Intermittent sampling control method for hypersonic rocket vehicle

Abstract

The invention relates to the field of control, and particularly discloses a hypersonic velocity rocket vehicle intermittent sampling control method, which comprises the following steps: constructing a model of a hypersonic velocity rocket vehicle control system; introducing an intermittent sampling control mechanism; establishing an intermittent sampling controller of the hypersonic rocket vehicle; and a Lyapunov functional based on time switching is designed, so that the index stability of the hypersonic velocity rocket vehicle control system is ensured, and an expected stable value is achieved. According to the invention, cruise control and surface temperature control of the hypersonic rocket vehicle are realized by using the intermittent sampling controller, the control cost is reduced, and the anti-interference capability is improved.

Description

Technical Field

[0001] The invention relates to the field of control, and in particular to an intermittent sampling control method for a hypersonic rocket vehicle. Background Art

[0002] The control of a hypersonic rocket vehicle is very complex. The difficulty lies in the coupling relationship between the speed of the hypersonic rocket vehicle and the temperature of its surface, and the temperature of the surface of the hypersonic rocket vehicle is not only related to time but also closely related to space. The cruise control and surface temperature control of a hypersonic rocket vehicle can be expressed by linear coupled partial differential equations (PDE) and ordinary differential equations (ODE). Therefore, the difficulty of the cruise control and surface temperature control of a hypersonic rocket vehicle can be summarized as the infinite-dimensional PDE state and the coupling relationship between PDE and ODE. Intermittent sampling control has the characteristics of low control cost, high control efficiency, easy implementation and strong anti-interference ability. For the control system of a hypersonic rocket vehicle, it is of great research value to develop an intermittent sampling control method. Summary of the invention

[0003] In order to realize the control of a hypersonic rocket vehicle, the present invention provides an intermittent sampling control method for a hypersonic rocket vehicle.

[0004] To achieve the above object, the present invention provides the following technical solutions: A hypersonic rocket vehicle intermittent sampling control method, the method comprising: S1, construct the model of the hypersonic rocket vehicle control system, including the cruise control and surface temperature control mathematical models of the hypersonic rocket vehicle; S2, introducing intermittent sampling control mechanism; S3, establish the intermittent sampling controller of the hypersonic rocket vehicle; S4, designs a Lyapunov functional based on time switching, which ensures the exponential stability of the hypersonic rocket vehicle control system and achieves the desired stability value.

[0005] As a further technical solution of the present invention, the steps of constructing a model of a hypersonic rocket vehicle control system, including a mathematical model of cruise control and surface temperature control of a hypersonic rocket vehicle, include: Formula 1: ; The boundary conditions are as follows: , ; And the initial conditions: , ; in, represents the mass of the hypersonic rocket vehicle, represents the displacement of the hypersonic rocket vehicle, and represents the velocity and acceleration of the hypersonic rocket vehicle, is the aerodynamic drag coefficient, is the viscous friction coefficient, represents the material density of the hypersonic rocket vehicle, represents the material specific heat of the hypersonic rocket vehicle, represents the temperature of the hypersonic rocket vehicle surface, which depends on time Spatial position with the surface of the rocket vehicle , subscript Indicates about The partial derivative of represents the thermal conductivity of the hypersonic rocket vehicle, represents the circumference of the hypersonic rocket vehicle, represents the convective heat transfer coefficient of the hypersonic rocket vehicle, represents the cross-sectional area of ​​the hypersonic rocket vehicle, represents the material emissivity of the hypersonic rocket vehicle, represents the Bolzmann constant, represents the temperature of the material surrounding the surface of the hypersonic rocket vehicle, represents the temperature of the material perpendicular to the surface of the hypersonic rocket vehicle, represents the dynamic viscosity, and are known parameters, represents the controller input, represents the length of the hypersonic rocket vehicle, and represents the initial value of the hypersonic rocket vehicle system; The required stable speed and temperature are as follows: Formula 2: ; The control goal is to make the speed and temperature of the hypersonic rocket vehicle reach the desired steady state. and ,In order to simplify the representation of the original system, the following dimensionless transformation is introduced: ; in, , ,After dimensionless transformation, substituting into formula 2, the original system is transformed into the following form: Formula 3: ; definition , , and define the coefficients: ; ; ; ; set up , , then the original system is transformed into the following: Formula 4: ; Subject to boundary and initial conditions: Formula 5: , ; Formula 6: , ; in, ,and ; Then, the model of the hypersonic rocket vehicle control system can be represented by the following model: Formula 7: ; in, ,and and Represents spatial position and time respectively.

