CN108646564A - A kind of design method of the uncertain reentry vehicle model based on event triggering - Google Patents

Abstract

The invention discloses a method for designing an uncertain re-entry aircraft model based on event triggering. The method includes: Step 1: establishing an uncertain re-entry aircraft system model, and designing a state observer and an output feedback controller to form a closed-loop control System; Step 2: Define Lyapunov function, design event trigger conditions based on this Lyapunov function; Step 3: Eliminate uncertain items, scale through event trigger conditions, and use linear matrix inequality technology to prove the stability of the closed-loop control system. The design method of the event-triggered uncertain reentry vehicle model of the present invention not only ensures the stability of the reentry vehicle system, but also reduces unnecessary waste of system resources and achieves higher resource utilization.

Description

A Design Method of Uncertain Reentry Vehicle Model Based on Event Triggering

technical field

The invention relates to the technical field of aircraft control, in particular to a design method of an event-triggered uncertain re-entry aircraft model.

Background technique

The guidance and control technology of re-entry aircraft has always been the focus of aircraft research in various countries. The flight mode of re-entry aircraft is different from that of other aircraft. It needs to be carried by other vehicles and then enter the atmosphere again. Therefore, this aircraft has a super high flight speed. It can reach anywhere in the world within one hour. During the reentry process of the reentry vehicle, various factors such as longer flight time, constant changes in the flight environment, and offset of the center of mass will affect the stability of the system, so the precise control of this supersonic vehicle is particularly important.

The event trigger mechanism was proposed to overcome the unnecessary waste of computing and communication resources by the time sampling mechanism. Later, many scholars devoted themselves to the research of the event trigger mechanism, mainly for the effective use of network resources in network control systems and the reduction of resource utilization. studied from one angle. The event-triggered mechanism only needs to perform sample transmission when a pre-set event condition occurs, and the performance of the control system is similar to that of the time-triggered system. By selecting the appropriate event conditions, the event trigger mechanism significantly reduces the sampling points, thereby effectively saving network bandwidth resources. For output feedback, output feedback is a partial feedback of system structure information, but since output is always measurable, output feedback is always physically achievable, and output feedback has low economic cost in engineering applications.

The patent application number is: 201710198546.6 A compound control method for hypersonic aircraft using state feedback and neural network. By measuring the attack angle and pitch angle velocity signals of hypersonic aircraft, first design a large gain state feedback controller. Due to the strong uncertainty of the aerodynamic parameters of the aircraft, a neural network structure with a sine function as the basis function is adopted, and the adaptive adjustment law of the weight of the neural network is designed, and finally a composite controller of the neural network and state feedback of the hypersonic aircraft is formed. , to realize the tracking of the expected angle of attack signal. This patent has the following disadvantages: (1) State feedback is generally physically impossible to realize, or even if it can be realized, the economic cost is high, so physical constraints make output feedback more commonly used. (2) The unmeasurable state of the system is not considered, and the state observer can be used to solve this problem.

The patent application number is: 201611100078.6 An extended robust H _∞ UAV control method based on control constraints. The method of this invention obtains the matrix inequality that the controller needs to satisfy when there are constraints on the control quantity, and can also determine the maximum disturbance In the case of , specific constraints are made on the control quantity, and in order to improve the performance of the controller under the condition of satisfying the constraints, the state variables are also expanded. This patent has the following disadvantages: (1) The event trigger mechanism is not considered, which will increase the pressure on data transmission and waste network bandwidth resources. (2) The influence of uncertain factors is not considered, and the stability of the system will be affected accordingly.

Contents of the invention

The technical problem to be solved by the present invention is that the prior art reentry vehicle system causes unnecessary waste of system resources and low resource utilization, and provides a design method of an uncertain reentry vehicle model based on event triggering.

The present invention is achieved through the following technical solutions: a design method based on an event-triggered uncertain re-entry vehicle model, the method comprising:

Step 1: Establish an uncertain reentry vehicle system model, and design a state observer and an output feedback controller to form a closed-loop control system;

Step 2: Define the Lyapunov function, and design event trigger conditions based on this Lyapunov function;

Step 3: Eliminate uncertain items, scale through event trigger conditions, and use linear matrix inequality technology to prove the stability of the closed-loop control system.

