Multi-constraint anti-saturation attitude control method for shape-variable aircraft

Abstract

The invention discloses a multi-constraint anti-saturation attitude control method for a variable-shape aircraft, and belongs to the field of aircraft guidance and control. The implementation method comprises the following steps: establishing a variable shape aircraft dynamics model, and writing the model in a control matrix form; considering attitude angle constraint, giving a state tracking error, constructing an asymmetric obstacle Lyapunov function, and introducing the attitude angle constraint into controller design; giving a state tracking error by considering an attitude angular rate constraint, constructing a symmetric obstacle Lyapunov function, and introducing the attitude angular rate constraint into controller design; a composite Lyapunov function is designed, control input constraints are considered, and an attitude angular rate subsystem virtual control law is designed; and realizing the multi-constraint anti-saturation attitude control of the variable shape aircraft according to the anti-saturation attitude control law under multiple constraints. According to the invention, under strict constraints of the attitude angle, the attitude angular rate and the control input, accurate tracking of the attitude angle and the attitude angular rate can be realized, and effective suppression of control buffeting can be realized.

Description

Technical Field

[0001] This invention relates to a multi-constraint anti-saturation attitude control method for variable-shape aircraft, belonging to the field of aircraft guidance and control technology. Background Technology

[0002] Variable-shape aircraft, by adjusting their aerodynamic configuration online in real time, can adapt to complex environments across wide speed ranges and varying airspace during transatmospheric flight, exhibiting ideal aerodynamic performance. Unlike traditional fixed-shape aircraft, which are limited in flight missions and flight ranges, variable-shape aircraft, especially high-speed variable-shape aircraft, can dynamically optimize their aerodynamic characteristics, handling performance, and thermal protection efficiency throughout the entire flight envelope by actively changing their shape and structure. This significantly improves the aircraft's adaptability, maneuverability, and range in response to different mission profiles and environmental conditions, effectively enhancing its mission effectiveness and penetration capability. It represents a key development direction for next-generation aerospace vehicles.

[0003] The configuration changes caused by active deformation also introduce changes in the center of mass and moment of inertia, further exacerbating aerodynamic parameter perturbations. This results in the aircraft's dynamics model exhibiting strong nonlinearity and strong coupling characteristics, thus imposing extremely stringent requirements on the control system design. Considering flight stability, structural strength, and mission profile, key state variables of the aircraft, such as angle of attack, sideslip angle, roll angle, and deflection of actuator surfaces, must be constrained within strict physical boundaries. Violation of these constraints can easily lead to mission failure, and in severe cases, may even cause the aircraft to disintegrate. Therefore, a new control method is needed to address the anti-saturation attitude control problem of variable-shape aircraft under multiple constraints. Summary of the Invention

[0004] To address the problem of anti-saturation attitude control in variable-shape aircraft under multiple constraints, the present invention aims to provide a multi-constraint anti-saturation attitude control method for variable-shape aircraft, which can achieve precise tracking of attitude angle and attitude rate under strict constraints of attitude angle, attitude angular rate and control input, and can effectively suppress control chattering.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses a multi-constraint anti-saturation attitude control method for variable-shape aircraft. It establishes a dynamic model of the variable-shape aircraft, considers attitude angle and attitude angular rate constraints, derives the state tracking error, constructs an asymmetric barrier Lyapunov function, and incorporates the attitude angle constraint into the controller design. Similarly, it constructs a symmetric barrier Lyapunov function based on the state tracking error and incorporates the attitude angular rate constraint into the controller design. Considering control input constraints, it designs a virtual control law for the attitude angular rate subsystem, obtaining the attitude control law under multiple constraints. Based on this multi-constraint attitude control law, it improves the system's stability and performance when the control input is saturated.

[0007] The attitude control problem of a variable-shape aircraft under multiple constraints disclosed in this invention includes the following steps:

[0008] Step 1: Establish a dynamic model of the variable-shape aircraft and write the dynamic model of the variable-shape aircraft in the form of a control matrix;

[0009]

[0010] in, For the speed of the aircraft, For the mass of the aircraft, It is the acceleration due to gravity. , , These are the angle of attack, sideslip angle, and roll angle, respectively. , and These are pitch, sideslip, and roll rates, respectively. For velocity tilt angle, , and They are respectively around , and Moment of inertia of the shaft , These are the lift and lateral forces acting on the aircraft, respectively. , and These are the roll moment, yaw moment, and pitch moment, respectively. , and This is the additional torque generated by deformation.