[0006] As a further technical solution of the present invention, the step of introducing the intermittent sampling control mechanism includes: Divide the total time interval into a series of disjoint time intervals , ,in satisfy , each control time interval The lounge area and work area composition, For interval Intermediate time variable, the controller only works in the working range, , are the two sampling moments before and after, is the sampling period, defining the working interval , sampling time interval , , set two positive scalars and , so that the working range meets , the controller looks like this: Formula 8: ; in, , is the controller gain, and the controller is put into formula 8 to obtain: Formula 9: .

[0007] As a further technical solution of the present invention, in step S4, the exponential stability condition is expressed by Theorem 1: Theorem 1: Given a scalar parameter ,matrix and column vector , if the following linear matrix inequality holds: Formula 10: ; Formula 11: ; Formula 12: ; Formula 13: ; Formula 14: ; in, , ; , ; , ; The specific matrix elements are as follows: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Then the control system of the hypersonic rocket vehicle is exponentially stable.

[0008] As a further technical solution of the present invention, in step S4, Lyapunov's theorem is used to prove its stability, and the adopted Lyapunov functional is as follows: Formula 15: ; in, ; ; ; ; ; ; ; And, among them , , , , , and there are ; when When , we get: ; in, , , considering , And formula 10 and 11, we get ,right The derivative is: ; ; ; ; ; ; ; definition , for any column vector and get: Formula 16: ; Formula 17: ; According to Formula 9, for any column vector ,get: Formula 18: ; According to Formula 9, for any column vector ,get: Formula 19: ; In addition, we get: Formula 20: ; Integrate the part of formula 19 and according to the boundary condition formula 5, we can get: Formula 21: ; According to formula 16-21, we can get: Formula 22: ; According to formulas 12 and 13, we can get: Formula 23: ; Then, integrating both sides, we can further obtain: Formula 24: ; when When, obviously, ,right The derivation yields: ; ; ; definition , according to Formula 9, for any column vector , then we can get: Formula 25: ; According to Formula 9, for any column vector , then we can get: Formula 26: ; Integrating the part of formula 26 and adding the boundary condition formula 5 gives: Formula 27: ; According to formulas 20 and 25-27, we can then obtain: Formula 28: ; According to formula 14, we can get: Formula 29: ; Further, we can get: Formula 30: ; Between the work area and the rest area, there is , ; Then we get: Formula 31: ; therefore, In the interval The above is continuous, based on formulas 24 and 30, we get: Formula 32: ; in is a positive scalar, so it can be deduced from the above formula that the control system of the hypersonic rocket vehicle is exponentially stable.

[0009] As a further technical solution of the present invention, the controller gain is obtained by Theorem 2, which is as follows: Given a scalar , , ,parameter , , , , , , , , , , ,matrix , and column vector , , if the following linear matrix inequality holds: Formula 33: ; Formula 34: ; Formula 35: ; Formula 36: ; Formula 37: ; in, , , , , , , The specific matrix elements are as follows: ; ; ; ; ; ; ; ; ; ; The controller gain is then: Formula 38: .

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention proposes an intermittent sampling control method for a hypersonic rocket vehicle; the intermittent sampling control combines the advantages of intermittent control and sampling control, has the advantages of strong anti-interference ability, low control cost, and easy implementation, while improving the sampling effectiveness and avoiding unnecessary repeated sampling; a Lyapunov functional based on time switching is designed to ensure the exponential stability of the hypersonic rocket vehicle control system and achieve the desired stability value. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention.

[0012] Figure 1 A flow chart of the intermittent sampling control method for a hypersonic rocket vehicle; Figure 2 When there is no control effect in the simulation results of the embodiment of the present invention of the image.

[0013] Figure 3 When there is no control effect in the simulation results of the embodiment of the present invention of the image.

[0014] Figure 4The simulation results of the embodiment of the present invention are shown in Figure 1 after applying intermittent sampling control. of the image.

[0015] Figure 5 The simulation results of the embodiment of the present invention are shown in Figure 1 after applying intermittent sampling control. of the image.

