Nonlinear dynamic inverse robust model predictive control method for hypersonic flight vehicle
Through dynamic inverse theory, the nonlinear motion equation of hypersonic aircraft is converted into an equivalent linear system, and a robust model prediction controller based on Tube is designed to solve the control problem of hypersonic aircraft in a nonlinear dynamic environment, achieving accurate tracking of altitude and speed and flight stability.
Patent Information
- Application Number
- CN202510438814.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-09
- Publication Date
- 2025-05-06
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Hypersonic aircraft are very sensitive to changes in appearance, aerodynamic parameters and atmospheric conditions during flight, and are affected by factors such as nonlinear dynamic characteristics, high temperature effects, control volume and control increment constraints, making flight control design extremely challenging.
Using a robust model prediction and control method based on dynamic inverse theory, the nonlinear motion equation of hypersonic aircraft is converted into an equivalent linear system through input and output feedback linearization, and a robust model prediction controller based on Tube is designed, taking into account state constraints, control amounts and control incremental constraints to achieve effective tracking of the aircraft altitude and speed.
Effectively compensate for the impact of external uncertain disturbances on hypersonic vehicles, improve altitude and speed tracking accuracy, enhance flight stability, and have good attitude adjustment and control incremental constraint capabilities.
Smart Images
Figure CN119937329A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of hypersonic aircraft control technology, and more specifically, to a robust model predictive control method based on nonlinear dynamic inversion of a hypersonic aircraft. Background Art
[0002] As a new domain combat force, hypersonic aircraft has the characteristics of fast response, strong penetration and defense, and high lethality. Currently, the major powers in the world are increasing their investment in the development of hypersonic technology to seize the initiative in the practical application of hypersonic technology.
[0003] Hypersonic vehicles refer to high-performance aircraft with a flight speed greater than Mach 5. Due to the design and flight conditions of high flight altitude and Mach number, such aircraft are very sensitive to changes in shape, aerodynamic parameters and atmospheric conditions. On the other hand, due to the nonlinear dynamic characteristics of supersonic combustion ramjet engines, high temperature effects, control quantities, control increment constraints, and mutual coupling of aerodynamic parameters at high speeds, the flight control design of hypersonic vehicles becomes extremely challenging.
[0004] Therefore, the present invention proposes a robust model predictive controller which takes into account the control quantity and control increment constraints for this situation, which effectively solves the influence of unknown disturbances on the tracking accuracy and flight stability of hypersonic aircraft, has strong feasibility, and is conducive to improving economic benefits. Summary of the invention
[0005] To achieve the above object, the present invention provides a hypersonic vehicle nonlinear dynamic inverse robust model predictive control method, which adopts the following technical solutions: A hypersonic vehicle nonlinear dynamic inverse robust model predictive control method comprises the following steps: S1. Based on the existing six-degree-of-freedom nonlinear model of hypersonic aircraft, the longitudinal motion equation of the model is derived; S2. Based on the dynamic inverse theory, the longitudinal motion equation is converted into an equivalent linear system through input-output feedback linearization; S3, solve the interference invariant set of the hypersonic vehicle subject to external uncertain disturbances, and derive the robust tightening constraints of the equivalent tracking system; S4. Considering the state constraints, control quantity and control increment constraints of the hypersonic aircraft, a robust model predictive controller based on Tube is designed to control the actual height and speed of the hypersonic aircraft to approach the expected height and speed while ensuring the stable flight of the fuselage.
[0006] Furthermore, in step S1, the longitudinal motion equation is as follows:
[0007] The longitudinal motion equation of a hypersonic vehicle contains five rigid body states: are speed, track angle, altitude, angle of attack and pitch velocity respectively; among them, is the acceleration due to gravity, is the mass of the hypersonic vehicle, For along The moment of inertia of the shaft; They are lift, drag, thrust and pitch moment during the motion, and the calculation expressions are:
[0008] in, They are dynamic pressure, fuselage reference area, and mean aerodynamic chord length; They are lift coefficient, drag coefficient, thrust coefficient and pitch moment coefficient respectively. The specific expressions are:
[0009] in, They are elevator deflection angle and engine valve opening respectively.
