude control system of the rotary wing aircraft according to the control input dynamic value of the control system, the nonlinear dynamic value of the control system and the sum of the comprehensive disturbance quantities;
the sliding mode observer establishing module is used for establishing a fixed time sliding mode observer according to an input dynamic value, a nonlinear dynamic value, an error variable and a state quantity of the sliding mode observer in a mathematical model of the attitude control system of the rotor type aircraft;
the fault-tolerant controller establishing module is used for establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system, a fixed time sliding mode observer and a tracking error;
and the control module is used for controlling the rotor type aircraft by utilizing the fault-tolerant controller.
Preferably, the model building module is further configured to: using formulas
Figure BDA0002482293620000061
Figure BDA0002482293620000062
Establishing a mathematical model of a rotary wing type aircraft attitude control system;
wherein X represents a state variable of the control system; x1A first state quantity representing the control system,
Figure BDA0002482293620000063
representing the first derivative of a first state quantity of the control system, and X1＝[α，β]T，[]TRepresenting the transpose of the matrix, α representing the yaw angle of the rotorcraft, β representing the pitch angle of the rotorcraft;
X2a second state quantity representing the control system,
Figure BDA0002482293620000064
represents a first derivative of a second state quantity of the control system, and
Figure BDA0002482293620000065
representing the first derivative of the yaw angle of the rotorcraft,
Figure BDA0002482293620000066
representing the first derivative of the pitch angle of the rotorcraft;
f (X) represents a nonlinear dynamic value of the control system, and
Figure BDA0002482293620000067
m represents the effective mass of the aircraft, g represents the gravitational acceleration constant, LaRepresenting the length of the center of the rotorcraft from the front motor;
g (X) represents a control input dynamic value of the control system, and
Figure BDA0002482293620000071
Kfrepresenting the coefficient of moment generated by the motor, JαRepresenting the moment of inertia of the yaw axis, JβRepresenting the moment of inertia of the pitch axis, LhRepresenting the length of the rear motor from the center of the rotorcraft;
u represents a matrix form of an input amount of the control system, and
Figure BDA0002482293620000072
Vfrepresenting the voltage, V, applied to the front motor of a rotorcraftbIndicating application to rotor planeVoltage on the rear motor of the traveling device;
Δ represents the integrated disturbance amount, and Δ ═ Δ f (x)) - (g (x)) + Δ g (x)) (ρi-1)U(t)+D(t),ρiFailure coefficient and p representing occurrence of actuator failure of rotorcrafti∈ [0, 1), Δ f (x) represents a first uncertainty value of the control system, Δ g (x) represents a second uncertainty value of the control system, u (t) represents a functional form of an input quantity of the control system, d (t) represents a functional form of an unknown external disturbance.
Preferably, the sliding-mode observer establishing module is further configured to: using formulas
Figure BDA0002482293620000073
Figure BDA0002482293620000074
Establishing a fixed time sliding-mode observer, wherein ξ1Representing a first quantity of state of the sliding-mode observer, ξ2A first state quantity of the sliding mode observer is represented,
Figure BDA0002482293620000075
a first derivative of a first state quantity representing a sliding mode observer,
Figure BDA0002482293620000076
denotes the first derivative of the first state quantity of the sliding-mode observer, e denotes the error variable, and e is ξ1-X1And | | represents a euclidean distance symbol, p is a power exponent and p > 1, sign () represents a sign function, λ1Is a predetermined observer first parameter, λ2Is a predetermined observer second parameter, λ3Is a predetermined observer third parameter, and λ1，λ2，λ3Are all constants greater than zero.
Preferably, the fault-tolerant controller establishing module is further configured to: using formulas
Figure BDA0002482293620000081
A fault tolerant controller is established in which, among other things,
Figure BDA0002482293620000082
is an estimate of the overall disturbance variable Delta, X2dTo control a second quantity of state X of the system2The reference signal of (a) is set,
Figure BDA0002482293620000083
for virtual control
Figure BDA0002482293620000084
An output through a differentiator;
Figure BDA0002482293620000085
is a preset second controller parameter, E2Is a second tracking error, and E2＝X2-X2d，
Figure BDA0002482293620000086
Is a first auxiliary function.