[0016] Figure 6 is the control signal in the simulation result of the embodiment of the present invention The image of the second norm of .

[0017] Figure 7 is the control signal in the simulation result of the embodiment of the present invention The image of the second norm of . DETAILED DESCRIPTION

[0018] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0019] The notation used in this invention is standard and is introduced here before proceeding. If the dimensions of a matrix are not explicitly stated, it is assumed to be compatible with algebraic operations. Represents a dimensional identity matrix. Represents a dimensional zero matrix. Represents the Euclidean norm of a vector. Both said dimensional Euclidean space, express A collection of real matrices. represents a diagonal matrix. For a symmetric matrix , Refers to the term caused by symmetry.

[0020] See also Figure 1 , an embodiment of the present invention provides an intermittent sampling control method for a hypersonic rocket vehicle, the method comprising: S1, construct the model of the hypersonic rocket vehicle control system, including the cruise control and surface temperature control mathematical models of the hypersonic rocket vehicle; S2, introducing intermittent sampling control mechanism; S3, establish the intermittent sampling controller of the hypersonic rocket vehicle; S4, designs a Lyapunov functional based on time switching, which ensures the exponential stability of the hypersonic rocket vehicle control system and achieves the desired stability value.

[0021] In this embodiment, the steps of constructing a model of a hypersonic rocket vehicle control system, including a cruise control and surface temperature control mathematical model of a hypersonic rocket vehicle, include: Formula 1: ; The boundary conditions are as follows: , ; And the initial conditions: , ; in, represents the displacement of the hypersonic rocket vehicle, and represents the velocity and acceleration of the hypersonic rocket vehicle, represents the temperature of the hypersonic rocket vehicle surface, which depends on time Spatial position with the surface of the rocket vehicle , subscript Indicates about The partial derivative of and are known parameters, represents the controller input, and It represents the initial value of the hypersonic rocket vehicle system, and the specific parameters are shown in Table 1 below; Table 1 Parameters of hypersonic rocket vehicle

[0022] The required stable speed and temperature are as follows: Formula 2: ; The control goal is to make the speed and temperature of the hypersonic rocket vehicle reach the desired steady state. and ,In order to simplify the representation of the original system, the following dimensionless transformation is introduced: ; in, , ,After dimensionless transformation, substituting into formula 2, the original system is transformed into the following form: Formula 3: ; definition , , and define the coefficients: ; ; ; ; set up , , then the original system is transformed into the following: Formula 4: ; Subject to boundary and initial conditions: Formula 5: , ; Formula 6: , ; in, ,and ; Then, the model of the hypersonic rocket vehicle control system can be represented by the following model: Formula 7: ; in, ,and and Represents spatial position and time respectively.

[0023] In this embodiment, the step of introducing the intermittent sampling control mechanism includes: Divide the total time interval into a series of disjoint time intervals , ,in satisfy , each control time interval The lounge area and work area composition, For interval Intermediate time variable, the controller only works in the working range, , are the two sampling moments before and after, is the sampling period, defining the working interval , sampling time interval , , set two positive scalars and , so that the working range meets , the controller looks like this: Formula 8: ; in, , is the controller gain, and the controller is put into formula 8 to obtain: Formula 9: .

[0024] In step S4 of this embodiment, the exponential stability condition is expressed by Theorem 1: Theorem 1: Given a scalar parameter ,matrix and column vector , if the following linear matrix inequality holds: Formula 10: ; Formula 11: ; Formula 12: ; Formula 13: ; Formula 14: ; in, , ; , ; , ; The specific matrix elements are as follows: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Then the control system of the hypersonic rocket vehicle is exponentially stable.