[0010] Further, step S2 includes: S2.1. Linearize the input and output of the hypersonic vehicle velocity subsystem based on the dynamic inversion method. Speed Ask about time The first derivative of , we get:
[0011] right Continue to derive until the third-order derivative, and we get:
[0012] in, is the state variable of the hypersonic vehicle, Contains , The control input contains the elevator angle , The control input contains the engine valve opening ; S2.2. Linearize the input and output of the hypersonic vehicle altitude subsystem based on the dynamic inversion method: For height Ask about time The derivative of and engine valve opening ,have to:
[0013] in, Contains control input quantity elevator deflection angle and engine valve opening ; S2.3. Design control variables for the altitude and speed subsystems of hypersonic vehicles; The parts of the speed subsystem and the height subsystem related to the control quantity are separately proposed, and the following output equation is obtained:
[0014] In the formula, They are the five rigid body states of the longitudinal motion equation of the hypersonic vehicle, the engine valve opening and the engine valve opening derivative, the engine valve opening command and the elevator deflection angle; is the function part that is independent of the control quantity obtained by nonlinear inversion, is the function part related to the control quantity obtained by nonlinear inversion; Design the following control quantity:
[0015] in, is the virtual control quantity; The speed subsystem is designed as follows: , define the system coordinate transformation , in the new coordinate system we get:
[0016] in, is the true speed, is the target speed, is the difference between the actual speed and the target speed, is the state variable after coordinate transformation; The speed decoupled subsystem is expressed as:
[0017] in, is the velocity subsystem state matrix, is the speed subsystem control matrix; The height subsystem is designed as follows: , define the system coordinate transformation , in the new coordinate system we get:
[0018] in, is the true height, is the target height, is the difference between the actual altitude and the target altitude, is the state variable after coordinate transformation; A highly decoupled subsystem is represented as:
[0019] in, is the height subsystem state matrix, It is the height subsystem control matrix.
[0020] Further, step S3 includes: First, the equivalent linear tracking system of a hypersonic vehicle subject to external uncertain disturbances is as follows:
[0021] in, are the system state, the control input vector, and the external disturbances to the equivalent linear tracking system; Due to the influence of disturbances, the state trajectory of the actual hypersonic vehicle Will deviate from the nominal optimal prediction trajectory , the upper bound of the state prediction deviation is calculated as follows: Assume that the actual system with uncertain disturbances and the nominal system have the same initial state at the same initial time. Evolved, subtracting the nominal system from the actual system, using the triangle inequality and Lipschitz conditions, we get:
[0022] Then using the Gronwall-Bellman inequality, we get:
[0023] in, ; Accordingly, using Minkowski subtraction, the robust tightened state constraint is estimated as:
[0024] in, is the state variable of the hypersonic vehicle, is the upper bound of external interference.
[0025] Further, step S4 includes: S4.1. Design a robust model predictive controller for the equivalent tracking system of a hypersonic vehicle based on a disturbance invariant set. The optimal control problem of the robust model predictive controller is as follows: , In the formula, are the feasible control inputs and the corresponding predicted state trajectories, respectively. represents the optimal situation, They are robust tightening state constraints, control input constraints, and control increment input constraints. are the state matrix and input matrix of the speed and altitude subsystems of the hypersonic vehicle, respectively. is the terminal state constraint matrix; S4.2、Explanation on the terminal invariant set and terminal controller existence of robust model predictive controller for equivalent tracking system of hypersonic vehicle; The equivalent linear nominal system is stabilizable at the equilibrium point (0,0). The following steps are used to illustrate the existence of the terminal invariant set and terminal controller of the robust model predictive controller of the equivalent tracking system of the hypersonic vehicle. When the nominal system , given the matrix , there is a constant and the unique matrix When the following conditions are met: Condition 1. ; Condition 2. ; Condition 3. ; Condition 4. It is a closed loop system The positive invariant set of ; Condition 5. in ; Then we can choose the following continuous-time Lyapunov equation:
[0026] because, , the above equation has a unique solution ; Secondly, due to , there is a constant , so that in the set If conditions 1-2 are met, then for any point , the following inequality holds:
[0027] definition , in the collection In, conditions 1-3 are satisfied; along right The derivative is:
[0028] because, , the above equation shows that for the closed loop system ,gather is unchanged, according to , meeting conditions 1-5.