[0011]

[0012] in, For dynamic pressure, This is the reference area before deformation. This is the lateral reference length. For longitudinal reference length, for right coefficient, and They are respectively and right coefficient, for right coefficient, for right coefficient, for right coefficient, The span-to-deformation ratio is a normalized descriptive parameter for the span-to-deformation of a morphing aircraft, with a deformation range of [0,1], and is defined as follows:

[0013]

[0014] in, This is the minimum span of the telescopic wing; This represents the maximum telescopic wing span.

[0015] To facilitate controller design, the dynamic model is written in control matrix form:

[0016]

[0017] Wherein, the state vector Represents the state variables of angle of attack, sideslip angle, and roll angle. Indicates pitch, yaw, and roll rates; control inputs Indicates the rudder deflection angle for each channel. , The input matrix includes unmodeled dynamics, aerodynamic parameter uncertainties, and deformation coupling effects. , The control gain matrix is ​​invertible, and its specific form is as follows:

[0018]

[0019] in, for The i-th component, .

[0020]

[0021] in, for The i-th component, .

[0022]

[0023] in, for The i-th component, .

[0024]

[0025] in, for The i-th component, .

[0026] For each attitude angle and attitude angular rate, they each satisfy the following corresponding constraints, where Represents the lower bound constraint. It represents the upper bound of the constraint.

[0027]

[0028] Step 2: Based on the dynamic model obtained in Step 1, considering attitude angle constraints, give the state tracking error. We construct an asymmetric obstacle Lyapunov function and introduce attitude angle constraints into the controller design.

[0029] The tracking error is defined as follows:

[0030]

[0031] in, For the desired attitude angle, For the virtual control commands to be designed in step three, regarding attitude angle tracking error Each component The constraints that need to be satisfied are related to the state variables, and in the initial state... The constraint boundary is: Therefore, we can obtain the result from formula (9). The initial constraint boundaries are: ,design The upper boundary constraint is The initial upper boundary constraint is ,design The lower boundary constraint is The initial lower boundary constraint is After the controller converges, The constraint boundary is set as The expected convergence time is ,design The time-varying function of the constraint boundary is:

[0032]

[0033] Design an asymmetric barrier Lyapunov function, specifically:

[0034]

[0035] Among them, parameters Represented as:

[0036]

[0037] To simplify the expression, define:

[0038]

[0039] right Differentiating, we get:

[0040]

[0041] Design virtual control law :

[0042]

[0043] in, It is a positive definite diagonal gain matrix. ;Will Substitution Later it was found that:

[0044]

[0045] Step 3: Based on the dynamic model obtained in Step 1, considering attitude angular rate constraints, give the state tracking error. We construct a symmetric barrier Lyapunov function and introduce attitude angular rate constraints into the controller design.

[0046] according to The symmetry constraints show that Therefore The initial constraint boundaries are: ,design The constraint boundary is In the initial state for Then there is The initial constraint boundary is After the controller converges, The constraint boundary is ,have to The time-varying function of the constraint boundary is:

[0047]

[0048] Design a symmetric barrier Lyapunov function, specifically:

[0049]

[0050] To simplify the expression, define ,but ;

[0051] Step 4: Based on the design of the composite Lyapunov function in Steps 2 and 3, and considering the control input constraints, design the virtual control law for the attitude angular rate subsystem; based on sliding mode control theory, obtain the anti-saturation attitude control law under multiple constraints, and realize the multi-constraint anti-saturation attitude control of the variable shape aircraft according to the anti-saturation attitude control law under multiple constraints.

[0052] Design a composite Lyapunov function :

[0053]

[0054] And on Differentiation yields:

[0055]

[0056] in, for The i-th component.

[0057] Design sliding surface Sliding surface coefficient matrix Therefore, the sliding mode control law is designed as follows:

[0058]

[0059] in

[0060]

[0061] in , , , It is a positive definite diagonal gain matrix. It is a vector-valued function. This is a superspiral integral term.

[0062] To prevent the control command calculated by formula (24) If the physical deflection limit of the aircraft's control surfaces is exceeded, amplitude constraints must be imposed on the control input.

[0063]

[0064] The saturation function is expressed as follows:

[0065]

[0066] Based on the saturation characteristics of the control input, static anti-saturation compensation is introduced to calculate the deviation between the ideal control command and the saturated output. :

[0067]

[0068] Then reduce the excessive portion proportionally.

[0069]

[0070] The actual control quantity obtained, i.e., the anti-saturation attitude control law under multiple constraints, is as follows:

[0071]

[0072] in, It is a diagonal matrix with diagonal elements greater than 0 and less than 1 that resists saturation gain.