Preferably, the fault-tolerant controller establishing module is further configured to: using formulas
Figure BDA0002482293620000087
Obtaining a function
Figure BDA0002482293620000088
Wherein z represents the state variable of the differentiator, z1Expressed as a first state quantity of the differentiator, z2A second state quantity representing a differentiator, s (t) being the input of the differentiator, representing a perturbation parameter and > 0;
using formulas
Figure BDA0002482293620000089
A function sat (z) is obtained in which,bis a preset constant greater than zero;
using formulas
Figure BDA00024822936200000810
Figure BDA00024822936200000811
zout＝z2
A differentiator is established in which, among other things,
Figure BDA00024822936200000812
is the first derivative of the first state quantity of the differentiator,
Figure BDA00024822936200000813
is the first derivative of the second state quantity of the differentiator, zoutIs the output of the differentiator.
Preferably, the fault-tolerant controller establishing module is further configured to: using formulas
Figure BDA00024822936200000814
Constructing a first auxiliary function, wherein E1Is a first tracking error, and E1＝x1-x1d，X1dFor controlling a first quantity of state X of the system1The reference signal of (a);
Figure BDA0002482293620000091
is an auxiliary variable, and
Figure BDA0002482293620000092
is the first derivative of the auxiliary variable,
Figure BDA0002482293620000093
is a preset first controller parameter, wherein,
Figure BDA0002482293620000094
for controlling a first quantity of state X of the system1The first derivative of the reference signal.
The invention has the advantages that: the method comprises the steps of obtaining system fault information by using a fixed time sliding mode observer, designing a mathematical model of a rotor type aircraft attitude control system containing comprehensive disturbance, establishing a fault-tolerant controller according to the mathematical model of the rotor type aircraft attitude control system and the fixed time sliding mode observer, controlling the rotor type aircraft by using the fault-tolerant controller, considering factors such as tracking error and the comprehensive disturbance by using the fault-tolerant controller, having small modeling error, effectively processing faults of the system and having stability.
Drawings
FIG. 1 is a flowchart of an active fault-tolerant control method based on a fixed time observer according to an embodiment of the present invention;
FIG. 2 is a block diagram of an active fault-tolerant control method based on a fixed time observer according to an embodiment of the present invention;
FIG. 3 is a simplified diagram of an experimental platform of an active fault-tolerant control method based on a fixed time observer according to an embodiment of the present invention;
FIG. 4 is a graph illustrating a change in attitude of a rotor-based aircraft at a yaw angle in an active fault-tolerant control method based on a fixed time observer according to an embodiment of the present invention;
fig. 5 is a graph of a change of attitude of a rotor type aircraft in a pitch angle in an active fault-tolerant control method based on a fixed time observer according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1 and fig. 2, an active fault-tolerant control method based on a fixed time observer is applied to fault-tolerant control of a rotor aircraft, and the method includes:
step S1: establishing a mathematical model of the attitude control system of the rotary wing aircraft according to the control input dynamic value of the control system, the nonlinear dynamic value of the control system and the sum of the comprehensive disturbance quantities; as can be seen in fig. 3, the twin-rotor aircraft has two motors, so that only two attitude angles can be arbitrarily controlled. Therefore, only two attitude angles, namely a yaw angle and a pitch angle, are studied, and the roll angle is changed under the influence of the yaw angle, the pitch angle and the voltage, and the roll angle is not studied.