[0029] The beneficial effects of the present invention are as follows:
[0030] 1. The present invention can effectively compensate for the influence of external uncertain disturbances on the height and speed tracking of hypersonic aircraft, solves the influence of unknown disturbances on the tracking accuracy and flight stability of hypersonic aircraft, has strong feasibility, and is conducive to improving economic benefits.
[0031] 2. The present invention can effectively improve the altitude and speed tracking accuracy of a hypersonic aircraft under the constraints of control quantity and control increment, so that the hypersonic aircraft has good flight speed and flight altitude tracking performance.
[0032] 3. The present invention has good attitude adjustment capability and good constraint capability on control increments, and can ensure stable flight of the fuselage while controlling the actual height and speed of the hypersonic aircraft to approach the desired height and speed. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 The present invention is a flowchart of the hypersonic vehicle nonlinear dynamic inverse robust model predictive control method.
[0034] Figure 2 The invention provides a speed and altitude instruction tracking curve diagram, an engine throttle control amount change diagram, and an elevator deflection angle change diagram.
[0035] Figure 3 It is a diagram showing changes in the flight path angle, angle of attack and pitch angular velocity of the hypersonic aircraft of the present invention.
[0036] Figure 4 The figure is a diagram showing the change of the engine throttle control amount increment and the elevator deflection angle of the hypersonic aircraft of the present invention. DETAILED DESCRIPTION
[0037] In order to explain the present invention more clearly, the present invention is further described below in conjunction with preferred embodiments and drawings. It should be understood by those skilled in the art that the content described below is illustrative rather than restrictive, and should not be used to limit the scope of protection of the present invention.
[0038] This embodiment provides a nonlinear dynamic inverse robust model predictive control method for a hypersonic vehicle, such as Figure 1 As shown, the following steps are included: S1. Based on the existing six-degree-of-freedom nonlinear model of hypersonic aircraft, the longitudinal motion equation of the model is derived; S2. Based on the dynamic inverse theory, the longitudinal motion equation is converted into an equivalent linear system through input-output feedback linearization; S3, solve the interference invariant set of the hypersonic vehicle subject to external uncertain disturbances, and derive the robust tightening constraints of the equivalent tracking system; S4. Considering the state constraints, control quantity and control increment constraints of the hypersonic aircraft, a robust model predictive controller based on Tube is designed to control the actual height and speed of the hypersonic aircraft to approach the expected height and speed while ensuring the stable flight of the fuselage.
[0039] As a specific implementation of this embodiment, in step S1, the longitudinal motion equation of the hypersonic aircraft is described as follows:
[0040] The longitudinal motion equation of a hypersonic vehicle contains five rigid body states: are speed, track angle, altitude, angle of attack and pitch velocity respectively; among them, is the acceleration due to gravity, is the mass of the hypersonic vehicle, For along The moment of inertia of the shaft; They are lift, drag, thrust and pitch moment during the motion, and the calculation expressions are:
[0041] in, They are dynamic pressure, fuselage reference area, and mean aerodynamic chord length; They are lift coefficient, drag coefficient, thrust coefficient and pitch moment coefficient respectively. The specific expressions are:
[0042] in, They are elevator deflection angle and engine valve opening respectively.