[0073] Multi-constraint anti-saturation attitude control of variable-shape aircraft is achieved based on the multi-constraint anti-saturation attitude control law.

[0074] Beneficial effects:

[0075] 1. The present invention discloses a multi-constraint anti-saturation attitude control method for variable-shape aircraft, which establishes a dynamic model of the variable-shape aircraft, considers attitude angle and attitude angular rate constraints, gives the state tracking error, constructs a barrier Lyapunov function, and introduces complex time-varying state constraints into the controller design, thereby achieving accurate tracking of attitude angle and attitude angular rate under strict constraints of attitude angle and attitude angular rate.

[0076] 2. The multi-constraint anti-saturation attitude control method for variable-shape aircraft disclosed in this invention considers control input constraints and uses a super-spiral algorithm to achieve high-order sliding mode control, thereby effectively suppressing control chattering while limiting the amplitude of the control input. Attached Figure Description

[0077] Figure 1 This is a flowchart of the multi-constraint anti-saturation attitude control method for variable-shape aircraft of the present invention;

[0078] Figure 2 This is an example of the three-channel attitude angle tracking response curve of this invention;

[0079] Figure 3 This is a schematic diagram of the three-channel attitude angle tracking error and asymmetric constraint boundary in an example of the present invention;

[0080] Figure 4 This is the three-channel attitude angular rate tracking response curve of an example of the present invention;

[0081] Figure 5 This is a schematic diagram of the three-channel attitude angular rate tracking error and asymmetric constraint boundary in an embodiment of the present invention;

[0082] Figure 6 The invention example generates a three-channel control input curve. Detailed Implementation

[0083] To better illustrate the purpose and advantages of the present invention, the following description, in conjunction with an embodiment and corresponding drawings, further explains the invention.

[0084] To verify the feasibility of the method, this embodiment uses the attitude control of a variable-span-length aircraft as an example for attitude control. The variable-span-length aircraft's mass... Reference area before deformation Moment of inertia initial velocity initial height Initial span-to-strain ratio The initial attitude is The initial angular velocity is The desired attitude angle command is: .

[0085] like Figure 1 As shown, according to one embodiment of the present invention, the multi-constraint anti-saturation attitude control method for variable-shape aircraft disclosed in the present invention has the following specific implementation steps:

[0086] Step 1: Establish a dynamic model of the variable-shape aircraft and write the model in the form of a control matrix;

[0087]

[0088] in, For the speed of the aircraft, For the mass of the aircraft, It is the acceleration due to gravity. , , These are the angle of attack, sideslip angle, and roll angle, respectively. , and These are pitch, sideslip, and roll rates, respectively. For velocity tilt angle, , and They are respectively around , and Moment of inertia of the shaft , These are the lift and lateral forces acting on the aircraft, respectively. , and These are the roll moment, yaw moment, and pitch moment, respectively. , and This is the additional torque generated by deformation.

[0089]

[0090] in, For dynamic pressure, This is the reference area before deformation. This is the lateral reference length. For longitudinal reference length, for right coefficient, and They are respectively and right coefficient, for right coefficient, for right coefficient, for right coefficient, The span-to-deformation ratio is a normalized descriptive parameter for the span-to-deformation of a morphing aircraft, with a deformation range of [0,1], and is defined as follows:

[0091]

[0092] in, This is the minimum span of the telescopic wing; This represents the maximum telescopic wing span.

[0093] To facilitate controller design, the dynamic model is written in control matrix form:

[0094]

[0095] Wherein, the state vector Represents the state variables of angle of attack, sideslip angle, and roll angle. Indicates pitch, yaw, and roll rates; control inputs Indicates the rudder deflection angle for each channel. , The input matrix includes unmodeled dynamics, aerodynamic parameter uncertainties, and deformation coupling effects. , The control gain matrix is ​​invertible, and its specific form is as follows:

[0096]

[0097] in, for The i-th component, .

[0098]

[0099] in, for The i-th component, .

[0100]

[0101] in, for The i-th component, .

[0102]

[0103] in, for The i-th component, .

[0104] For each attitude angle and attitude angular rate, they each satisfy the following corresponding constraints, where Represents the lower bound constraint. It represents the upper bound of the constraint.

[0105]

[0106] Step 2: Based on the dynamic model obtained in Step 1, considering attitude angle constraints, give the state tracking error. We construct an asymmetric obstacle Lyapunov function and introduce attitude angle constraints into the controller design.