As one of the preferred modes of the present invention, the specific process of establishing an uncertain reentry aircraft model in the step 1 is:

First build the reentry vehicle model:

q=0.5ρ ₁ v ² , ρ ₁ =ρ ₀ e ^-ξh ,

In the formula: m, v are the mass and speed of the aircraft respectively; ω _x , ω _y , ω _z are the angular velocities of the _x -axis, y-axis, and z _- axis of the body respectively; Power; M _x , M _y , M _z are the moments of the x-axis, y-axis, and z-axis respectively; γ, ψ are the track angle and heading angle; R is the radius of the earth; θ, are the longitude and latitude respectively; ξ is the tilt angle of the re-entry vehicle; I _x , I _y , I _z , I _xy , I _yz , I _zx represent the moment of inertia of the body axis; r is the height of the center of mass relative to the center of the earth; q is the dynamic pressure; ρ ₁ is the atmospheric density, ρ ₀ is the atmospheric density at sea level; x, z are the horizontal and lateral distances; C _D , C _L are the drag and lift coefficients respectively; S is the reference area of the aircraft; ω _e , g ₀ is the earth's angular velocity and gravitational acceleration; ξ, h are the density coefficient and altitude respectively; after first-order linearization, the above equation can be expressed as

in, is the state vector of the controlled object; u(t)=(αβξδ _e δ _a δ _r ) ^T is the input vector of the controlled object; α, β, ξ, δ _e , δ _a and δ _r are the reentry vehicle’s Angle of attack, yaw angle, tilt angle, deflection of elevator, aileron and rudder; A and B are system matrix and input matrix respectively;

Secondly, the uncertain re-entry aircraft model is obtained by adding uncertain factors: during the re-entry process of the re-entry aircraft, the system will be affected by uncertain factors and change, and the stability of the system will also be affected; therefore, The present invention considers a re-entry vehicle model with uncertain terms.

Among them, x(t)∈R ^n×1 is the state vector of the controlled object; u(t)∈R ^m×1 is the input vector of the controlled object; y(t)∈R ^q×1 is the controlled object’s Output vector; A, B, and C are system matrix, input matrix, and output matrix respectively; ΔA is an uncertain item of A, and satisfies ΔA=DF(t)E, D, E are known constant matrices, F(t ) satisfy F ^T (t)F(t)≤I; assuming (A, C) is considerable, (A, B) is controllable.

As one of the preferred modes of the present invention, since not all state variables in the actual system can be obtained directly, in order to estimate the unknown actual state, the design state observer is as follows:

in, is the state vector of the state observer, The output vector of the microstate observer, L∈R ^n×q is the gain matrix of the state observer;

According to the state observer, the designed output feedback controller is as follows:

Among them, K∈R ^m×n is the feedback gain matrix to be determined.

As one of the preferred modes of the present invention, in the step 2: the event trigger condition is described by an inequality about the output variable of the state observer; the event detection device has a built-in event trigger condition event, and the event detection device continuously receives output from the sensor Variable information, when the event trigger condition is satisfied, the sampled output information at this moment is passed to the output feedback controller, which is called the trigger moment and recorded as t _k ; due to the effect of the zero-order keeper, in the Before the arrival of a trigger moment t _k+1 , the output feedback controller keeps the information of the last trigger moment.

As one of the preferred modes of the present invention, the output feedback controller based on the event trigger mechanism is only updated at the moment tk, where _tk represents the trigger moment corresponding to the _kth sampling period:

Define the output error:

in, is the current sampling signal, is the sampling signal sent by the event detection device to the output feedback controller last time. Due to the function of the zero-order keeper, the output feedback controller keeps the information of the previous trigger moment until the next trigger moment t _k+1 arrives;

Define the state estimation error vector as:

Then the state estimation error equation is:

Define the event trigger condition as:

Among them, σ>0. When formula (9) is not satisfied, the sampling value at the current moment is recorded and sent to the output feedback controller to update the input of the output feedback controller.

Then, we can get the new closed-loop system expression:

Define the Lyapunov function as:

Wherein, P ₁ , P ₂ , and P ₃ are positive definite matrices respectively.

As one of the preferred modes of the present invention, the specific process of step 3 is: to prove the stability of the system by Lyapunov's second method, that is, to ensure However, in the process of proving the stability of the system, the uncertain term ΔA needs to be eliminated. The uncertain term ΔA can be eliminated by the following lemma, which can be described as:

Suppose x(t)∈R ^n×1 , y(t)∈R ^q×1 , ε>0, D and E are respectively known real matrixes of suitable dimensions, F(t) is an unknown matrix and satisfies F ^T (t)F(t)≤I, where I is the identity matrix, then

^{( 12 ) _ _ _}

After eliminating the uncertainty term ΔA through this lemma, it is necessary to continue to prove the stability of the system; to ensure the stability of the system, Scaling can be performed through event trigger conditions, and then it can be transformed into a linear matrix inequality solving problem, the inequality is:

When the parameters of the system are obtained, solve the appropriate P ₁ , P ₂ , P ₃ , σ to satisfy this linear matrix inequality, that is, the system is Lyapunov stable.