First, using a formula
Figure BDA0002482293620000101
Figure BDA0002482293620000102
Establishing a mathematical model of the attitude control system of the rotor type aircraft without considering the fault condition;
wherein X represents a state variable of the control system; x1A first state quantity representing the control system,
Figure BDA0002482293620000103
representing the first derivative of a first state quantity of the control system, and X1＝[α，β]T，[]TRepresenting the transpose of the matrix, α representing the yaw angle of the rotorcraft, β representing the pitch angle of the rotorcraft;
X2a second state quantity representing the control system,
Figure BDA0002482293620000104
represents a first derivative of a second state quantity of the control system, and
Figure BDA0002482293620000105
representing rotorcraftThe first derivative of the yaw angle is,
Figure BDA0002482293620000106
representing the first derivative of the pitch angle of the rotorcraft;
f (X) represents a nonlinear dynamic value of the control system, and
Figure BDA0002482293620000111
m represents the effective mass of the aircraft, g represents the gravitational acceleration constant, LaRepresenting the length of the center of the rotorcraft from the front motor;
g (X) represents a control input dynamic value of the control system, and
Figure BDA0002482293620000112
Kfrepresenting the coefficient of moment generated by the motor, JαRepresenting the moment of inertia of the yaw axis, JβRepresenting the moment of inertia of the pitch axis, LhRepresenting the length of the rear motor from the center of the rotorcraft;
u represents a matrix form of an input amount of the control system, and
Figure BDA0002482293620000113
Vfrepresenting the voltage, V, applied to the front motor of a rotorcraftbRepresenting the voltage applied to the rear motor of the rotorcraft; the voltage applied to the front motor of the rotorcraft and the voltage applied to the rear motor of the rotorcraft are the objects of the present invention to be obtained, and the present invention finally obtains the voltage applied to the front motor of the rotorcraft and the voltage applied to the rear motor of the rotorcraft, that is, the input of the control system, by derivation in steps and steps.
When considering system uncertainties, external disturbances and actuator faults, the mathematical model of the attitude control system of a rotary wing aircraft can be rewritten in the form:
Figure BDA0002482293620000114
Figure BDA0002482293620000115
where Δ F (X) represents a first uncertainty value of the control system, Δ G (X) represents a second uncertainty value of the control system, D represents a matrix form of the unknown external disturbance, UfAn input quantity matrix representing the control system with the fault is represented as follows:
Figure BDA0002482293620000116
Figure BDA0002482293620000121
ρi(t) a functional form of a failure coefficient representing the occurrence of an actuator failure of a rotorcraft, tfIndicating the time at which a failure of an actuator of a rotorcraft has occurred, i being an index value of the input variable with the failed control system, uiThe ith failure information element of the control system with the failure.
Then, the integrated disturbance amount is designed, and is represented by a symbol Δ ═ Δ f (x) - (g (x)) + Δ g (x)) (ρ ═ f (x)), (g (x)) + Δ g (x)), (ρi-1)U(t)+D(t),ρiFailure coefficient and p representing occurrence of actuator failure of rotorcrafti∈ [0, 1), U (t) is a function of the input of the control system, D (t) is a function of the unknown external disturbance, and p is expanded by the comprehensive disturbance quantity formulaiU (t) and
Figure BDA0002482293620000122
the expressions are synonymous and are each an element of the input variable matrix of the control system with the fault.
Finally, the mathematical model of the attitude control system of the rotor aircraft considering the fault condition is as follows:
Figure BDA0002482293620000123
step S2: establishing a fixed-time sliding mode observer according to an input dynamic value, a nonlinear dynamic value, an error variable and a state quantity of the sliding mode observer in a mathematical model of the attitude control system of the rotor type aircraft; the specific process is as follows: using formulas
Figure BDA0002482293620000124
Figure BDA0002482293620000125
Establishing a fixed time sliding-mode observer, wherein ξ1Representing a first quantity of state of the sliding-mode observer, ξ2A first state quantity of the sliding mode observer is represented,
Figure BDA0002482293620000126
a first derivative of a first state quantity representing a sliding mode observer,
Figure BDA0002482293620000127
denotes the first derivative of the first state quantity of the sliding-mode observer, e denotes the error variable, and e is ξ1-X1And | | represents a euclidean distance symbol, p is a power exponent and p > 1, sign () represents a sign function, λ1Is a predetermined observer first parameter, λ2Is a predetermined observer second parameter, λ3Is a predetermined observer third parameter, and λ1，λ2，λ3Are all constants greater than zero.
λ1，λ2，λ3The following conditions are satisfied:
Figure BDA0002482293620000131
l represents an upper bound of the integrated disturbance quantity.
