A dynamic sliding mode based attitude control method for underactuated non-minimum phase RLV

Abstract

The application provides a dynamic sliding mode based attitude control method for an underactuated non-minimum phase RLV, which can realize accurate tracking control of longitudinal and lateral attitudes and stabilize the sideslip angle to zero by using only two movable flaps of the RLV, and solves the underactuated non-minimum phase control problem in the reentry process of the RLV. The control design is relatively simple, and has certain robustness to system state and parameter changes.

Description

Technical Field

[0001] This invention belongs to the field of attitude control technology, and in particular relates to an underactuated non-minimum phase RLV attitude control method based on dynamic sliding mode. Background Technology

[0002] With the rapid development of aerospace technology, human exploration of the universe has deepened, and aerospace activities have increased. However, the high cost and non-reusability of conventional launch vehicles make aerospace activities prohibitively expensive, significantly hindering the development of human spaceflight. Furthermore, humanity not only desires aerospace launch vehicles capable of delivering satellites, instruments, and other payloads into space, but also to bring back costly, critical instruments, core components, and vital data to Earth, even achieving takeoff and landing like airplanes for reuse. Against this backdrop, Reusable Launch Vehicles (RLVs) have emerged. Employing a single-stage-to-orbit approach, they can be launched into space by rockets, re-enter the atmosphere after completing their mission, and land back on Earth, allowing for repeated use. This significantly reduces the launch costs of aerospace activities, making RLVs an increasingly cost-effective medium for such activities.

[0003] During its return to Earth, the Reentry Vehicle (RLV) undergoes an atmospheric reentry phase. This phase involves significant dynamic pressure and generates substantial aerodynamic heat. Since the RLV's rudder is highly sensitive to aerodynamic heat, it may burn out due to excessive heat during reentry. Furthermore, due to its fuselage configuration, the large fuselage and wings can obstruct airflow at the rudder during high angles of attack, reducing rudder control efficiency. Therefore, before the aircraft's speed drops to Mach 6 during reentry, the rudder typically retracts into the fuselage for safety. At this point, only the two flaps remain as attitude control actuators, making the RLV's attitude control system an underactuated system with second-order zero dynamics. Research indicates that the RLV attitude control model is unstable in its zero dynamics, exhibiting non-minimum phase characteristics, which poses a significant challenge to RLV reentry attitude control.

[0004] Most existing control techniques, such as sliding mode control, fractional-order control, and model-free control using neural networks, require the Reentry Vehicle (RLV) to have three available control inputs, neglecting its underactuated and non-minimum phase characteristics during reentry. While the ideal internal model calculation method based on output redefinition solves the underactuated and non-minimum phase problem, it is computationally complex, highly dependent on modeling accuracy, and has poor robustness. Summary of the Invention

[0005] This invention addresses the underactuated non-minimum phase attitude control problem during RLV reentry by proposing a dynamic sliding mode-based underactuated non-minimum phase RLV attitude control method. This method utilizes only the two movable flaps of the RLV to achieve precise longitudinal and lateral attitude tracking control while simultaneously stabilizing the sideslip angle to zero, thus solving the challenge of underactuated non-minimum phase control during RLV reentry. The control design is relatively simple and exhibits robustness to changes in system state and parameters.

[0006] This invention is achieved through the following technical solution: This invention proposes an underactuated non-minimum phase RLV attitude control method based on dynamic sliding mode, the method comprising the following steps:

[0007] Step 1: For the angle-of-attack control subsystem with minimum phase, namely:

[0008]

[0009]

[0010] Where α, β, and μ are the angle of attack, sideslip angle, and roll angle, respectively; p, q, and r are the roll, pitch, and yaw rates, respectively; and I x ,I y and I z It refers to the moment of inertia in the three directions of the body's coordinate axes, I. xz It is the inertial vector product; m0, V0, and g0 are the aircraft mass, flight velocity, and gravitational acceleration, respectively; L = L a Δα+m0g0 is the lift force, L α M′ α and These are aerodynamic parameters, Δα=α-α T ,Δδ e =δ e -δ eT It is the angle of attack α and the elevator deflection angle δ e The deviation between their nominal values, where α T It is the nominal angle of attack, δ eT It is the nominal value of the elevator deflection angle;

