A mode switching control method for vertical take-off and landing aircraft based on switching MPC

Abstract

The present invention discloses a mode switching control method for a vertical take-off and landing aircraft based on switching model predictive control (MPC). The method designs a control strategy for aircraft mode switching by using switching MPC and switching control obstacle function. First, a dynamic model of the aircraft in different flight modes is established, flight limit attitude constraints are added for different modes, and control input constraints in different modes are clarified according to the dynamic characteristics of the propeller and the rudder. The optimal control quantity is obtained by repeatedly solving the optimization problem, thereby ensuring the recursive feasibility of the switching model prediction, and a control obstacle function sub-controller considering the safety constraint of the attitude change rate is introduced to continuously correct the control input to ensure the smoothness and stability of the mode switching process. Through the switching model predictive control design, the obtained control quantity can achieve the minimum trajectory tracking error and attitude jitter while satisfying the constraint conditions.

Description

Technical Field

[0001] The present invention relates to the field of vertical take-off and landing aircraft control strategies, and in particular to a vertical take-off and landing aircraft mode switching control method based on switching MPC. Background Art

[0002] With the acceleration of urbanization, traffic congestion has become a global problem, and traditional ground transportation methods are unable to meet the demand for efficient travel. Electric vertical take-off and landing vehicles (eVTOLs) are an innovative solution to overcome this bottleneck, providing a fast air transportation option. However, the control of eVTOLs during complex flight mode switching still faces many challenges. To ensure smooth and safe mode switching, efficient and precise control methods are urgently needed.

[0003] Model predictive control (MPC) can optimize control inputs in real time by predicting future states to cope with the complexity and uncertainty of aircraft.

[0004] However, MPC faces challenges in eVTOL mode switching control. The dynamic characteristics of eVTOLs vary significantly across different flight modes, requiring precise models for each mode. Furthermore, environmental changes and flight conditions affect parameter stability, increasing system uncertainty. While traditional MPC performs well in a single mode, its control effectiveness degrades significantly when faced with rapidly changing dynamic characteristics and system parameters during mode switching.

[0005] At present, the mode switching control of eVTOL has received widespread attention from researchers at home and abroad, and many applied results have been achieved. However, the following problems still exist in the overall vehicle: First, the switching smoothness of the existing switching methods is difficult to guarantee, and the switching process has obvious jitter; Second, the dynamic characteristics under different flight modes vary greatly, and the existing methods are difficult to take into account the control optimization of each mode, resulting in less than ideal control performance; Third, environmental changes and the dynamic characteristics of the flight state will affect the system parameters of the eVTOL, making the controller design more difficult and the switching accuracy difficult to guarantee.

[0006] To improve the switching performance of eVTOLs, switching MPC methods have attracted widespread attention due to their ability to design dedicated controllers for different modes and intelligently implement switching strategies. By introducing mechanisms such as control barrier functions, switching MPC can achieve smooth transitions, avoid attitude instability and control jitter, and enhance flight safety and control accuracy. However, the complex nonlinear dynamics and environmental factors of eVTOLs, coupled with uncertainties in model construction and parameter identification for each mode, have limited research progress in switching MPC.

[0007] Therefore, designing an eVTOL control method that can ensure accurate and stable switching remains a difficult problem that needs to be solved urgently. Summary of the Invention

[0008] 1. Purpose of the invention:

[0009] Addressing the limitations of current technologies, this invention aims to provide an advanced and stable control strategy for hybrid eVTOLs. This approach integrates switching MPC and control barrier functions, defines constraints based on different flight modes, solves optimization problems, and modifies control variables, effectively improving the stability of eVTOLs during mode transitions and reducing trajectory tracking errors.

[0010] 2. Technical solution:

[0011] The present invention discloses a modularly reconfigurable field multifunctional wheeled unmanned vehicle platform. Blade battery packs of a frame module and a grid module are used as a power source for the vehicle platform's movement and for adjusting the wheel height, wheelbase, and track width. The Beidou navigation system is used to locate the platform's position, and the surrounding environment is observed through four side-view cameras and two surround-view cameras. A remote control system sends AES-encrypted control instructions to the information processing system and control system of each module to achieve control of the platform. The modules of the vehicle platform are highly integrated and can be assembled concisely and simply, enabling rapid assembly and disassembly. In general field environments, the platform can travel in a 6×6, 5×5, 4×4, 3×3, or 2×2 configuration. When navigating wide trenches or high steps, the operator can use the remote control system to simultaneously adjust the vehicle platform's wheel height, wheelbase, and track width to enable the platform to cross the trench or step.

[0012] The present invention discloses a modular reconfigurable field multifunctional wheeled unmanned vehicle platform, comprising a power module, a frame module, a grid module, a hollow telescopic shaft, and a remote control system, characterized in that: the power module controls the movement of the vehicle platform through a wheel hub motor system; at least two power modules are installed at the lower part of each frame module, and the installation requirements at both ends are preferentially met to ensure the movement stability of the platform; the power modules at both ends of the frame module fix the height spring mounting seat to the lower part of the bolt insert plate through bolts; the power modules at both ends of the frame module are fixed to the inner side of the frame inner plate through the running pins and bolts on the connecting plate; the frame

[0013] To achieve the above objectives, the specific implementation steps are as follows:

[0014] Step 1 begins by establishing a reasonable reference flight trajectory for the electric vertical take-off and landing (eVTOL) vehicle, consisting of five phases: takeoff, ascent, cruise, descent, and landing. At each phase, specific target points are designed, along with the time intervals between adjacent waypoints, to create a complete flight path. The trajectory is then differentiated to obtain the position, velocity, and acceleration of the eVTOL at each point in flight. The eVTOL's attitude is also determined at specific locations, generating a reference value for the system's state while tracking along the established trajectory.