Step S3: establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system, a fixed time sliding mode observer and a tracking error; the specific process is as follows: using formulas
B1＝x1-x1d
E2＝x2-x2d
Tracking error of design system, wherein E1For the first tracking error, X1dFor controlling a first quantity of state X of the system1The reference signal of (a); e2For the second tracking error, X2dTo control a second quantity of state X of the system2The reference signal of (a);
then, using the formula
Figure BDA0002482293620000132
Obtaining a function
Figure BDA0002482293620000133
Wherein z represents the state variable of the differentiator, z1Expressed as a first state quantity of the differentiator, z2A second state quantity representing a differentiator, s (t) being the input of the differentiator, representing a perturbation parameter and > 0;
then, using the formula
Figure BDA0002482293620000134
A function sat (z) is obtained in which,bis a preset constant greater than zero;
then, using the formula
Figure BDA0002482293620000141
Figure BDA0002482293620000142
zout＝z2
A differentiator is established in which, among other things,
Figure BDA0002482293620000143
is a differentialThe first derivative of the first state quantity of the device,
Figure BDA0002482293620000144
is the first derivative of the second state quantity of the differentiator, zoutIs the output of the differentiator.
To further reduce tracking error, equations are used
Figure BDA0002482293620000145
A first auxiliary function is constructed, wherein,
Figure BDA0002482293620000146
is an auxiliary variable, and
Figure BDA0002482293620000147
is the first derivative of the auxiliary variable,
Figure BDA0002482293620000148
is a preset first controller parameter, wherein,
Figure BDA0002482293620000149
for controlling a first quantity of state X of the system1The first derivative of the reference signal.
For the first auxiliary function
Figure BDA00024822936200001410
The derivation results were as follows:
Figure BDA00024822936200001411
for tracking error E2The derivation was performed with the following results:
Figure BDA00024822936200001412
through derivation of all the formulas, the formula is constructed
Figure BDA00024822936200001413
As a fault-tolerant controller, where U is the same as before, is in the form of a matrix of input quantities to the control system, and
Figure BDA00024822936200001414
will be provided with
Figure BDA00024822936200001415
Substitution into
Figure BDA00024822936200001416
The left side of the front panel is just the right side,
Figure BDA00024822936200001417
is an estimate of the integrated disturbance variable delta,
Figure BDA00024822936200001418
for virtual control
Figure BDA00024822936200001419
An output through a differentiator;
Figure BDA00024822936200001420
is a preset second controller parameter,
Figure BDA0002482293620000151
is a first auxiliary function.
Step S4: and controlling the rotor type aircraft by using a fault-tolerant controller.
The stability, i.e. the feasibility, of the scheme designed by the present invention is demonstrated below by the lyapunov function, which is designed as follows:
Figure BDA0002482293620000152
bonding system
Figure BDA0002482293620000153
Sum equation
Figure BDA0002482293620000154
Derivation of the Lyapunov function yields the following equation
Figure BDA0002482293620000155
Wherein the content of the first and second substances,
Figure BDA0002482293620000156
therefore, according to the lyapunov stability theorem, the stability of the system can be ensured when the system fails, and the tracking error can be finally converged into a small range.
FIG. 4 is a graph of attitude change of a rotary wing aircraft at yaw angle, C1The curve represents the reference signal for yaw angle; b is1The curve represents the actual change of the yaw angle under the condition that the controller contains fault compensation; a. the1The curve represents the change in yaw angle without fault compensation by the controller. Comparison B1And A1It can be seen from the curve that when faults and disturbances occur in the system with t > 20s, the fault compensation scheme provided by the invention can enable the yaw angle of the aircraft to be hardly influenced by the faults and disturbances, and when fault compensation is not performed, the yaw angle of the aircraft has large fluctuation.
FIG. 5 is a graph of the attitude change in pitch angle of the rotary wing aircraft of the present invention; b is2The curve represents a reference signal for the pitch angle; a. the2The curve represents the actual change of the depression elevation angle under the condition that the controller contains fault compensation; c2The curve represents the change in pitch angle without fault compensation for the controller. Comparison A2And C2The curve shows that when the system has faults and disturbance in t > 20s, the fault compensation scheme provided by the invention can ensure that the pitching angle of the aircraft is hardly influenced by the faults and disturbance, and when the system has no fault compensation, the pitching angle of the aircraft has large fluctuation.
According to the active fault-tolerant control method based on the fixed time observer, the fault-tolerant controller is established according to the mathematical model of the attitude control system of the rotor type aircraft and the fixed time sliding-mode observer, the rotor type aircraft is controlled by the fault-tolerant controller, faults occurring in the system are effectively processed, the modeling error is small, and the system has stability.