Compared with the prior art, the present invention has the advantages that: the design method of the present invention based on the event-triggered uncertain re-entry aircraft model, while ensuring the stability of the re-entry aircraft system, reduces unnecessary waste of system resources and achieves higher resource utilization.

Description of drawings

Fig. 1 is a control algorithm flow chart of the present invention;

FIG. 2 is a structural diagram of the event-based triggering mechanism of the re-entry vehicle of the present invention.

Detailed ways

The embodiments of the present invention are described in detail below. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation methods and specific operating procedures are provided, but the protection scope of the present invention is not limited to the following implementation example.

As shown in Figure 1-2: a design method of an uncertain reentry vehicle model based on event triggering, the method includes:

Step 1: Establish an uncertain reentry vehicle system model, and design a state observer and an output feedback controller to form a closed-loop control system;

The specific process of establishing an uncertain reentry vehicle model is as follows:

First build the reentry vehicle model:

q=0.5ρ ₁ v ² , ρ ₁ =ρ ₀ e ^-ξh ,

In the formula: m, v are the mass and speed of the aircraft respectively; ω _x , ω _y , ω _z are the angular velocities of the _x -axis, y-axis, and z _- axis of the body respectively; Power; M _x , M _y , M _z are the moments of the x-axis, y-axis, and z-axis respectively; γ, ψ are the track angle and heading angle; R is the radius of the earth; θ, are the longitude and latitude respectively; ξ is the tilt angle of the re-entry vehicle; I _x , I _y , I _z , I _xy , I _yz , I _zx represent the moment of inertia of the body axis; r is the height of the center of mass relative to the center of the earth; q is the dynamic pressure; ρ ₁ is the atmospheric density, ρ ₀ is the atmospheric density at sea level; x, z are the horizontal and lateral distances; C _D , C _L are the drag and lift coefficients respectively; S is the reference area of the aircraft; ω _e , g ₀ is the earth's angular velocity and gravitational acceleration; ξ, h are the density coefficient and altitude respectively; after first-order linearization, the above equation can be expressed as

in, is the state vector of the controlled object; u(t)=(αβξδ _e δ _a δ _r ) ^T is the input vector of the controlled object; α, β, ξ, δ _e , δ _a and δ _r are the reentry vehicle’s Angle of attack, yaw angle, tilt angle, deflection of elevator, aileron and rudder; A and B are system matrix and input matrix respectively;

Secondly, the uncertain re-entry aircraft model is obtained by adding uncertain factors: during the re-entry process of the re-entry aircraft, the system will be affected by uncertain factors and change, and the stability of the system will also be affected; therefore, The present invention considers a re-entry vehicle model with uncertain terms.

Among them, x(t)∈R ^n×1 is the state vector of the controlled object; u(t)∈R ^m×1 is the input vector of the controlled object; y(t)∈R ^q×1 is the controlled object’s Output vector; A, B, and C are system matrix, input matrix, and output matrix respectively; ΔA is an uncertain item of A, and satisfies ΔA=DF(t)E, D, E are known constant matrices, F(t ) satisfy F ^T (t)F(t)≤I; assuming (A, C) is considerable, (A, B) is controllable;

Since not all state variables in the actual system can be obtained directly, in order to estimate the unknown actual state, the state observer is designed as follows:

in, is the state vector of the state observer, The output vector of the microstate observer, L∈R ^n×q is the gain matrix of the state observer;

According to the state observer, the designed output feedback controller is as follows:

Among them, K∈R ^m×n is the feedback gain matrix to be determined;

Step 2: Define the Lyapunov function, and design event trigger conditions based on this Lyapunov function;

The event trigger condition is described by an inequality about the output variable of the state observer; the event detection device has a built-in event trigger condition event, and the event detection device continuously receives the information of the output variable from the sensor, and only when the event trigger condition is met will the sampled The output information at this moment is transmitted to the output feedback controller, which is called the triggering moment and recorded as t _k ; due to the function of the zero-order keeper, the output feedback controller keeps up until the next triggering moment t _k+1 arrives. a trigger moment information;

The output feedback controller based on the event trigger mechanism is only updated at the moment t _k , where t _k represents the trigger moment corresponding to the kth sampling period:

Define the output error:

in, is the current sampling signal, is the sampling signal sent by the event detection device to the output feedback controller last time. Due to the function of the zero-order keeper, the output feedback controller keeps the information of the previous trigger moment until the next trigger moment t _k+1 arrives;

Define the state estimation error vector as:

Then the state estimation error equation is:

Define the event trigger condition as:

Among them, σ>0; when formula (9) is not satisfied, the sampling value at the current moment is recorded and sent to the output feedback controller to update the input of the output feedback controller.