[0015] Step 2: In order to accurately describe the state changes of the system during flight, in addition to clarifying the position and attitude [xyzΦθψ] of the eVTOL in the inertial coordinate system during flight, T To establish the unique state information, the linear velocity and angular velocity measured by the sensor group in the fuselage coordinate system [uvwpqr] T Also used as a state variable to describe its own attitude; for the quadrotor mode, the speed of the four propellers [Ω1Ω2Ω3Ω4] T As the system input, the eVTOL then tilts the forward propellers 1 and 2 as the power output in the fixed-wing mode when switching modes. Therefore, the speed of the two propellers needs to be combined with the deflection of the aileron and elevator [Ω1Ω2δ e δ e ] T As system input in fixed-wing mode;

[0016] Therefore, a six-degree-of-freedom aircraft model is established. The linear velocity information along the X, Y, and Z axes and the angular velocity information about the X, Y, and Z axes during flight are also introduced as described above. The final system state is expressed as [x yz φ θ ψ uvwpqr] T ; To establish the dynamic and kinematic equations, the inertial coordinate system E and the non-inertial coordinate system B are clearly defined. The coordinate system transformation is achieved by the rotation matrix R and the angle transformation matrix T;

[0017]

[0018] x, y, z, φ, θ, ψ represent the position coordinates of the eVTOL and the Euler angles of its attitude in the inertial coordinate system. These three angles are the pitch angle, roll angle, and yaw angle, respectively. u, v, w, p, q, r are the linear velocities along the X, Y, and Z axes and the angular velocities around the X, Y, and Z axes in the non-inertial coordinate system collected by the sensor group; the linear velocity and angular velocity information measured by the sensor group in the non-inertial coordinate system are converted to the inertial coordinate system by multiplying the rotation matrix on the left;

[0019]

[0020] The global dynamics equation is described as:

[0021]

[0022] F and M are the net external force and torque on the eVTOL during flight, respectively; m is the mass of the eVTOL; is the linear acceleration vector in the inertial coordinate system; Represents the angular acceleration vector in the inertial coordinate system; v = [uvw] TAnd ω=[p qr] T ; ω×v and ω×(Iω) both represent vector cross product operations; I is a 3×3 inertia matrix, representing the moment of inertia of the object around each axis;

[0023]

[0024] Among them, I xx , I yy and I zz is the principal inertia around the XY and Z axes; I xy =I yx , I xz =I zs and I yz =I zy is the product inertia;

[0025] Combined with aerodynamics, the eVTOL modes in the two modes are analyzed to establish dynamic and kinematic equations; thus, the forces and moments in the quadrotor mode are described;

[0026]

[0027] F Body =F Wing +F Fus +F HTail

[0028]

[0029] Where F is the total external force under rotor mode, which is composed of three parts; F Grav For the gravity part, it needs to be multiplied by the rotation matrix on the left to transform into the inertial coordinate system; F Aero The air resistance part includes the air resistance F generated by the lateral movement of the vertical tail. VTail , and the air resistance F generated by the entire eVTOL during longitudinal motion Body ; F Body It consists of three parts, including the wing part F Wing 、Body part F Fus and horizontal tail section F HTail ; m is the mass of the eVTOL; g is the local acceleration of gravity; θ, Φ are the roll angle and pitch angle in the inertial coordinate system respectively; v, w are the linear velocities along the Y and Z axes; ρ is the air density; S VTail is the projected area of ​​the vertical tail in the XZ plane; is the drag coefficient of the vertical tail; S Wing is the projected area of ​​the wing on the horizontal plane; is the drag coefficient of the wing; S Fus is the projected area of ​​the fuselage on the horizontal plane; is the drag coefficient of the fuselage; S HTail is the projected area of ​​the horizontal tail on the horizontal plane; is the drag coefficient of the horizontal tail; U1 is the lift generated by the rotation of the four propellers; U2, U3, and U4 are the torques generated by the eVTOL rotating around the XYZ axes; b is the lift coefficient; d is the drag coefficient; l is the distance between the centers of adjacent propellers; Ω (·) Indicates the rotational speed of the four propellers, which serves as the control input in rotor mode;

[0030] Then describe the forces and moments in fixed-wing mode;

[0031] F Grav =mg[-sinθ cosθsinφ cosθcosφ] T

[0032]

[0033]

[0034] Where F Grav Same as rotor mode; F Prop The power generated by the propeller after tilting; F Aero is the aerodynamic force generated in fixed-wing mode; ρ is the air density; V Air is the relative air speed; S is the projected area of ​​the entire aircraft on the XY plane; α is the angle of attack; β is the sideslip angle; C D , C Y , C L are the drag, lateral force and lift coefficients respectively; u, v, w are the linear velocities along the X, Y and Z axes respectively collected by the sensor group; p, q, r are the angular velocities around the X, Y and Z axes respectively collected by the sensor group; is the zero lift drag coefficient, that is, the drag coefficient in the absence of lift; It is the additional drag coefficient which is proportional to the square of the lift coefficient and is related to the aspect ratio and aerodynamic efficiency of the aircraft; is the zero lift side force coefficient; is the influence coefficient of sideslip angle on side force coefficient; is the influence coefficient of aileron deflection angle on the side force coefficient; is the influence coefficient of the angle of attack on the lift coefficient; is the influence coefficient of elevator deflection angle on lift coefficient; δ a , δ e Respectively represent the aileron and elevator deflection, and together with the speed of propellers 1 and 2, serve as the control input in fixed-wing mode; L a is the wingspan; L0 is the mean aerodynamic chord; C l , Cm , C n are the roll, pitch and yaw moment coefficients respectively; is the initial rolling moment coefficient; is the influence coefficient of sideslip angle on rolling moment; C lp is the coefficient of influence of roll rate on roll moment; C lr is the influence coefficient of yaw rate on rolling moment; is the coefficient of influence of aileron deflection angle on rolling moment; is the initial pitching moment coefficient; is the influence coefficient of the attack angle on the pitching moment; C mq is the influence coefficient of pitch rate on pitch moment; is the influence coefficient of the elevator deflection angle on the pitching moment; is the initial yaw moment coefficient; is the influence coefficient of sideslip angle on yaw moment; C np is the coefficient of influence of roll rate on yaw moment; C nr is the influence coefficient of yaw rate on yaw moment;

[0035] Step 3: Based on the objective conditions during flight, establish a maintenance model for dual-mode stable flight and a model for inter-mode transition.