Example 2
Corresponding to embodiment 1 of the present invention, embodiment 2 of the present invention further provides an active fault-tolerant control device based on a fixed time observer, which is applied to fault-tolerant control of a rotor aircraft, and the device includes:
the model establishing module is used for establishing a mathematical model of the attitude control system of the rotary wing aircraft according to the control input dynamic value of the control system, the nonlinear dynamic value of the control system and the sum of the comprehensive disturbance quantities;
the sliding mode observer establishing module is used for establishing a fixed time sliding mode observer according to an input dynamic value, a nonlinear dynamic value, an error variable and a state quantity of the sliding mode observer in a mathematical model of the attitude control system of the rotor type aircraft;
the fault-tolerant controller establishing module is used for establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system, a fixed time sliding mode observer and a tracking error;
and the control module is used for controlling the rotor type aircraft by utilizing the fault-tolerant controller.
Preferably, the model building module is further configured to: using formulas
Figure BDA0002482293620000171
Figure BDA0002482293620000172
Establishing a mathematical model of a rotary wing type aircraft attitude control system;
wherein X represents a state variable of the control system; x1A first state quantity representing the control system,
Figure BDA0002482293620000173
representing the first derivative of a first state quantity of the control system, and X1＝[α，β]T，[]TRepresenting the transpose of the matrix, α representing the yaw angle of the rotorcraft, β representing the pitch angle of the rotorcraft;
X2a second state quantity representing the control system,
Figure BDA0002482293620000174
represents a first derivative of a second state quantity of the control system, and
Figure BDA0002482293620000175
representing the first derivative of the yaw angle of the rotorcraft,
Figure BDA0002482293620000176
representing the first derivative of the pitch angle of the rotorcraft;
f (X) represents a nonlinear dynamic value of the control system, and
Figure BDA0002482293620000177
m represents the effective mass of the aircraft, g represents the gravitational acceleration constant, LaRepresenting the length of the center of the rotorcraft from the front motor;
g (X) represents a control input dynamic value of the control system, and
Figure BDA0002482293620000178
Kfrepresenting the coefficient of moment generated by the motor, JαRepresenting the moment of inertia of the yaw axis, JβRepresenting the moment of inertia of the pitch axis, LhRepresenting the length of the rear motor from the center of the rotorcraft;
u represents a matrix form of an input amount of the control system, and
Figure BDA0002482293620000179
Vfrepresenting the voltage, V, applied to the front motor of a rotorcraftbIndicating application to the rear of a rotorcraftThe voltage across the motor;
Δ represents the integrated disturbance amount, and Δ ═ Δ f (x)) - (g (x)) + Δ g (x)) (p)i-1)U(t)+D(t),ρiFailure coefficient and p representing occurrence of actuator failure of rotorcrafti∈ [0, 1), Δ f (x) represents a first uncertainty value of the control system, Δ g (x) represents a second uncertainty value of the control system, u (t) represents a functional form of an input quantity of the control system, d (t) represents a functional form of an unknown external disturbance.
Specifically, the sliding-mode observer establishing module is further configured to: using formulas
Figure BDA0002482293620000181
Figure BDA0002482293620000182
Establishing a fixed time sliding-mode observer, wherein ξ1Representing a first quantity of state of the sliding-mode observer, ξ2A first state quantity of the sliding mode observer is represented,
Figure BDA0002482293620000183
a first derivative of a first state quantity representing a sliding mode observer,
Figure BDA0002482293620000184
denotes the first derivative of the first state quantity of the sliding-mode observer, e denotes the error variable, and e is ξ1-X1And | | represents a euclidean distance symbol, p is a power exponent and p > 1, sign () represents a sign function, λ1Is a predetermined observer first parameter, λ2Is a predetermined observer second parameter, λ3Is a predetermined observer third parameter, and λ1，λ2，λ3Are all constants greater than zero.
Specifically, the fault-tolerant controller establishing module is further configured to: using formulas
Figure BDA0002482293620000185
A fault tolerant controller is established in which, among other things,
Figure BDA0002482293620000186
is an estimate of the overall disturbance variable Delta, X2dTo control a second quantity of state X of the system2The reference signal of (a) is set,
Figure BDA0002482293620000187
for virtual control
Figure BDA0002482293620000188
An output through a differentiator;
Figure BDA0002482293620000189
is a preset second controller parameter, E2Is a second tracking error, and E2＝X2-X2d，
Figure BDA00024822936200001810
Is a first auxiliary function.