[0011] Using δ e To achieve angle-of-attack command tracking, design a PD controller: in K p K d For control parameters;

[0012] Step 2: For the non-minimum phase velocity tilt angle and sideslip angle control subsystem, namely:

[0013]

[0014]

[0015]

[0016]

[0017] Where Y = Y β β is the lateral force; Y β , L′ β , N′ β , These are aerodynamic parameters;

[0018] Define second-order external and second-order internal states, and perform a canonical transformation on the system:

[0019]

[0020]

[0021] in

[0022] The system is transformed into regular form:

[0023]

[0024]

[0025] That is, the internal dynamics are not affected by the control quantity;

[0026] Step 3: Define the dynamic sliding surface:

[0027]

[0028]

[0029] Where f = [f1 f2 f3 f4 f5] T g = [g1 g2 g3 g4 g5] T For control parameters;

[0030] Step 4: Design parameters f and g to make the matrix:

[0031]

[0032] The Hurwitz condition is satisfied;

[0033] Step 5: Design virtual control variables:

[0034] v=-λsign(S)+g1ξ1+g2ξ2+g3η1+g4η2+g5χ

[0035] Where λ is the parameter to be designed, and sign(·) is the sign function;

[0036] Step 6: Based on the virtual control variables designed in Step 5, design the dynamic inverse control law:

[0037]

[0038] Thus, the design of the lateral control system for underactuated non-minimum phase characteristics is complete.

[0039] The beneficial effects of this invention are:

[0040] (1) The dynamic sliding mode attitude control method provided by the present invention only requires two control inputs, namely δ e δ a It achieves attitude tracking and can stabilize the system's unstable zero dynamics. It solves the underactuation problem and the non-minimum phase problem of attitude control during RLV reentry.

[0041] (2) The dynamic sliding mode attitude control method provided by the present invention does not require finding the minimum phase output or solving the ideal internal model. It only requires designing parameters that satisfy a matrix Hurwitz condition. The design process is simple and reliable. Attached Figure Description

[0042] Figure 1 It is a block diagram of the control system structure.

[0043] Figure 2 This is a schematic diagram of the eigenvalue distribution of parameter matrix A.

[0044] Figure 3 This is a schematic diagram of the angle of attack tracking curve.

[0045] Figure 4 This is a schematic diagram of the velocity tilt angle tracking curve.

[0046] Figure 5 This is a schematic diagram of the sideslip angle curve.

[0047] Figure 6 It is the control input δ e Schematic diagram of the curve.

[0048] Figure 7 It is the control input δ a Schematic diagram of the curve.

[0049] Figure 8 This is a schematic diagram of the S-curve variation of the sliding surface. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention aims to design an attitude control method based on dynamic sliding mode to solve the underactuation problem and non-minimum phase problem of the attitude control system during RLV reentry into the atmosphere. (See reference...) Figures 1-8 This invention proposes an underactuated non-minimum phase RLV attitude control method based on dynamic sliding mode, the method comprising the following steps:

[0052] Step 1: For the angle-of-attack control subsystem with minimum phase, namely:

[0053]

[0054]

[0055] Where α, β, and μ are the angle of attack, sideslip angle, and roll angle, respectively; p, q, and r are the roll, pitch, and yaw rates, respectively; and I x ,I y and I z It refers to the moment of inertia in the three directions of the body's coordinate axes, I. xz It is the inertial vector product; m0, V0, and g0 are the aircraft mass, flight velocity, and gravitational acceleration, respectively; L = L a Δα+m0g0 is the lift force, L α M′ α and These are aerodynamic parameters, Δα=α-α T ,Δδ e =δ e -δ eT It is the angle of attack α and the elevator deflection angle δ e The deviation between their nominal values, where α T It is the nominal angle of attack, δ eT It is the nominal value of the elevator deflection angle;

[0056] Using δ e To achieve angle-of-attack command tracking, design a PD controller: in K p K d For control parameters;

[0057] Step 2: For the non-minimum phase velocity tilt angle and sideslip angle control subsystem, namely:

[0058]

[0059]

[0060]

[0061]

[0062] Where Y = Y β β is the lateral force; Y β , L′ β , N′ β , These are aerodynamic parameters;