[0036] eVTOLs have multiple modes during mode transitions, including stable ascent and descent, cruise hold mode, ascent transition mode when transitioning from rotor to fixed wing, and descent mode when transitioning from fixed wing to rotor. eVTOLs must maintain stability during ascent and descent, and maintain a high speed during cruise.

[0037] Combined with the state space model at the equilibrium point, the dynamics can be described by a switching system. The sampling period Ts is set, and each mode is discretized to obtain a discrete switching system model when the eVTOL mode switches.

[0038] Determine the modal dependent state constraint set and input constraint set for different models;

[0039] In order to keep the eVTOL stable during flight, it is necessary to determine the state of each mode and constrain it. Whether it is vertical take-off and landing or horizontal cruising, it is not desirable for its attitude to change significantly. Therefore, the attitude has the same constraints in both modes. In order to make the transition process smoother, the system state is constrained in the same way. Therefore, in different modes, They have the same state constraints To ensure stable attitude during flight;

[0040] But for different modes The power composition of eVTOL has changed significantly. The input control constraints have changed from the four propeller speeds in quadrotor mode to the two propeller speeds and two rudder deflections in fixed-wing mode, resulting in different input constraints.

[0041] For different flight modes, set each modal equilibrium point and the input u of the equilibrium point to 0;

[0042] Then, based on the actual situation during the eVTOL transition process, the switching conditions between the dual modes are established and the multimodal switching diagram is determined;

[0043] Two common constraints on switching sequences are dwell time limits and mode transition limits;

[0044] When the eVTOL mode is switched, it indicates the mode The dwell time of the switching sequence Minimum time to stay in the mode; limiting the dwell time means that only The residence time is at least d i The resulting σ switching sequence; the unrestricted case is a special case of the constrained case, for each mode d i = 1; the properties of the discrete switching system depend on the remaining dwell time, which will be represented by δ(t), where

[0045]

[0046] Another common constraint on the switching sequence σ is a restriction on the acceptable mode transitions; the allowed mode transitions are given by the directed graph Specify where the graph nodes is the total mode of the discrete switching system, each directed edge Indicates that the mode σ(τ s )=i switches to mode σ(τ s+1 )=j.

[0047] Step 4: Based on the cost function of the state deviation and propeller input energy consumption involved in the rotor mode and the cost function of the state deviation, propeller input energy consumption and rudder deflection amplitude designed for the fixed-wing mode, the optimization objectives to be achieved in the two modes are obtained respectively;

[0048] In order to ensure the rapid and stable transition of eVTOL, minimum tracking error, minimum energy consumption and other goals, a target optimization model is constructed.

[0049] Where: x 0|t =x(t) is the current state of the system; σ 0|t is the current mode of the system; x k|tThe system controls the input u k|t Under the action of the prediction range N≥d i The predicted state; terminal cost P σ(0|t) (·) and the stage cost will be selected according to the optimization goal;

[0050] Combining the system dynamics and constraints, the following constrained finite-time optimal control problem is established:

[0051]

[0052] Among them: J σ(0|t) is the cost function of the current mode; Q σ(0|t) is the system state matrix; R σ(0|t) Input matrix for system control; and are the state constraints and input constraints of the current mode; is the terminal constraint of the current mode; δ 0|t is the remaining dwell time of the current mode;

[0053] To ensure the feasibility of switching model predictive control, there must be a control law k(x,σ,δ) to ensure that for all moments and the allowed switching order σ∈∑, state constraints and input constraints To satisfy the requirement, it is necessary to ensure that the initial state x(t0), modal σ(t0), and remaining residence time δ(t0) of the model predictive control are in the initial operating state set composed of the partial switching robust control invariant set;

[0054] Step 5: Based on the standard control invariant set algorithm, calculate the maximum switching robust control invariant set:

[0055] Input: each modal information of the discrete switching system as well as state constraints and input constraints;

[0056] Output: Maximum switching robust control invariant set;

[0057] First, the switching robust control invariant set Initialize and use the outer approximation method to give each mode The initial set and

[0058] Then, update the set of each modality The pre-operator satisfies During the iteration, just by removing the state To improve the estimation set There is no guarantee that the system will be in a modal The system state is always in the collection when running under and cannot be guaranteed to be in the modal When the system state is running under the state of the dwell time d j arrive To this end, by designing the collection With the preceding collection and Intersection is used to ensure that the switching robust control invariant set is robust to mode switching;

[0059] Design stop condition when When , the iteration stops, otherwise the iteration process is repeated;

[0060] Finally, the invariant condition for the maximum switching robust control of discrete switched systems is obtained That is, the initial running state set is obtained;

[0061] Step 6: Solve the finite-time optimal problem and obtain the eVTOL transition control variable;

[0062] Set the reference state during eVTOL flight;

[0063] Obtain the system state collected by the sensor group and the current operating mode; ensure that the initial state is in the switching robust control invariant set and meets the feasibility conditions;

[0064] Step 7: Solve the constrained finite-time optimal control problem based on the current state and its operating mode to obtain the optimal open-loop input sequence for model predictive control

[0065] Enter the first term of the optimal open loop into the sequence As the corrected quantity of the control obstacle function controller, At the same time, according to the system status x of eVTOL k|t , the action instruction u of the control quantity obtained by solving the optimal control problem rl(t) Make corrections to meet the safety guarantee and output the corrected control instruction u cbf(t) ;

[0066] Update the eVTOL operating state and mode. If the mode remains unchanged, update the target optimization model state and shorten the remaining residence time in the terminal constraint until δ 0|t =0; if the mode switches, the target optimization model is replaced and the remaining residence time of the current mode is set; the updated constrained finite-time optimal control problem is solved, and the rolling optimization is stopped until the state enters the terminal set.