Specifically, the fault-tolerant controller establishing module is further configured to: using formulas
Figure BDA00024822936200001811
Obtaining a function
Figure BDA00024822936200001812
Wherein z represents the state variable of the differentiator, z1Expressed as a first state quantity of the differentiator, z2A second state quantity representing a differentiator, s (t) being the input of the differentiator, representing a perturbation parameter and > 0;
using formulas
Figure BDA0002482293620000191
A function sat (z) is obtained in which,bis a preset constant greater than zero;
using formulas
Figure BDA0002482293620000192
Figure BDA0002482293620000193
zout＝z2
A differentiator is established in which, among other things,
Figure BDA0002482293620000194
is the first derivative of the first state quantity of the differentiator,
Figure BDA0002482293620000195
is the first derivative of the second state quantity of the differentiator, zoutIs the output of the differentiator.
Specifically, the fault-tolerant controller establishing module is further configured to: using formulas
Figure BDA0002482293620000196
Constructing a first auxiliary function, wherein E1Is a first tracking error, and E1＝x1-x1d，X1dFor controlling a first quantity of state X of the system1The reference signal of (a);
Figure BDA0002482293620000197
is an auxiliary variable, and
Figure BDA0002482293620000198
is the first derivative of the auxiliary variable,
Figure BDA0002482293620000199
is a preset first controller parameter, wherein,
Figure BDA00024822936200001910
for controlling a first quantity of state X of the system1Reference signal ofThe first derivative of (a).
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. An active fault-tolerant control method based on a fixed time observer is applied to fault-tolerant control of a rotor type aircraft, and comprises the following steps:
the method comprises the following steps: establishing a mathematical model of the attitude control system of the rotary wing aircraft according to the control input dynamic value of the control system, the nonlinear dynamic value of the control system and the sum of the comprehensive disturbance quantities;
step two: establishing a fixed-time sliding mode observer according to an input dynamic value, a nonlinear dynamic value, an error variable and a state quantity of the sliding mode observer in a mathematical model of the attitude control system of the rotor type aircraft;
step three: establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system, a fixed time sliding mode observer and a tracking error;
step four: and controlling the rotor type aircraft by using a fault-tolerant controller.
2. The active fault-tolerant control method based on the fixed time observer is characterized in that the first step comprises the following steps: using formulas
Figure FDA0002482293610000011
Figure FDA0002482293610000012
Establishing a mathematical model of a rotary wing type aircraft attitude control system;
wherein X represents a state variable of the control system; x1A first state quantity representing the control system,
Figure FDA0002482293610000013
representing the first derivative of a first state quantity of the control system, and X1＝[α，β]T，[]TRepresenting the transpose of the matrix, α representing the yaw angle of the rotorcraft, β representing the pitch angle of the rotorcraft;
X2a second state quantity representing the control system,
Figure FDA0002482293610000014
represents a first derivative of a second state quantity of the control system, and
Figure FDA0002482293610000015
Figure FDA0002482293610000016
representing the first derivative of the yaw angle of the rotorcraft,
Figure FDA0002482293610000017
representing the first derivative of the pitch angle of the rotorcraft;
f (X) represents a nonlinear dynamic value of the control system, and
Figure FDA0002482293610000018
m represents the effective mass of the aircraft, g represents the gravitational acceleration constant, LaRepresenting the length of the center of the rotorcraft from the front motor;
g (X) represents a control input dynamic value of the control system, and
Figure FDA0002482293610000021
Kfrepresenting the coefficient of moment generated by the motor, JαRepresenting the moment of inertia of the yaw axis, JβRepresenting the moment of inertia of the pitch axis, LhRepresenting the length of the rear motor from the center of the rotorcraft;
u represents a matrix form of an input amount of the control system, and
Figure FDA0002482293610000022
Vfrepresenting the voltage, V, applied to the front motor of a rotorcraftbRepresenting the voltage applied to the rear motor of the rotorcraft;
Δ represents the integrated disturbance amount, and Δ ═ Δ f (x)) - (g (x)) + Δ g (x)) (ρi-1)U(t)+D(t)，ρiFailure coefficient and p representing occurrence of actuator failure of rotorcrafti∈ [0, 1), Δ f (x) represents a first uncertainty value of the control system, Δ g (x) represents a second uncertainty value of the control system, u (t) represents a functional form of an input quantity of the control system, d (t) represents a functional form of an unknown external disturbance.