Then, we can get the new closed-loop system expression:

Define the Lyapunov function as:

Among them, P ₁ , P ₂ , and P ₃ are positive definite matrices respectively;

Step 3: Eliminate uncertain items, scale through event trigger conditions, and use linear matrix inequality technology to prove the stability of the closed-loop control system; the specific process is: prove the stability of the system through Lyapunov's second method, that is, guarantee However, in the process of proving the stability of the system, the uncertain term ΔA needs to be eliminated. The uncertain term ΔA can be eliminated by the following lemma, which can be described as:

Suppose x(t)∈R ^n×1 , y(t)∈R ^q×1 , ε>0, D and E are respectively known real matrixes of suitable dimensions, F(t) is an unknown matrix and satisfies F ^T (t)F(t)≤I, where I is the identity matrix, then

^{( 12 ) _ _ _}

After eliminating the uncertainty term ΔA through this lemma, it is necessary to continue to prove the stability of the system; to ensure the stability of the system, Scaling can be performed through event trigger conditions, and then it can be transformed into a linear matrix inequality solving problem, the inequality is:

When the parameters of the system are obtained, solve the appropriate P ₁ , P ₂ , P ₃ , σ to satisfy this linear matrix inequality, that is, the system is Lyapunov stable.

Referring to Fig. 1: below in conjunction with the example given above, briefly describe the control algorithm of the present invention:

(1) In this example, we consider the reentry vehicle model, and set the algorithm parameters and system matrix data;

(2) The node is initialized to get the initial state get the output again value, calculate the output error Carry out the following judgments and operations: when the inequality (9) is established, the output Perform non-uniform sampling to obtain event-triggered sampling output If the inequality (9) is not established, continue to calculate (9), and start sampling until it is established;

(3) Trigger the sampling output of the event obtained in step (2) Substitute into the designed output feedback controller input formula (5) to calculate and update the control input u(t);

(4) Continue to update the system output and error Go back to step 2 and continue to follow the steps above.

The system stability is demonstrated as follows:

Take the Lyapunov function

Among them, P ₁ , P ₂ , and P ₃ are positive definite matrices, which can be obtained by solving inequality (13). Deriving the Lyapunov function along the trajectory of the closed-loop system (10), we have

The formula 2x ^T (t)P ₁ ΔAx(t) containing uncertain terms appearing in the above formula and The uncertainty term ΔA can be eliminated by the aforementioned lemma, and the detailed process is:

and

Consider event trigger conditions right Zooming in, we get

When it is guaranteed that inequality (13) holds, it can be guaranteed that The event trigger condition (9) is feasible and can guarantee the stability of the closed-loop system.

The design method of the event-triggered uncertain reentry vehicle model of the present invention not only ensures the stability of the reentry vehicle system, but also reduces unnecessary waste of system resources and achieves higher resource utilization.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims (6)

1. A method for designing an uncertain reentry aircraft model based on event triggering is characterized by comprising the following steps:

step 1: establishing an uncertain reentry aircraft system model, and designing a state observer and an output feedback controller to form a closed-loop control system;

step 2: defining a Lyapunov function, and designing an event triggering condition based on the Lyapunov function;

and step 3: and eliminating uncertain items, zooming by an event triggering condition, and proving the stability of the closed-loop control system by using a linear matrix inequality technology.

2. The method for designing the uncertain re-entry aircraft model based on event triggering according to claim 1, wherein the specific process for establishing the uncertain re-entry aircraft model in the step 1 is as follows:

firstly, establishing a reentry aircraft model:

in the formula: m, v are the mass and velocity of the aircraft, respectively; omega_x，ω_y，ω_zThe angular velocities of the machine body are respectively the x axis, the y axis and the z axis; t, F_T，F_NAerodynamic body axis to centre of massForce; m_x，M_y，M_zThe moments of the x axis, the y axis and the z axis are respectively; gamma and psi are respectively a track angle and a course angle; r is the radius of the earth; the number of the theta's is,longitude and latitude, respectively, ξ the angle of inclination of the reentry vehicle, I_x，I_y，I_z，I_xy，I_yz，I_zxRepresenting the moment of inertia of the body axis; r is the height of the centroid relative to the geocentric; q is dynamic pressure; rho₁Is the atmospheric density, p₀Is sea level atmospheric density; x and z are transverse and lateral distances; c_D，C_LRespectively are resistance and lift coefficient; s is the aircraft reference area; omega_e，g₀Angular velocity and gravitational acceleration of earth, ξ, h are density coefficient and altitude, respectively, and after first-order linearization, the above equation can be expressed as