[0067] 3. The present invention provides a method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC, which has the following advancements and advantages over the prior art:

[0068] (1) Based on the multiple modal characteristics of the eVTOL at different stages of transition, dynamic models under two flight modes are established. The state constraints under complex flight environments and the different input constraints that need to be considered before and after mode switching due to changes in power composition are considered for each mode, and the operational correlation between different modes is established through the switching strategy. This modeling method can effectively improve the accuracy of the modeling while avoiding the problem of over-complexity of traditional single modeling methods;

[0069] (2) An invariant set for switching robust control is established. This invariant set calculation method designed through multi-vertex constraints can ensure that there is always a feasible control sequence when the system switches between different modes. Therefore, as long as the initial state of the system meets the conditions of the initial invariant set, the recursive feasibility of the designed switching model predictive control will always be guaranteed;

[0070] (3) Designed flight safety constraints. Based on the control obstacle function, safety constraints were designed to ensure that the aircraft always maintains a stable attitude during mode switching, avoiding excessive jitter or even system instability. These constraints help monitor the aircraft's system status in real time and prevent unsafe flight attitudes. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a flow chart of the switching model prediction control provided by the present invention;

[0072] Figure 2 is a schematic diagram of different stages of quadrotor and cruise eVTOL flight provided by the present invention;

[0073] Figure 3 Schematic diagram of the corresponding relationship between the propellers in the quadrotor mode provided by the present invention;

[0074] Figure 4 This is a schematic diagram of the corresponding relationship between the propeller and the rudder in the fixed-wing mode provided by the present invention;

[0075] Figure 5 This is a schematic diagram of eVTOL mode switching provided by the present invention;

[0076] Figure 6 This is a simulation diagram of the eVTOL flight trajectory and the reference trajectory provided by the present invention; DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be 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.

[0078] On the contrary, the present invention covers any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention as defined by the claims. Furthermore, to facilitate a better understanding of the present invention, certain specific details are described in detail below in the detailed description of the present invention. Those skilled in the art will be able to fully understand the present invention without these details.

[0079] Example

[0080] Step 1: Set a reasonable reference flight trajectory for eVTOL, including five stages: takeoff, ascent, cruise, descent and landing, such as Figure 2 As shown in the figure, a specific target point is designed for each stage, and the time interval between adjacent waypoints is specified. The waypointTrajector() function in MATLAB is called to create a complete flight path. The lookupPose() function is then called to solve the position, velocity, acceleration, and pose of the eVTOL at each time point during the flight process, and to generate a reference value for the system state when tracking along the established trajectory.

[0081] Step 2: Determine the position and attitude of the eVTOL in the inertial coordinate system during flight [xyzΦθψ] T To establish a unique state information, and at the same time clarify the linear velocity and angular velocity measured by the sensor group in the fuselage coordinate system [uvwpqr] T As a state variable to describe its own posture;

[0082] S1: For quadrotor mode, set the speed of the four propellers to [Ω1Ω2Ω3Ω4] T As the system input, the eVTOL then tilts the forward propellers 1 and 2 as the power output in the fixed-wing mode when switching modes, and the speed of the two propellers is combined with the deflection of the aileron and elevator [Ω1Ω2δ a δ e ] T As system input in fixed-wing mode;

[0083] Establish a six-degree-of-freedom aircraft model, introduce linear velocity information and angular velocity information, and express the final system state as [xyz φ θ ψ uvwpqr] T ; Clearly define the inertial coordinate system E and the non-inertial coordinate system B. The coordinate system transformation is achieved by the rotation matrix R and the angle transformation matrix T;

[0084]

[0085] x, y, z, φ, θ, ψ represent the position coordinates of the eVTOL and the Euler angles of its attitude in the inertial coordinate system. These three angles are the pitch angle, roll angle, and yaw angle, respectively. u, v, w, p, q, r are the linear velocities along the X, Y, and Z axes and the angular velocities around the X, Y, and Z axes in the non-inertial coordinate system collected by the sensor group; the linear velocity and angular velocity information measured by the sensor group in the non-inertial coordinate system are converted to the inertial coordinate system by multiplying the rotation matrix on the left;

[0086]

[0087] The global dynamics equation is described as:

[0088]

[0089] F and M are the net external force and torque on the eVTOL during flight, respectively; m is the mass of the eVTOL; is the linear acceleration vector in the inertial coordinate system; Represents the angular acceleration vector in the inertial coordinate system; v = [uvw] T And ω=[pqr] T ; ω×v and ω×(Iω) both represent vector cross product operations; I is a 3×3 inertia matrix, representing the moment of inertia of the object around each axis;

[0090]

[0091] Among them, I xx , I yy and I zz is the principal inertia of the eVTOL around the X, Y, and Z axes; I xy =I yx , I zx =I zx and I yz =I zy is the product of inertia;

[0092] Combined with aerodynamics, the eVTOL modes in the two modes are analyzed to establish dynamic and kinematic equations; then the forces and torques in the quadrotor mode are described. The corresponding relationships of each rotor are as follows: Figure 3 As shown;

[0093]

[0094] F Body =F Wing +F Fus +F HTail

[0095]

[0096] The meaning of the unknown quantity in the formula is consistent with the above description;

[0097] Clarify the forces and moments in fixed-wing mode, and the corresponding relationship between the rotor and the control surface is as follows Figure 4 As shown;

[0098] F Grav =mg[-sinθ cosθsinφ cosθcosφ] T

[0099]

[0100]

[0101] The meaning of the unknown quantity in the formula is also consistent with the above description;

[0102] Clarify the state update equation where x k is the system state at time k; is the state derivative solved by the above dynamic and kinematic equations at time k; T s is the sampling period;

[0103] S2: Based on the objective conditions during flight, establish a maintenance model for dual-mode stable flight and a model for inter-modal transition;

[0104] eVTOLs have multiple modes during mode transitions, including stable ascent and descent, cruise hold mode, ascent transition mode when transitioning from rotor to fixed wing, and descent mode when transitioning from fixed wing to rotor. eVTOLs must maintain stability during ascent and descent, and maintain a high speed during cruise.