[0043] As a specific implementation of this embodiment, step S2 includes: S2.1. Linearize the input and output of the hypersonic vehicle velocity subsystem based on the dynamic inversion method. Speed Ask about time The first derivative of , we get:
[0044] right Continue to derive until the third-order derivative, and we get:
[0045] in, is the state variable of the hypersonic vehicle, Contains , The control input contains the elevator angle , The control input contains the engine valve opening ; S2.2. Linearize the input and output of the hypersonic vehicle altitude subsystem based on the dynamic inversion method; For height Ask about time The derivative of and engine valve opening ,have to:
[0046] in, Contains control input quantity elevator deflection angle and engine valve opening ; S2.3. Design control variables for the altitude and speed subsystems of hypersonic vehicles; The parts of the speed subsystem and the height subsystem related to the control quantity are separately proposed, and the following output equation is obtained:
[0047] In the formula, They are the five rigid body states of the longitudinal motion equation of the hypersonic vehicle, the engine valve opening and the engine valve opening derivative, the engine valve opening command and the elevator deflection angle; is the function part that is independent of the control quantity obtained by nonlinear inversion, is the function part related to the control quantity obtained by nonlinear inversion; Design the following control quantity:
[0048] in, is the virtual control quantity; The speed subsystem is designed as follows: , define the system coordinate transformation , in the new coordinate system we get:
[0049] in, is the true speed, is the target speed, is the difference between the actual speed and the target speed, is the state variable after coordinate transformation; The speed decoupled subsystem is expressed as:
[0050] in, is the velocity subsystem state matrix, is the speed subsystem control matrix; The height subsystem is designed as follows: , define the system coordinate transformation , in the new coordinate system we get:
[0051] in, is the true height, is the target height, is the difference between the actual altitude and the target altitude, is the state variable after coordinate transformation; A highly decoupled subsystem is represented as:
[0052] in, is the height subsystem state matrix, It is the height subsystem control matrix.
[0053] As a specific implementation of this embodiment, step S3 includes: First, the equivalent linear tracking system of a hypersonic vehicle subject to external uncertain disturbances is as follows:
[0054] in, are the system state, the control input vector, and the external disturbances to the equivalent linear tracking system; Due to the influence of disturbances, the state trajectory of the actual hypersonic vehicle Often deviates from the nominal optimal prediction trajectory , the upper bound of the state prediction deviation is calculated as follows: Assume that the actual system with uncertain disturbances and the nominal system have the same initial state at the same initial time. Evolved, subtracting the nominal system from the actual system, using the triangle inequality and Lipschitz conditions, we get:
[0055] Then using the Gronwall-Bellman inequality, we get:
[0056] in, ; Accordingly, using Minkowski subtraction, the robust tightened state constraint can be estimated as:
[0057] in, is the state variable of the hypersonic vehicle, is the upper bound of external interference.
[0058] As a specific implementation of this embodiment, step S4 includes: S4.1. Design a robust model predictive controller for the equivalent tracking system of a hypersonic vehicle based on a disturbance invariant set. The optimal control problem of the robust model predictive controller is as follows:
[0059] In the formula, are the feasible control inputs and the corresponding predicted state trajectories, respectively. represents the optimal situation, They are robust tightening state constraints, control input constraints, and control increment input constraints. are the state matrix and input matrix of the speed and altitude subsystems of the hypersonic vehicle, respectively. is the terminal state constraint matrix; S4.2、Explanation on the terminal invariant set and terminal controller existence of robust model predictive controller for equivalent tracking system of hypersonic vehicle; Since the equivalent linear nominal system is stabilizable at the equilibrium point (0,0), the following steps are used to illustrate the existence of the terminal invariant set and terminal controller of the robust model predictive controller of the equivalent tracking system of the hypersonic vehicle; When the nominal system , given the matrix , there is a constant and the unique matrix When the following conditions are met: Condition 1. ; Condition 2. ; Condition 3. ; Condition 4. It is a closed loop system The positive invariant set of ; Condition 5. in ; Then we can choose the following continuous-time Lyapunov equation:
[0060] because, , the above equation has a unique solution ; Secondly, due to , there is a constant , so that in the set If conditions 1-2 are met, then for any point , the following inequality holds:
[0061] definition , in the collection In, conditions 1-3 are satisfied; along right The derivative is:
[0062] because, , the above equation shows that for the closed loop system ,gather is unchanged, according to , meeting conditions 1-5.