[0107] The tracking error is defined as follows:

[0108]

[0109] in, For the desired attitude angle, For the virtual control commands to be designed in step three, regarding attitude angle tracking error Each component The constraints that need to be satisfied are related to the state variables, and in the initial state... The constraint boundary is: Therefore, we can obtain the result from formula (9). The initial constraint boundaries are: ,design The upper boundary constraint is The initial upper boundary constraint is ,design The lower boundary constraint is The initial lower boundary constraint is After the controller converges, The constraint boundary is set as The expected convergence time is ,design The time-varying function of the constraint boundary is:

[0110]

[0111] Design an asymmetric barrier Lyapunov function, specifically:

[0112]

[0113] Among them, parameters Represented as:

[0114]

[0115] To simplify the expression, define:

[0116]

[0117] right Differentiation yields:

[0118]

[0119] Design virtual control law :

[0120]

[0121] in, It is a positive definite diagonal gain matrix. ;Will Substitution Later it was found that:

[0122]

[0123] Step 3: Based on the dynamic model obtained in Step 1, considering attitude angular rate constraints, give the state tracking error. We construct a symmetric barrier Lyapunov function and introduce attitude angular rate constraints into the controller design.

[0124] according to The symmetry constraints show that Therefore The initial constraint boundaries are: ,design The constraint boundary is In the initial state for Then there is The initial constraint boundary is After the controller converges, The constraint boundary is , can be obtained The time-varying function of the constraint boundary is:

[0125]

[0126] Design a symmetric barrier Lyapunov function, specifically:

[0127]

[0128] To simplify the expression, define ,but ;

[0129] Step 4: Considering control input constraints, design a virtual control law for the attitude angular rate subsystem, and finally obtain the attitude control law under multiple constraints, thereby improving the stability and performance of the system when the control input is saturated.

[0130] Design a composite Lyapunov function :

[0131]

[0132] And on Differentiation yields:

[0133]

[0134] in, for The i-th component.

[0135] Design sliding surface Sliding surface coefficient matrix Therefore, the sliding mode control law is designed as follows:

[0136]

[0137] in

[0138]

[0139] in , , , It is a positive definite diagonal gain matrix. It is a vector-valued function. This is a superspiral integral term.

[0140] To prevent the control command calculated by formula (24) If the physical deflection limit of the aircraft's control surfaces is exceeded, amplitude constraints must be imposed on the control input.

[0141]

[0142] The saturation function is expressed as follows:

[0143]

[0144] Based on the saturation characteristics of the control input, static anti-saturation compensation is introduced. First, the deviation between the ideal control command and the saturated output is calculated. :

[0145]

[0146] Then reduce the excessive portion proportionally.

[0147]

[0148] Ultimately, the actual execution control quantity is obtained.

[0149]

[0150] The parameters of each controller are shown in Table 2.

[0151] Table 2 Controller Parameters

[0152]

[0153] The simulation results are shown in the attached figures in the instruction manual. Figures 2 to 6 As shown.

[0154] Figure 2 This is an example of the three-channel attitude angle tracking response of the present invention. The curves show that the angle of attack, sideslip angle and roll angle channels all stably track the desired command.

[0155] Figure 3 This is a schematic diagram of the three-channel attitude angle tracking error and asymmetric constraint boundary in an example of the present invention, showing that the angle tracking error of the three channels is controlled within the time-varying asymmetric constraint range.

[0156] Figure 4 The three-channel attitude angular rate tracking response curves are examples of this invention. The pitch, yaw, and roll angular rates all converge rapidly to the virtual control commands.

[0157] Figure 5 The diagram below illustrates the three-channel attitude angular rate tracking error and asymmetric constraint boundary in an embodiment of the present invention, showing that the angular rate tracking error of the three channels is controlled within the time-varying symmetric constraint range.

[0158] Figure 6 The three-channel control input curves generated for this invention example show that the three-channel rudder deflection angle commands are all within ±20°. Within the physical limit range.

[0159] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-constraint anti-saturation attitude control method for variable-shape aircraft, characterized in that: Includes the following steps: Step 1: Establish a dynamic model of the variable-shape aircraft and write the dynamic model of the variable-shape aircraft in the form of a control matrix; Step 2: Based on the dynamic model obtained in Step 1, considering attitude angle constraints, give the state tracking error. We construct an asymmetric obstacle Lyapunov function and introduce attitude angle constraints into the controller design. Step 3: Based on the dynamic model obtained in Step 1, considering attitude angular rate constraints, give the state tracking error. We construct a symmetric barrier Lyapunov function and introduce attitude angular rate constraints into the controller design. Step 4: Based on the design of the composite Lyapunov function in Steps 2 and 3, and considering the control input constraints, design the virtual control law for the attitude angular rate subsystem; based on sliding mode control theory, obtain the anti-saturation attitude control law under multiple constraints, and realize the multi-constraint anti-saturation attitude control of the variable shape aircraft according to the anti-saturation attitude control law under multiple constraints.