[0105] According to the above process, eVTOL has five modes during flight, among which modes 1 and 5 are the lift and drop in quadrotor mode, modes 2 and 4 are the transition modes from rotor mode to fixed wing and from fixed wing to rotor mode, respectively, and mode 3 is the cruise mode when completing the fixed wing mode.

[0106] Therefore, the mode switching dynamics can be described by the switching system

[0107]

[0108] where the system state x = [xyzΦθψuvwpqr] T , the system input in quadrotor mode is [Ω1Ω2Ω3Ω4] T , in fixed-wing mode, [Ω1Ω2δ a δ e ] T ,σ:t→I={1,2,3,4,5} represents the signal of different mode switching;

[0109] Set the sampling period T s =0.2s, for each mode discretization, the discrete switching system model is obtained:

[0110] x(k+1)=Q σ(k) x(k)+R σ(k) u(k)

[0111] in

[0112] S3: Determine the modal dependency state constraint set and input constraint set for different models;

[0113] In order to keep the eVTOL stable during flight, it is necessary to determine the state of each mode and constrain it. The same constraints are imposed on the attitude in both modes. In order to make the transition process smoother, the same constraints are imposed on the system state. They have the same state constraints To ensure stable attitude during flight;

[0114] For different modes The power composition of eVTOL has changed significantly. The input control constraints have changed from the four propeller speeds in the quadrotor mode to the two propeller speeds and the deflection of the two rudders in the fixed-wing mode. The same input constraints apply to rotor mode. Same constraints as for bimodal conversion

[0115] S4: For different flight modes, set each modal equilibrium point and the equilibrium point input u=0;

[0116] Then, based on the actual situation during the eVTOL transition process, the switching conditions between the two modes are established and the dual-mode switching process is determined;

[0117] Two common constraints on switching sequences are dwell time limits and mode transition limits;

[0118] When the eVTOL mode is switched, it indicates the mode The dwell time of the switching sequence The minimum time to stay in this mode is expressed as

[0119] The switching sequence is a discrete time series at which the system mode switches σ(t s )≠σ(t s -1);

[0120] Limiting the dwell time means that only the The residence time is at least d i The resulting σ switching sequence; the unrestricted case is a special case of the constrained case, for each mode d i = 1; the properties of the discrete switching system depend on the remaining dwell time, denoted by δ(t), where

[0121]

[0122] Another common constraint on the switching sequence σ is a restriction on the acceptable mode transitions; the allowed mode transitions are given by the directed graph Specify where the graph nodes is the total mode of the discrete switching system, each directed edge Indicates that the mode σ(τ s )=i switches to mode σ(τ s+1 )=j. The unrestricted case is a special case of the constrained case, where the mode transition diagram is a complete graph.

[0123] The set of switching sequences σ that satisfy the dwell time and mode transition constraints is described by the following interference set:

[0124]

[0125] In this example, based on the actual situation of eVTOL mode switching, it is considered to allow mode switching. Figure 5 As shown, given the switching diagram The vertex set of the graph Represents five flight modes, and its edge set represents all switching paths.

[0126] First, when the eVTOL needs to switch to cruise in rotor mode i=1 for vertical ascent, it needs to increase the cruise speed 0 to a certain value, and at the same time, the take-off and landing speed gradually decreases to 0, that is, switch from the take-off mode i=1 to the transition mode from rotor to fixed wing i=2; then, switch from the transition mode i=2 to the fixed wing cruise mode i=3 to complete the long-distance flight mission; when landing, return to the rotor mode through a similar switching process, that is, switch from i=3 to i=4 and then from i=4 to i=5; without loss of generality, each mode of the vehicle changing lanes maintains at least τ a seconds, so the mode i=2,4 of the switching system satisfies the minimum dwell time τ≥τ a , while other modes have no restrictions;

[0127] Step 4: Design a mode switching control method for electric vertical take-off and landing aircraft based on switching model predictive control, such as Figure 1 As shown;

[0128] S5: Based on the cost function of the state deviation and propeller input energy consumption involved in the rotor mode and the cost function of the state deviation, propeller input energy consumption and rudder deflection amplitude designed in the fixed-wing mode, the optimization objectives to be achieved in the two modes are obtained respectively;

[0129] In order to ensure the rapid and stable transition of eVTOL, minimum tracking error, minimum energy consumption and other goals, a target optimization model is constructed. where x 0| t = x(t) is the current state of the system; σ 0| t is the current mode of the system; x k|t The system controls the input u k|t The prediction range under the action N≥d i The predicted state; terminal cost P σ(0|t) (·) and the stage cost will be selected according to the optimization goal;

[0130] Combining the system dynamics and constraints, the following constrained finite-time optimal control problem is established:

[0131]

[0132] stx k+1|t =Q σ(0|t) x k|t +R σ(0|t) u k|t

[0133]

[0134] Among them J σ(0|t) is the cost function of the current mode; Q σ(0|t) is the system state matrix; R σ(0|t) Input matrix for system control; and are the state constraints and input constraints of the current mode; is the terminal constraint of the current mode; δ 0| t is the remaining dwell time of the current mode;