[0063] Next, in order to verify the effectiveness of the hypersonic vehicle nonlinear dynamic inverse robust model predictive control method provided in this embodiment, MATLAB is used to conduct simulation experiments and provide detailed explanations.
[0064] The longitudinal motion model provided in this embodiment comprehensively considers the influence of factors such as the nonlinear dynamic characteristics of the engine, the high temperature effect, and the mutual coupling of aerodynamic parameters at high speed on the flight altitude and speed tracking performance of the hypersonic aircraft, and adopts a nonlinear dynamic inverse robust model predictive control method to make the closed-loop system asymptotically stable, with good altitude and speed tracking performance, while ensuring the stable flight of the fuselage and having good suppression of unknown disturbances.
[0065] In the simulation experiment, the total mass of the hypersonic aircraft is 136820kg, the reference area is 334.73㎡, and the gravity acceleration is , average aerodynamic chord length 24.38m, y-axis moment of inertia ; Based on the above parameters, the composite control strategy proposed by the present invention is simulated and verified. Figure 2-4 .
[0066] Figure 2The speed and altitude command tracking curves, engine throttle control quantity change diagram, and elevator angle change diagram under the nonlinear dynamic inverse robust model predictive control method of the hypersonic aircraft are displayed in turn; according to Figure 2 It can be obtained that the system has good height and speed tracking performance; Figure 3 The change diagrams of the flight path angle, angle of attack and pitch angular velocity of the hypersonic aircraft are shown in sequence; Figure 3 It can be seen that the system has good posture adjustment ability; Figure 4 The change diagrams of the engine throttle control amount increment and the elevator deflection angle of the hypersonic aircraft are shown in sequence; Figure 4 It can be seen that the predictive control method of this embodiment has good constraint capability on the control increment; The above analysis proves the effectiveness of the hypersonic vehicle nonlinear dynamic inverse robust model predictive control method provided in this embodiment.
[0067] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the protection scope of the present invention.
Claims
1. A nonlinear dynamic inverse robust model predictive control method for a hypersonic vehicle, characterized in that: The steps include: S1. Based on the existing six-degree-of-freedom nonlinear model of hypersonic aircraft, the longitudinal motion equation of the model is derived; S2. Based on the dynamic inverse theory, the longitudinal motion equation is converted into an equivalent linear system through input-output feedback linearization; S3, solve the interference invariant set of the hypersonic vehicle subject to external uncertain disturbances, and derive the robust tightening constraints of the equivalent tracking system; S4. Considering the state constraints, control quantity and control increment constraints of the hypersonic aircraft, a robust model predictive controller based on Tube is designed to control the actual height and speed of the hypersonic aircraft to approach the expected height and speed while ensuring the stable flight of the fuselage.
2. The hypersonic vehicle nonlinear dynamic inverse robust model predictive control method according to claim 1, characterized in that: In step S1, the longitudinal motion equation is as follows: , The longitudinal motion equation of a hypersonic vehicle contains five rigid body states: are speed, track angle, altitude, angle of attack and pitch velocity respectively; among them, is the acceleration due to gravity, is the mass of the hypersonic vehicle, For along The moment of inertia of the shaft; They are lift, drag, thrust and pitch moment during the motion, and the calculation expressions are: , in, They are dynamic pressure, fuselage reference area, and mean aerodynamic chord length; They are lift coefficient, drag coefficient, thrust coefficient and pitch moment coefficient respectively. The specific expressions are: , in, They are the elevator deflection angle and engine valve opening respectively.
3. The hypersonic vehicle nonlinear dynamic inverse robust model predictive control method according to claim 2, characterized in that: Step S2 includes: S2.
1. Linearize the input and output of the hypersonic vehicle velocity subsystem based on the dynamic inversion method. Speed Ask about time The first derivative of , we get: , right Continue to derive until the third-order derivative, and we get: , in, is the state variable of the hypersonic vehicle, Contains , The control input contains the elevator angle , The control input contains the engine valve opening ; S2.