[0025] In step S4 of this embodiment, the Lyapunov theorem is used to prove its stability, and the adopted Lyapunov functional is as follows: Formula 15: ; in, ; ; ; ; ; ; ; And, among them , , , , , and there are ; when When , we get: ; in, , , considering , And formula 10 and 11, we get ,right The derivative is: ; ; ; ; ; ; ; definition , for any column vector and get: Formula 16: ; Formula 17: ; According to Formula 9, for any column vector ,get: Formula 18: ; According to Formula 9, for any column vector ,get: Formula 19: ; In addition, we get: Formula 20: ; Integrate the part of formula 19 and according to the boundary condition formula 5, we can get: Formula 21: ; According to formula 16-21, we can get: Formula 22: ; According to formulas 12 and 13, we can get: Formula 23: ; Then, integrating both sides, we can further obtain: Formula 24: ; when When, obviously, ,right The derivation yields: ; ; ; definition , according to Formula 9, for any column vector , then we can get: Formula 25: ; According to Formula 9, for any column vector , then we can get: Formula 26: ; Integrating the part of formula 26 and adding the boundary condition formula 5 gives: Formula 27: ; According to formulas 20 and 25-27, we can then obtain: Formula 28: ; According to formula 14, we can get: Formula 29: ; Further, we can get: Formula 30: ; Between the work area and the rest area, there is , ; Then we get: Formula 31: ; therefore, In the interval The above is continuous, based on formulas 24 and 30, we get: Formula 32: ; in is a positive scalar, so it can be deduced from the above formula that the control system of the hypersonic rocket vehicle is exponentially stable.

[0026] The controller gain is obtained by Theorem 2, which is as follows: Given a scalar , , ,parameter , , , , , , , , , , ,matrix , and column vector , , if the following linear matrix inequality holds: Formula 33: ; Formula 34: ; Formula 35: ; Formula 36: ; Formula 37: ; in, , , , , , , The specific matrix elements are as follows: ; ; ; ; ; ; ; ; ; ; The controller gain is then: Formula 38: .

[0027] prove: definition: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Obviously, by multiplying the formula in Theorem 1 by 10 , formula 11 is multiplied by , formula 13 is multiplied by , formula 13 is multiplied by , formula 14 is multiplied by This yields equations 33-37 and controller gains.

[0028] The effect of the present invention can be further illustrated by the following simulation experiment.

[0029] choose Sampling period , working range , then we can obtain , apply Theorem 2, use MATLAB's LMI toolbox to solve equations 34-38 and we get: ; And set the initial conditions , the control duration is Now, we substitute the parameters in Table 1 into the hypersonic rocket vehicle control system, and apply the intermittent sampling controller of the controller gain mentioned above to the system to obtain simulation results. Figure 2 and Figure 3 Represents the time when there is no control effect and of the image. Figure 4 and Figure 5 Represents the intermittent sampling control and From the image, it can be seen that and It quickly tends to 0, which means that the speed and temperature of the hypersonic rocket vehicle quickly reach the control target under control. Figure 6 and Figure 7 For control signal and The image of the second norm of .

[0030] It should be noted that, in this article, the term "comprises" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0031] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A hypersonic rocket vehicle intermittent sampling control method, characterized in that: The method comprises: S1, construct the model of the hypersonic rocket vehicle control system, including the cruise control and surface temperature control mathematical models of the hypersonic rocket vehicle; S2, introducing intermittent sampling control mechanism; S3, establish the intermittent sampling controller of the hypersonic rocket vehicle; S4, designs a Lyapunov functional based on time switching, which ensures the exponential stability of the hypersonic rocket vehicle control system and achieves the desired stability value.

2. The intermittent sampling control method of a hypersonic rocket vehicle according to claim 1, characterized in that: The steps of constructing a model of a hypersonic rocket vehicle control system, including a cruise control and surface temperature control mathematical model of a hypersonic rocket vehicle, include: Formula 1: ; The boundary conditions are as follows: ， ； And the initial conditions: ， ； in, represents the mass of the hypersonic rocket vehicle, represents the displacement of the hypersonic rocket vehicle, and represents the velocity and acceleration of the hypersonic rocket vehicle, is the aerodynamic drag coefficient, is the viscous friction coefficient, represents the material density of the hypersonic rocket vehicle, represents the material specific heat of the hypersonic rocket vehicle, represents the temperature of the hypersonic rocket vehicle surface, which depends on time Spatial position with the surface of the rocket vehicle , subscript Indicates about The partial derivative of represents the thermal conductivity of the hypersonic rocket vehicle, represents the circumference of the hypersonic rocket vehicle, represents the convective heat transfer coefficient of the hypersonic rocket vehicle, represents the cross-sectional area of ​​the hypersonic rocket vehicle, represents the material emissivity of the hypersonic rocket vehicle, represents the Bolzmann constant, represents the temperature of the material surrounding the surface of the hypersonic rocket vehicle, represents the temperature of the material perpendicular to the surface of the hypersonic rocket vehicle, represents the dynamic viscosity, and are known parameters, represents the controller input, represents the length of the hypersonic rocket vehicle, and represents the initial value of the hypersonic rocket vehicle system; The required stable speed and temperature are as follows: Formula 2: ; The control goal is to make the speed and temperature of the hypersonic rocket vehicle reach the desired steady state. and ,In order to simplify the representation of the original system, the following dimensionless transformation is introduced: ； in, , ,After dimensionless transformation, substituting into formula 2, the original system is transformed into the following form: Formula 3: ; definition , , and define the coefficients: ； ； ； ； set up , , then the original system is transformed into the following: Formula 4: ; Subject to boundary and initial conditions: Formula 5: , ; Formula 6: , ; in, ,and ; Then, the model of the hypersonic rocket vehicle control system can be represented by the following model: Formula 7: ； in, ,and and Represents spatial position and time respectively.