[0135] S6: Based on the obtained switching system model, the maximum switching positive invariant set is calculated to ensure the feasibility of switching model predictive control;

[0136] To ensure the feasibility of switching model predictive control, there exists a control law κ(x,σ,δ) that guarantees that for all moments and the allowed switching order σ∈∑, state constraints and input constraints To satisfy the requirement, it is necessary to ensure that the initial state x(t0), modal σ(t0), and remaining residence time δ(t0) of the model predictive control are in the initial operating state set composed of the partial switching robust control invariant set;

[0137] Based on the standard control invariant set algorithm, the maximum switching robust control invariant set is calculated:

[0138] First, the switching robust control invariant set Initialize and use the outer approximation method to give each mode The initial set and

[0139] Then, update the set of each modality The pre-operator satisfies During the iteration, just by removing the state To improve the estimation set There is no guarantee that the system will be in a modal The system state is always in the collection when running under and cannot be guaranteed to be in the modal When the system state is running under the state of the dwell time d j arrive To this end, by designing the collection With the preceding collection and Intersection is used to ensure that the switching robust control invariant set is robust to mode switching;

[0140] Design stop condition when When , the iteration stops, otherwise the iteration process is repeated;

[0141] Finally, the invariant condition for the maximum switching robust control of discrete switched systems is obtained That is, the initial running state set is obtained;

[0142] Step 6: Solve the finite-time optimal problem and obtain the eVTOL transition control variable;

[0143] S7: Setting the reference state during eVTOL flight;

[0144] Obtain the system state collected by the sensor group and the current operating mode; ensure that the initial state is in the switching robust control invariant set and meets the feasibility conditions;

[0145] According to the current state and its operating mode, solve the constrained finite time optimal control problem and obtain the optimal open-loop input sequence of the model predictive control

[0146] Enter the first term of the optimal open loop into the sequence As the corrected quantity of the control obstacle function controller, At the same time, according to the system status x of eVTOL k|t , the action instruction u of the control quantity obtained by solving the optimal control problem rl(t) Make corrections to meet the safety guarantee and output the corrected control instruction u cbf(t) ;

[0147] In the obstacle control function sub-controller, angular velocity safety conditions are set and constraints are used to stabilize the eVTOL's attitude within a fixed range.

[0148] Specifically, the safety condition is: the range of p, q, r is between [-ε, ε], and the corresponding boundary function h is:

[0149] h1=p+ε

[0150] h2=-p+ε

[0151] h3=q+ε

[0152] h4=-q+ε

[0153] h5=r+ε

[0154] h6=-r+ε

[0155] The first and second order differentials of the boundary function are determined by the dynamic and kinematic equations; in this example, the constraints controlling the obstacle function subcontroller are limited to:

[0156]

[0157] Thus, the final representation of the control obstacle function sub-controller is obtained:

[0158] min|u cbf(t) -u rl(t) |

[0159]

[0160] Where h ( · ) represents the boundary function; Respectively represent the first-order differential and second-order differential of the boundary function; where α 11 ,α 10 ,α 21 ,α 20 ,α 31 ,α 30 ,α 41 ,α 40 ,α 51 ,α 50 ,α61 ,α 60 are parameters, each parameter satisfies: F b -G b α belongs to the Hurwitz matrix; where α∈[α 11 ,α 10 ,α 21 ,α 20 ,α 31 ,α 30 ,α 41 ,α 40 ,α 51 ,α 50 ,α 61 ,α 60 ];

[0161]

[0162] S8: Update the eVTOL operating state and mode according to the corrected control input. If the mode remains unchanged, update the target optimization model state and shorten the remaining residence time in the terminal constraint until δ 0| t=0; if the mode is switched, the target optimization model is replaced and the remaining dwell time of the current mode is set;

[0163] Solve the updated constrained finite-time optimal control problem and perform rolling optimization until the state enters the terminal set, at which point the rolling optimization is stopped.

[0164] Figure 6 The target trajectory and actual flight trajectory of eVTOL are shown in the figure. It can be seen from the figure that the algorithm can significantly improve the tracking accuracy of the flight trajectory in the flight control of eVTOL. After calculation, in the fixed flight mode, the eVTOL can maintain the position error close to zero, ensuring the accurate tracking of the flight trajectory. However, the mode switching will cause a large position error. The position error increases rapidly to ±0.5 meters at the moment of switching from rotor mode to fixed-wing mode. In a short time after the switch, the error decreases rapidly from ±0.5 meters to close to zero. The algorithm can effectively reduce the instantaneous error generated during mode switching and quickly restore the error to the minimum value, thereby achieving smooth and accurate mode switching. It can be seen that the present invention realizes stability control during eVTOL mode switching.