[0063] Define second-order external and second-order internal states, and perform a canonical transformation on the system:

[0064]

[0065]

[0066] in

[0067] The system is transformed into regular form:

[0068]

[0069]

[0070] That is, the internal dynamics are not affected by the control quantity;

[0071] Step 3: Define the dynamic sliding surface:

[0072]

[0073]

[0074] Where f = [f1 f2 f3 f4 f5] T g = [g1 g2 g3 g4 g5] T For control parameters;

[0075] Step 4: Design parameters f and g to make the matrix:

[0076]

[0077] The Hurwitz condition is satisfied;

[0078] Step 5: Design virtual control variables:

[0079] v=-λsign(S)+g1ξ1+g2ξ2+g3η1+g4η2+g5χ

[0080] Where λ is the parameter to be designed, and sign(·) is the sign function;

[0081] Step 6: Based on the virtual control variables designed in Step 5, design the dynamic inverse control law:

[0082] Thus, the design of the lateral control system for underactuated non-minimum phase characteristics is complete.

[0083] Example 1

[0084] The aircraft parameters in this embodiment are shown in Table 1, and the aerodynamic parameters are shown in Table 2.

[0085] Table 1 Aircraft Parameters

[0086]

[0087] Table 2 Aerodynamic parameters

[0088]

[0089]

[0090] The attitude control method used in Example 1 includes the following steps:

[0091] Step 1: Design δ for the angle-of-attack control subsystem with minimum phase. e PD control law:

[0092]

[0093] Where parameter K p =30, K d =15.

[0094] Step 2: Design the dynamic sliding surface:

[0095]

[0096]

[0097] The control parameter f = [50 -2.2 -100 -29.6 -8.25] T , g=[-24.8 -17 -8.2 -12.952.96] T , such that the matrix:

[0098]

[0099] Eigenvalue distribution as Figure 2 It satisfies the Hurwitz condition.

[0100] Step 3: Design virtual control variables:

[0101] v=-λsign(S)+g1ξ1+g2ξ2+g3η1+g4η2+g5χ

[0102] Where λ = 1.

[0103] Step 4: Design the dynamic inverse control law:

[0104]

[0105] At this point, the control law design for the two control inputs is complete.

[0106] Next, we will use the commonly used sinusoidal attitude command to verify the effectiveness of the method provided in this invention. Therefore, the tracking command function is set as follows:

[0107]

[0108]

[0109] β d =0

[0110] Control effect such as Figures 3-8 The technical solution provided by this invention enables attitude tracking control to be completed using only two control inputs to the flaps, with good tracking performance, effective stabilization of zero dynamics, and stable control inputs. It also solves the underactuation problem and non-minimum phase problem of RLV reentry.

Claims

1. A method for underactuated non-minimum phase RLV attitude control based on dynamic sliding mode, characterized in that, The method includes the following steps: Step 1: For the angle-of-attack control subsystem with minimum phase, namely: in, , and These are the angle of attack, sideslip angle, and roll angle. , and These are roll rate, pitch rate, and yaw rate. , and It refers to the moment of inertia in the three directions of the machine's coordinate axes. It is the product of inertial vectors; , and These are the aircraft's mass, flight speed, and gravitational acceleration; It's lift. and These are aerodynamic parameters. , It is an angle of attack and elevator deflection angle The deviation between their nominal values, of which It is the nominal angle of attack. It is the nominal value of the elevator deflection angle; use To achieve angle-of-attack command tracking, design a PD controller: ,in , , For control parameters; Step 2: For the tilt and sideslip angle control subsystems that are not at their minimum phase, i.e.: in, It is a lateral force; , , , , These are aerodynamic parameters; Define second-order external and second-order internal states, and perform a canonical transformation on the system: in ; The system is transformed into regular form: That is, the internal dynamics are not affected by the control quantity; Step 3: Define the dynamic sliding surface: in , For control parameters; Step 4, Design Parameters , Make the matrix: The Hurwitz condition is satisfied; Step 5: Design virtual control variables: in For the parameters to be designed, It is a symbolic function; Step 6: Based on the virtual control variables designed in Step 5, design the dynamic inverse control law: Thus, the design of the lateral control system for underactuated non-minimum phase characteristics is complete.

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