2. Linearize the input and output of the hypersonic vehicle altitude subsystem based on the dynamic inversion method: For height Ask about time The derivative of and engine valve opening ,have to: , in, Contains control input quantity elevator deflection angle and engine valve opening ; S2.
3. Design control variables for the altitude and speed subsystems of hypersonic vehicles; The parts of the speed subsystem and the height subsystem related to the control quantity are separately proposed, and the following output equation is obtained: , In the formula, They are the five rigid body states of the longitudinal motion equation of the hypersonic vehicle, the engine valve opening and the engine valve opening derivative, the engine valve opening command and the elevator deflection angle; is the function part that is independent of the control quantity obtained by nonlinear inversion, is the function part related to the control quantity obtained by nonlinear inversion; Design the following control quantity: , in, is the virtual control quantity; The speed subsystem is designed as follows: , define the system coordinate transformation , we get in the new coordinate system: , in, is the true speed, is the target speed, is the difference between the actual speed and the target speed, is the state variable after coordinate transformation; The speed decoupled subsystem is expressed as: , in, is the velocity subsystem state matrix, is the speed subsystem control matrix; The height subsystem is designed as follows: , define the system coordinate transformation , we get in the new coordinate system: , in, is the true height, is the target height, is the difference between the actual altitude and the target altitude, is the state variable after coordinate transformation; A highly decoupled subsystem is represented as: , in, is the height subsystem state matrix, It is the height subsystem control matrix.
4. The hypersonic vehicle nonlinear dynamic inverse robust model predictive control method according to claim 3, characterized in that: Step S3 includes: First, the equivalent linear tracking system of a hypersonic vehicle subject to external uncertain disturbances is as follows: , in, are the system state, the control input vector, and the external disturbances to the equivalent linear tracking system; Due to the influence of disturbances, the state trajectory of the actual hypersonic vehicle Will deviate from the nominal optimal prediction trajectory , the upper bound of the state prediction deviation is calculated as follows: Assume that the actual system with uncertain disturbances and the nominal system have the same initial state at the same initial time. Evolved, subtracting the nominal system from the actual system, using the triangle inequality and Lipschitz conditions, we get: , Then using the Gronwall-Bellman inequality, we get: , in, ; Accordingly, using Minkowski subtraction, the robust tightened state constraint is estimated as: , in, is the state variable of the hypersonic vehicle, is the upper bound of external disturbance.
5. The hypersonic vehicle nonlinear dynamic inverse robust model predictive control method according to claim 4, characterized in that: Step S4 includes: S4.
1. Design a robust model predictive controller for the equivalent tracking system of a hypersonic vehicle based on a disturbance invariant set. The optimal control problem of the robust model predictive controller is as follows: , In the formula, are the feasible control inputs and the corresponding predicted state trajectories, respectively. represents the optimal situation, They are robust tightening state constraints, control input constraints, and control increment input constraints. are the state matrix and input matrix of the speed and altitude subsystems of the hypersonic vehicle, respectively. is the terminal state constraint matrix; S4.2、Explanation on the terminal invariant set and terminal controller existence of robust model predictive controller for equivalent tracking system of hypersonic vehicle; The equivalent linear nominal system is stabilizable at the equilibrium point (0,0). The following steps are used to illustrate the existence of the terminal invariant set and terminal controller of the robust model predictive controller of the equivalent tracking system of the hypersonic vehicle. When the nominal system , given the matrix , there is a constant and the unique matrix When the following conditions are met: Condition 1. ; Condition 2. ; Condition 3. ; Condition 4. It is a closed loop system The positive invariant set of ; Condition 5. in ; Then we can choose the following continuous-time Lyapunov equation: , because, , the above equation has a unique solution ; Secondly, due to , there is a constant , so that in the set If conditions 1-2 are met, then for any point , the following inequality holds: , definition , in the collection In, conditions 1-3 are satisfied; along right The derivative is: , because, , the above equation shows that for the closed loop system ,gather is unchanged, according to , meeting conditions 1-5.