Claims

1. A method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC, characterized in that: The following steps are involved: Step 1: Set a reasonable reference flight trajectory for the electric vertical take-off and landing vehicle (eVTOL), including five phases: takeoff, ascent, cruise, descent, and landing. Create a flight path by designing corresponding target points based on different flight modes and specifying the time required to reach adjacent waypoints. Derivative the trajectory to obtain the position, velocity, and acceleration of the eVTOL at each time point during flight. Also, determine its attitude at specific locations to generate a reference value for the system state when tracking along the established trajectory. Step 2: The position and attitude of the eVTOL in the inertial coordinate system during flight [xyz Φ θ ψ] T As a state variable to describe the unique attitude in the coordinate system during flight, the linear velocity and angular velocity [uvwpqr] measured by the sensor group in the fuselage coordinate system are T Also used as a state variable to describe its own posture; the speed of the four propellers in the quadrotor mode [Ω1 Ω2 Ω3 Ω4] T As the system input, the No. 1 and No. 2 propellers tilted forward during the transition are used as the power output in the fixed-wing mode. The speed of the two propellers is correlated with the deflection of the aileron and elevator [Ω1 Ω2 δ a δ e ] T As system input; combined with aerodynamics, the eVTOL modal analysis in the two modes is carried out to establish the dynamic and kinematic equations; and then the trajectory tracking state space model at equilibrium is established; Step 3: According to the objective conditions during the flight, establish the dual-mode stable flight maintenance model and the model during the transition between modes, that is, determine its mode-dependent state constraint set and input constraint set; in different modes i∈II, it has the same state constraint To ensure attitude stability and different input constraints u during flight; then, according to the actual situation during the eVTOL transition process, establish the switching conditions between the two modes and determine the multi-modal switching diagram; Step 4: Based on the cost function of the state deviation and propeller input energy consumption involved in the rotor mode and the cost function of the state deviation, propeller input energy consumption and rudder deflection amplitude designed in the fixed-wing mode, the optimization objectives to be achieved in the two modes are obtained respectively; construct the target optimization model Step 5: Based on the established switching system model, calculate the maximum switching positive invariant set to ensure the feasibility of switching model predictive control; calculate the maximum switching robust control invariant set based on the standard control invariant set algorithm; Step 6: Solve the finite-time optimal problem and obtain the eVTOL transition control variable; Set the reference state during eVTOL flight; obtain the system state collected by the sensor group and the current operating mode; Ensure that the initial state is in the switching robust control invariant set and meets the feasibility conditions; Step 7: Solve the constrained finite-time optimal control problem based on the current state and its operating mode to obtain the optimal open-loop input sequence for model predictive control Enter the first term of the optimal open loop into the sequence As the corrected quantity of the control obstacle function controller, At the same time, according to the system status x of eVTOL k|t , the action instruction u of the control quantity obtained by solving the optimal control problem rl(t) Make corrections to meet the safety guarantee and output the corrected control instruction u cbf(t) ; Update the eVTOL operating state and mode. If the mode remains unchanged, update the target optimization model state and shorten the remaining residence time in the terminal constraint until δ 0|t = 0; if the mode switches, the target optimization model is replaced and the remaining residence time of the current mode is set; the updated constrained finite time optimal control problem is solved, and the rolling optimization is stopped until the state enters the terminal set; Its characteristics are: The constructed target optimization model Where: x 0|t =x(t) is the current state of the system; σ 0|t is the current mode of the system; x k|t The system controls the input u k|t Under the action of the prediction range N≥d i The predicted state; terminal cost P σ (0|t)(·) and the stage cost will be selected according to the optimization goal; Combining the system dynamics and constraints, the following constrained finite-time optimal control problem is established: Among them: J σ(0|t) is the cost function of the current mode; Q σ(0|t) is the system state matrix; P σ(0|t) Input matrix for system control; and are the state constraints and input constraints of the current mode; is the terminal constraint of the current mode; δ 0|t The remaining dwell time of the current mode.

2. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claim 1, characterized in that: A six-degree-of-freedom aircraft model is established, and the linear velocity and angular velocity states are introduced at the same time, so that the system state is expressed as [xy z φ θ ψ uvwpqr] T ; To establish the dynamic and kinematic equations, the inertial coordinate system E and the non-inertial coordinate system B are clearly defined. The coordinate system transformation is achieved by the rotation matrix R and the angle transformation matrix T; x, y, z, φ, θ, ψ are the position and pitch, roll, and yaw angles in the inertial coordinate system, respectively; u, v, w, p, q, r are the linear velocities along the X, Y, and Z axes and the angular velocities around the X, Y, and Z axes in the non-inertial coordinate system, respectively; the linear and angular velocity information measured by the sensor group in the non-inertial coordinate system is converted to the inertial coordinate system by multiplying the rotation matrix on the left; The kinetic equation is described as: F and M are the net external force and torque on the eVTOL during flight, respectively; m is the mass of the eVTOL; is the linear acceleration vector in the inertial coordinate system; Represents the angular acceleration vector in the inertial coordinate system; v = [uvw] T And ω=[pqr] T ; ω×v and ω×(Iω) both represent vector cross product operations; I is a 3×3 inertia matrix, representing the moment of inertia of the object around each axis; Among them, I xx , I yy and I zz is the principal inertia around the XY and Z axes; I xy =I yx , I xz =I zx and I yz =I zy is the product of inertia.

3. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claims 1 and 2, characterized in that: The description of the forces and torques in quadrotor mode is: F Body＝ F Wing +F Fus +F HTail Where F is the total external force under the rotor mode, which is composed of three parts; F Grav For the gravity part, it needs to be multiplied by the rotation matrix on the left to transform into the inertial coordinate system; F Aero The air resistance part includes the air resistance F generated by the lateral movement of the vertical tail. VTail , and the air resistance F generated by the entire eVTOL during longitudinal motion Body ; F Body It consists of three parts, including the wing part F Wing 、Body part F Fus and horizontal tail section F HTail ; m is the mass of the eVTOL; g is the local acceleration of gravity; θ, Φ are the roll angle and pitch angle in the inertial coordinate system respectively; v, w are the linear velocities along the Y and Z axes; ρ is the air density; S VTail is the projected area of ​​the vertical tail in the XZ plane; is the drag coefficient of the vertical tail; S Wing is the projected area of ​​the wing on the horizontal plane; is the drag coefficient of the wing; S Fus is the projected area of ​​the fuselage on the horizontal plane; is the drag coefficient of the fuselage; S HTail is the projected area of ​​the horizontal tail on the horizontal plane; is the drag coefficient of the horizontal tail; U1 is the lift generated by the rotation of the four propellers; U2, U3, and U4 are the torques generated by the eVTOL rotating around the XYZ axes; b is the lift coefficient; d is the drag coefficient; l is the distance between the centers of adjacent propellers; Ω (·) Indicates the rotational speed of the four propellers, which serves as the control input in rotor mode.

4. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to any one of claims 1 and 2, characterized in that: The description of the forces and moments in fixed-wing mode is: F Grav =mg[-sinθ cosθsinΦ cosθcosΦ] T Where F Grav Same as rotor mode; F Prop The power generated by the propeller after tilting; F Aero is the aerodynamic force generated in fixed-wing mode; ρ is the air density; V Air is the relative air speed; S is the projected area of ​​the entire aircraft on the XY plane; α is the angle of attack; β is the sideslip angle; C D , C Y , C L are the drag, side force and lift coefficients respectively; u, v, w are the linear velocities along the X, Y, and Z axes respectively, as detected by the sensor group; p, q, r are the angular velocities around the X, Y, and Z axes respectively, as detected by the sensor group; is the zero lift drag coefficient, that is, the drag coefficient in the absence of lift; It is the additional drag coefficient which is proportional to the square of the lift coefficient and is related to the aspect ratio and aerodynamic efficiency of the aircraft; is the zero lift side force coefficient; is the influence coefficient of sideslip angle on side force coefficient; is the influence coefficient of aileron deflection angle on the side force coefficient; is the influence coefficient of the angle of attack on the lift coefficient; is the influence coefficient of elevator deflection angle on lift coefficient; δ a , δ e Respectively represent the aileron and elevator deflection, and together with the speed of propellers 1 and 2, serve as the control input in fixed-wing mode; L a is the wingspan; L0 is the mean aerodynamic chord; C l , C m , C n are the roll, pitch and yaw moment coefficients respectively; is the initial rolling moment coefficient; is the influence coefficient of sideslip angle on rolling moment; C lp is the coefficient of influence of roll rate on roll moment; C lr is the influence coefficient of yaw rate on rolling moment; is the coefficient of influence of aileron deflection angle on rolling moment; is the initial pitching moment coefficient; is the influence coefficient of the angle of attack on the pitching moment; C mq is the influence coefficient of pitch rate on pitch moment; is the influence coefficient of the elevator deflection angle on the pitching moment; is the initial yaw moment coefficient; C nβ is the influence coefficient of sideslip angle on yaw moment; C np is the coefficient of influence of roll rate on yaw moment; C nr is the influence coefficient of yaw rate on yaw moment.

5. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claim 1, characterized in that: eVTOLs have multiple modes during mode transitions, including stable ascent and descent, cruise hold modes, ascent transition modes when transitioning from rotor to fixed wing, and descent modes when transitioning from fixed wing to rotor. Stability must be maintained during ascent and descent, and a high speed must be maintained during cruise. Combined with the state-space model at the equilibrium point, the dynamics can be described by a switching system. The sampling period Ts is set, and each mode is discretized to obtain the discrete switching system model of the eVTOL mode switching.

6. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claim 1, characterized in that: Two common constraints on switching sequences are dwell time limits and mode transition limits; when an eVTOL mode switches, the dwell time of the mode is the switching sequence. The minimum time to stay in this mode; limiting the residence time means only considering each mode i∈Ⅱ with a residence time of at least d i The switching sequence of time instances σ; the unrestricted case is a special case of the constrained case, for each mode i∈II, d i = 1; the properties of the discrete switching system depend on the remaining dwell time, which will be represented by δ(t), where Another common constraint on the switching sequence σ is a restriction on the acceptable mode transitions; the allowed mode transitions are given by the directed graph Specify, where graph node II is the total mode of the discrete switching system and each directed edge Indicates that the mode σ(τ s )=i switches to mode σ(τ s+1 )=j.

7. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claim 1, characterized in that: To ensure the feasibility of switching model predictive control, there exists a control law κ(x, σ, δ) that guarantees that for all moments and the allowed switching order σ∈∑, state constraints and input constraints To satisfy this, it is necessary to ensure that the initial state x(t0), modal σ(t0), and residual residence time δ(t0) of the model predictive control are in the initial operating state set composed of the partial switching robust control invariant set.

8. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claim 1, characterized in that: The steps to calculate the maximum switching robust control invariant set are as follows: S1: Invariant set of switching robust control {C i } i∈II Initialize and use the external approximation method to give the initial set and S2: Update the collection of each modality The pre-operator satisfies During the iteration, just by removing the state To improve the estimation set There is no guarantee that the system state is always in the set when the system is running under mode i∈II And it cannot be guaranteed that the system state will pass the residence time d when running under mode j∈II j arrive To this end, by designing the collection With the preceding collection and Intersection is used to ensure that the switching robust control invariant set is robust to mode switching; the stopping condition is designed, when When , the iteration stops, otherwise the iteration process is repeated; S3: Obtain the invariant conditions for the maximum switching robust control of discrete switching systems That is, the initial operating state set of eVTOL is obtained.

9. The method for controlling mode switching of a vertical take-off and landing aircraft based on switching MPC according to claim 1, characterized in that: The safety condition is: the angular velocity range is between [-ε, ε]; Taking the roll angular velocity p as an example, the boundary functions are designed as h1 = p + ε and h2 = -p + ε; and their differentials are solved by the kinematic and dynamic equations. The same is true for the pitch and yaw angular velocities. The control obstacle function sub-controller is set to: where h (·) represents the boundary function; Respectively represent the first-order differential and second-order differential of the boundary function; where α 11 , α 10 , α 21 , α 20 , α 31 , α 30 , α 41 , α 40 , α 51 , α 50 , α 61 , α 60 are parameters, each parameter satisfies: F b -G b α belongs to the Hurwitz matrix; where α∈[α 11 , α 10 , α 21 , α 20 , α 31 , α 30 , α 41 , α 40 , α 51 , α 50 , α 61 , α 60 ] .

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