3. The intermittent sampling control method of a hypersonic rocket vehicle according to claim 2 is characterized in that: The steps of introducing the intermittent sampling control mechanism include: Divide the total time interval into a series of disjoint time intervals , ,in satisfy , each control time interval The lounge area and work area composition, For interval Intermediate time variable, the controller only works in the working range, , are the two sampling moments before and after, is the sampling period, defining the working interval , sampling time interval , , set two positive scalars and , so that the working range meets , the controller looks like this: Formula 8: ; in, , is the controller gain, and the controller is put into formula 8 to obtain: Formula 9: 。 4. The intermittent sampling control method of a hypersonic rocket vehicle according to claim 1, characterized in that: In step S4, the exponential stability condition is expressed by Theorem 1: Theorem 1: Given a scalar parameter ,matrix and column vector , if the following linear matrix inequality holds: Formula 10: ; Formula 11: ; Formula 12: ; Formula 13: ; Formula 14: ; in, , ; ， ； ， ； The specific matrix elements are as follows: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； Then the control system of the hypersonic rocket vehicle is exponentially stable.

5. The intermittent sampling control method of a hypersonic rocket vehicle according to claim 1, characterized in that: In step S4, Lyapunov's theorem is used to prove its stability, and the Lyapunov functional used is as follows: Formula 15: ; in, ; ； ； ； ； ； ； And, among them , , , , , and there are ; when When , we get: ； in, , , considering , And formula 10 and 11, we get ,right The derivative is: ； ； ； ； ； ； ； definition , for any column vector and get: Formula 16: ; Formula 17: ; According to Formula 9, for any column vector ,get: Formula 18: ； According to Formula 9, for any column vector ,get: Formula 19: ； In addition, we get: Formula 20: ； Integrate the part of formula 19 and obtain the following formula 5 based on the boundary condition: Formula 21: ； According to formula 16-21, we can get: Formula 22: ； According to formulas 12 and 13, we can get: Formula 23: ; Then, integrating both sides, we can further obtain: Formula 24: ; when When, obviously, ,right The derivation yields: ； ； ； definition , according to Formula 9, for any column vector , then we can get: Formula 25: ； According to Formula 9, for any column vector , then we can get: Formula 26: ； Integrating the part of formula 26 and adding the boundary condition formula 5 gives: Formula 27: ； According to formulas 20 and 25-27, we can then obtain: Formula 28: ; According to formula 14, we can get: Formula 29: ; Further, we can get: Formula 30: ; Between the work area and the rest area, there is , ; Then we get: Formula 31: ； therefore, In the interval The above is continuous, based on formulas 24 and 30, we get: Formula 32: ; in is a positive scalar, so it can be deduced from the above formula that the control system of the hypersonic rocket vehicle is exponentially stable.

6. The intermittent sampling control method for a hypersonic rocket vehicle according to claim 3 is characterized in that: The controller gain is obtained by Theorem 2, which is as follows: Given a scalar , , ,parameter , , , , , , , , , , ,matrix , and column vector , , if the following linear matrix inequality holds: Formula 33: ; Formula 34: ; Formula 35: ; Formula 36: ; Formula 37: ; in, , ; ， ； ， ； The specific matrix elements are as follows: ； ； ； ； ； ； ； ； ； ； The controller gain is then: Formula 38: .

Images