3. The active fault-tolerant control method based on the fixed time observer according to claim 2, wherein the second step comprises: using formulas
Figure FDA0002482293610000023
Figure FDA0002482293610000024
Establishing a fixed time sliding-mode observer, wherein ξ1Representing a first quantity of state of the sliding-mode observer, ξ2A first state quantity of the sliding mode observer is represented,
Figure FDA0002482293610000025
a first derivative of a first state quantity representing a sliding mode observer,
Figure FDA0002482293610000026
denotes the first derivative of the first state quantity of the sliding-mode observer, e denotes the error variable, and e is ξ1-X1And | | represents a euclidean distance symbol, p is a power exponent and p > 1, sign () represents a sign function, λ1Is a predetermined observer first parameter, λ2Is a predetermined observer second parameter, λ3Is a predetermined observer third parameter, and λ1，λ2，λ3Are all constants greater than zero.
4. The active fault-tolerant control method based on the fixed time observer according to claim 3, wherein the third step comprises: using formulas
Figure FDA0002482293610000031
A fault tolerant controller is established in which, among other things,
Figure FDA0002482293610000032
is an estimate of the overall disturbance variable Delta, X2dTo control a second quantity of state X of the system2The reference signal of (a) is set,
Figure FDA0002482293610000033
for virtual control
Figure FDA0002482293610000034
An output through a differentiator;
Figure FDA0002482293610000035
is a preset second controller parameter, E2Is a second tracking error, and E2＝X2-X2d，
Figure FDA0002482293610000036
Is a first auxiliary function.
5. The active fault-tolerant control method based on the fixed time observer according to claim 4, wherein the third step further comprises: using formulas
Figure FDA0002482293610000037
Obtaining a function
Figure FDA0002482293610000038
Wherein z represents the state variable of the differentiator, z1Expressed as a first state quantity of the differentiator, z2A second state quantity representing a differentiator, s (t) being the input of the differentiator, representing a perturbation parameter and > 0;
using formulas
Figure FDA0002482293610000039
A function sat (z) is obtained in which,bis a preset constant greater than zero;
using formulas
Figure FDA00024822936100000310
Figure FDA00024822936100000311
zout＝z2
A differentiator is established in which, among other things,
Figure FDA00024822936100000312
is the first derivative of the first state quantity of the differentiator,
Figure FDA00024822936100000313
is the first derivative of the second state quantity of the differentiator, zoutIs the output of the differentiator.
6. The active fault-tolerant control method based on the fixed time observer according to claim 5, wherein the third step further comprises: using formulas
Figure FDA0002482293610000041
Constructing a first auxiliary function, wherein E1Is a first tracking error, and E1＝X1-X1d，X1dFor controlling a first quantity of state X of the system1The reference signal of (a);
Figure FDA0002482293610000042
is an auxiliary variable, and
Figure FDA0002482293610000043
is the first derivative of the auxiliary variable,
Figure FDA0002482293610000044
Figure FDA0002482293610000045
is a preset first controller parameter, wherein,
Figure FDA0002482293610000046
Figure FDA0002482293610000047
for controlling a first quantity of state X of the system1The first derivative of the reference signal.
7. An active fault-tolerant control device based on a fixed time observer, which is applied to fault-tolerant control of a rotor type aircraft, and comprises:
the model establishing module is used for establishing a mathematical model of the attitude control system of the rotary wing aircraft according to the control input dynamic value of the control system, the nonlinear dynamic value of the control system and the sum of the comprehensive disturbance quantities;
the sliding mode observer establishing module is used for establishing a fixed time sliding mode observer according to an input dynamic value, a nonlinear dynamic value, an error variable and a state quantity of the sliding mode observer in a mathematical model of the attitude control system of the rotor type aircraft;
the fault-tolerant controller establishing module is used for establishing a fault-tolerant controller according to a mathematical model of a rotary wing type aircraft attitude control system, a fixed time sliding mode observer and a tracking error;
and the control module is used for controlling the rotor type aircraft by utilizing the fault-tolerant controller.