2. The method as described in claim 1, characterized in that: The dynamic model of the variable-shape aircraft in step one is expressed as follows: in, For the speed of the aircraft, For the mass of the aircraft, It is the acceleration due to gravity. , , These are the angle of attack, sideslip angle, and roll angle, respectively. , and These are pitch, sideslip, and roll rates, respectively. For velocity tilt angle, , and They are respectively around , and Moment of inertia of the shaft , These are the lift and lateral forces acting on the aircraft, respectively. , and These are the roll moment, yaw moment, and pitch moment, respectively. , and The additional torque generated by deformation; in, For dynamic pressure, This is the reference area before deformation. This is the lateral reference length. For longitudinal reference length, for right coefficient, and They are respectively and right coefficient, for right coefficient, for right coefficient, for right coefficient, The span-to-deformation ratio is a normalized descriptive parameter for the span-to-deformation of a morphing aircraft, with a deformation range of [0,1], and is defined as follows: in, This is the minimum span of the telescopic wing; This represents the maximum wing span.

3. The method as described in claim 1, characterized in that: The method described in step one for writing the dynamic model of the variable-shape aircraft in control matrix form is as follows: To facilitate controller design, the dynamic model is written in matrix form: Wherein, the state vector Represents the state variables of angle of attack, sideslip angle, and roll angle. Indicates pitch, yaw, and roll rates; control inputs Indicates the rudder deflection angle for each channel. , The input matrix includes unmodeled dynamics, aerodynamic parameter uncertainties, and deformation coupling effects. , The control gain matrix is ​​invertible, and its specific form is as follows: in, for The i-th component, ; in, for The i-th component, ; in, for The i-th component, ; in, for The i-th component, .

4. The method as described in claim 1, characterized in that: Each attitude angle and attitude angular rate satisfies the following constraints: in, Represents the lower bound constraint. It represents the upper bound of the constraint.

5. The method as described in claim 1, characterized in that: The implementation method for step two is as follows: Tracking error is defined as: in, For the desired attitude angle, For virtual control commands, regarding attitude angle tracking errors Each component Constraints and attitude angles to be satisfied Related, in the initial state The constraint boundary is: Therefore, we can obtain the result from formula (9). The initial constraint boundaries are: ,design The upper boundary constraint is The initial upper boundary constraint is ,design The lower boundary constraint is The initial lower boundary constraint is After the controller converges, The constraint boundary is set as The expected convergence time is ,design The time-varying function of the constraint boundary is: The asymmetric barrier Lyapunov function is represented as: Among them, parameters Represented as: To simplify the expression, define: right Differentiating, we get: Virtual control law Represented as: in, It is a positive definite diagonal gain matrix. ;Will Substitution Later it was found that:

6. The method as described in claim 1, characterized in that: The implementation method for step three is as follows: according to The symmetry constraints show that Therefore The initial constraint boundaries are: ,design The constraint boundary is In the initial state for Then there is The initial constraint boundary is After the controller converges, The constraint boundary is ,have to The time-varying function of the constraint boundary is: The symmetry-barrier Lyapunov function is expressed as: definition ,but .

7. The method as described in claim 1, characterized in that: The implementation method for step four is as follows: Design a composite Lyapunov function : And on Differentiation yields: in, for The i-th component; Design sliding surface Sliding surface coefficient matrix Therefore, the sliding mode control law is designed as follows: in in , , , It is a positive definite diagonal gain matrix. It is a vector-valued function. For the superspiral integral term; multi-constraint anti-saturation attitude control of variable-shape aircraft is achieved based on the sliding mode control law.

8. The method as described in claim 1, characterized in that: The implementation method for step four is as follows: To prevent the attitude control command in step four Exceeding the physical deflection limit of the aircraft's control surfaces, an amplitude constraint is imposed on the control input; in, The saturation function is specifically expressed as follows: in, for The components; calculate the deviation between the ideal control command and the saturated input. : Then reduce the excessive portion proportionally. The actual control quantity obtained, i.e., the anti-saturation attitude control law under multiple constraints, is as follows: in, It is a diagonal matrix with diagonal elements greater than 0 and less than 1 that resists saturation gain. Multi-constraint anti-saturation attitude control of variable-shape aircraft is achieved based on the multi-constraint anti-saturation attitude control law.

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