Wherein,is the state vector of the controlled object, u (t) ═ (αβξ delta)_eδ_aδ_r)^Tα, β, ξ, delta as input vector of controlled object_e、δ_aAnd delta_rThe angle of attack, the angle of yaw, the angle of inclination, the degree of deflection of the elevator, the aileron and the rudder of the reentry vehicle are respectively; a and B are respectively a system matrix and an input matrix;

secondly, adding uncertainty factors to obtain an uncertain reentry aircraft model:

wherein x (t) e R^n×1Is a state vector of a controlled object; u (t) e R^m×1Is input to the controlled objectAn amount; y (t) ε R^{q ×1}The vector is an output vector of a controlled object; A. b, C is system matrix, input matrix, and output matrix; Δ a is an uncertainty term for a, and satisfies Δ a ═ df (t) E, D, E are known constant matrices, F (t) satisfies F^T(t) F (t) is less than or equal to I; assuming (A, C) is observable, (A, B) is controllable.

3. The method for designing an uncertain re-entry aircraft model based on event triggering according to claim 1, wherein the design state observer is as follows:

wherein,is a state vector of the state observer,output vector of micro-state observer, L ∈ R^n×qA gain matrix that is a state observer;

according to the state observer, the design output feedback controller is as follows:

wherein K ∈ R^m×nIs the feedback gain matrix to be determined.

4. The method for designing the uncertain re-entry aircraft model based on event triggering according to claim 1, wherein in the step 2: the event trigger condition is described by an inequality with respect to the state observer output variable; event trigger condition events are built in the event detection device, the event detection device continuously receives information of output variables from the sensor, and the sampled information is only sampled when the event trigger condition is metThe output information at the moment is transmitted to the output feedback controller, and the moment is called as the trigger moment and is recorded as t_k(ii) a At the next trigger time t due to the action of the zero order keeper_k+1Before the arrival, the output feedback controller keeps the information of the last trigger moment.

5. The method for designing an uncertain re-entry aircraft model based on event triggering according to claim 4, wherein the output feedback controller based on event triggering mechanism is only at t_kAt this time, where t_kRepresents the trigger time corresponding to the k-th sampling period:

defining an output error:

wherein,is the current sample signal of the signal being sampled,is the sampling signal last transmitted by the event detector to the output feedback controller, and is used as the zero-order retainer for the next trigger time t_k+1Before the arrival, the output feedback controller keeps the information of the last trigger moment;

defining the state estimation error vector as:

the state estimation error equation is then:

defining event triggering conditions as follows:

wherein σ > 0. And when the formula (9) is not satisfied, recording the sampling value at the current moment, transmitting the sampling value to the output feedback controller, and updating the input of the output feedback controller.

Thus, we can get a new closed-loop system expression:

defining the Lyapunov function as:

wherein, P₁、P₂、P₃Respectively positive definite matrices.

6. The method for designing the uncertain re-entry aircraft model based on event triggering according to claim 1, wherein the specific process of the step 3 is as follows: the stability of the system is demonstrated by the Lyapunov second method, i.e. the assuranceHowever, the need to eliminate the uncertainty term Δ a in demonstrating system stability can be eliminated by the following theorem, which can be described as:

let x (t) be R^n×1，y(t)∈R^q×1ε > 0, D and E are each known real matrices of suitable dimensions, F (t) is an unknown matrix and satisfies F^T(t) F (t). ltoreq.I, where I is the identity matrix, then

2x^T(t)DF(t)Ey(t)≤εx^T(t)DD^Tx(t)+ε^-1y^T(t)E^TEy(t)； (12)

After the uncertainty delta A is eliminated through the theorem, the stability of the system needs to be continuously proved; if it is desired to ensure that the system is stable,scaling can be performed through event triggering conditions, and then the scaling can be converted into a linear matrix inequality to solve a problem, wherein the inequality is as follows:

when obtaining each parameter of the system, solving out proper P₁，P₂，P₃And sigma satisfies the linear matrix inequality, namely the system Lyapunov is stable.