8. The active fault-tolerant control device based on the fixed-time observer of claim 7, wherein the model building module is further configured to: using formulas
Figure FDA0002482293610000051
Figure FDA0002482293610000052
Establishing a mathematical model of a rotary wing type aircraft attitude control system;
wherein X represents a state variable of the control system; x1A first state quantity representing the control system,
Figure FDA0002482293610000053
representing the first derivative of a first state quantity of the control system, and X1＝[α，β]T，[]TRepresenting the transpose of the matrix, α representing the yaw angle of the rotorcraft, β representing the pitch angle of the rotorcraft;
X2a second state quantity representing the control system,
Figure FDA0002482293610000054
represents a first derivative of a second state quantity of the control system, and
Figure FDA0002482293610000055
Figure FDA0002482293610000056
representing the first derivative of the yaw angle of the rotorcraft,
Figure FDA0002482293610000057
representing the first derivative of the pitch angle of the rotorcraft;
f (X) represents a nonlinear dynamic value of the control system, and
Figure FDA0002482293610000058
m represents the effective mass of the aircraft, g represents the gravitational acceleration constant, LaRepresenting the length of the center of the rotorcraft from the front motor;
g (X) represents a control input dynamic value of the control system, and
Figure FDA0002482293610000059
Kfrepresenting the coefficient of moment generated by the motor, JαRepresenting the moment of inertia of the yaw axis, JβRepresenting the moment of inertia of the pitch axis, LhRepresenting the length of the rear motor from the center of the rotorcraft;
u represents a matrix form of an input amount of the control system, and
Figure FDA00024822936100000510
Vfrepresenting the voltage, V, applied to the front motor of a rotorcraftbRepresenting the voltage applied to the rear motor of the rotorcraft;
Δ represents the integrated disturbance amount, and Δ ═ Δ f (x)) - (g (x)) + Δ g (x)) (ρi-1)U(t)+D(t)，ρiFailure coefficient and p representing occurrence of actuator failure of rotorcrafti∈ [0, 1), Δ F (X) represents a first uncertainty value of the control system, Δ G (X) represents a second uncertainty value of the control system, U (t) represents the control systemD (t) represents a functional form of the unknown external disturbance.
9. The active fault-tolerant control device based on the fixed-time observer according to claim 8, wherein the sliding-mode observer establishing module is further configured to: using formulas
Figure FDA0002482293610000061
Figure FDA0002482293610000062
Establishing a fixed time sliding-mode observer, wherein ξ1Representing a first quantity of state of the sliding-mode observer, ξ2A first state quantity of the sliding mode observer is represented,
Figure FDA0002482293610000063
a first derivative of a first state quantity representing a sliding mode observer,
Figure FDA0002482293610000064
denotes the first derivative of the first state quantity of the sliding-mode observer, e denotes the error variable, and e is ξ1-X1And | | represents a euclidean distance symbol, p is a power exponent and p > 1, sign () represents a sign function, λ1Is a predetermined observer first parameter, λ2Is a predetermined observer second parameter, A3Is a predetermined observer third parameter, and λ1，λ2，λ3Are all constants greater than zero.
10. The active fault-tolerant control device based on the fixed-time observer of claim 9, wherein the fault-tolerant controller establishing module is further configured to: using formulas
Figure FDA0002482293610000065
A fault tolerant controller is established in which, among other things,
Figure FDA0002482293610000066
is an estimate of the overall disturbance variable Delta, X2dTo control a second quantity of state X of the system2The reference signal of (a) is set,
Figure FDA0002482293610000067
for virtual control
Figure FDA0002482293610000068
An output through a differentiator;
Figure FDA0002482293610000069
is a preset second controller parameter, E2Is a second tracking error, and E2＝X2-X2d，
Figure FDA00024822936100000610
Is a first auxiliary function.
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CN113325717B (en) * 2021-06-10 2022-01-28 哈尔滨工业大学 Optimal fault-tolerant control method, system, processing equipment and storage medium based on interconnected large-scale system

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