State feedback control method for longitudinal motion flight control system of tiltrotor

Abstract

The application discloses a state feedback control method of a longitudinal motion flight control system of a tilt rotor aircraft, considers the influence of time lag on the system, proposes a novel Lyapunov-Krasovskii functional, further reduces the conservativeness of a system stability criterion, and enlarges the stable operation area of the longitudinal motion flight control system of the tilt rotor aircraft. A state feedback controller is designed for the longitudinal motion flight control system of the tilt rotor aircraft with actuator saturation, a switching system model of multiple subsystems is established, and accurate and effective control of the tilt rotor aircraft is realized.

Description

Technical Field

[0001] This invention belongs to the field of aircraft control technology. Specifically, it designs a convex hull-based state feedback controller for the longitudinal motion flight control system of a tiltrotor aircraft. By constructing a novel Lyapunov-Krasovskii functional, a stability criterion with lower conservatism is obtained, thus expanding the system's stable operating region. Background Technology

[0002] Currently, heavier-than-air aircraft in the aviation field are divided into two categories: fixed-wing aircraft (airplanes, gliders) and rotorcraft (helicopters, autogyros). Fixed-wing aircraft have high speeds and long ranges, but their takeoff and landing conditions are limited, making them difficult to navigate complex terrains. Autogyros have very few restrictions on takeoff and landing conditions, but their disadvantages are also obvious: slower speeds and shorter ranges. Tiltrotor aircraft, as a new type of aircraft, combine the advantages of both rotorcraft and fixed-wing aircraft, and have promising prospects in various fields.

[0003] A tiltrotor aircraft possesses a pair of tiltable nacelles, allowing control of the rotor plane. When the nacelle tilt angle is fixed at 0°, the tiltrotor can perform low-speed flight and takeoff and landing in complex terrain, operating in rotorcraft mode. When the nacelle tilt angle is fixed at 90°, the tiltrotor can perform high-speed flight, operating in fixed-wing mode. Therefore, tiltrotor aircraft can perform the specialized tasks of rotorcraft as well as the transport tasks of fixed-wing aircraft, especially under extremely restrictive environmental conditions, such as transport and rescue in natural disaster areas.

[0004] Existing longitudinal motion flight feedback control methods for tiltrotor aircraft rarely consider the impact of actuator saturation and state delay on flight control. This results in inaccurate and effective control of the longitudinal motion of tiltrotor aircraft, leading to frequent flight malfunctions. Therefore, further research is needed to reduce the conservatism of system stability criteria and to achieve accurate and effective control of tiltrotor aircraft. Summary of the Invention

[0005] This invention takes into account the impact of time delay on the system and proposes a novel Lyapunov-Krasovskii functional to expand the stable operating range of the longitudinal motion flight control system of a tiltrotor aircraft. Specifically, it is a state feedback control method for the longitudinal motion flight control system of a tiltrotor aircraft.

[0006] This invention considers the influence of actuator saturation in the longitudinal motion flight control system of a tiltrotor aircraft and designs a state feedback controller based on the convex hull method. This invention establishes a dynamic model of the longitudinal motion flight control system of a tiltrotor aircraft with actuator saturation. Considering the characteristic that the state of the tiltrotor aircraft itself changes continuously with the nacelle tilt angle, this invention establishes a switching system model of multiple subsystems, achieving accurate and effective control of the tiltrotor aircraft.

[0007] This invention discloses a state feedback control method for a tiltrotor aircraft's longitudinal motion flight control system, the specific steps of which are as follows:

[0008] Step 1: Establish the longitudinal dynamics model of the tiltrotor aircraft;

[0009] Tiltrotor aircraft have a bilaterally symmetrical structure. Based on the condition of horizontal, sideslip-free flight, simplified to a longitudinal dynamic model, the entire external pod can tilt from 0° to 90° in the entire longitudinal plane. Assuming the fuselage and blades are rigid bodies; and assuming no other motion occurs during the transition, the product of inertia I... xy ,I zy The value is 0; the atmospheric density remains constant, and the compressibility of air and the interference of the rotor downwash on the fuselage are not considered.

[0010] Under the above assumptions, the longitudinal dynamic model of the tiltrotor aircraft is as follows:

[0011]

[0012] Where v, w, q, and θ represent the forward velocity, vertical velocity, pitch rate, and pitch angle, respectively. m is the mass of the aircraft, I y For pitch rotation inertia, F x F is the component of the net force acting on the body along the x-axis of the body. z M is the component of the net force acting on the body along the z-axis. y The pitching moment is generated by the resultant force. v0, w0, and g represent the initial forward velocity, initial vertical velocity, and gravitational acceleration, respectively.

[0013] Step 2: Establish the state-space model of the tiltrotor aircraft;

[0014] The aerodynamic characteristics of tiltrotor aircraft are

[0015]

[0016]

[0017] Aircraft torque characteristics are

[0018]

[0019] Nacelle Incline I n During the transition, it can change from 0° to 90°. As the nacelle inclination angle changes, I... y It will also change, and can be approximated by a linear formula as I. y =I y0 -KI n In the formula: X v X w X q , Z v Z w Z q , M is the aerodynamic coefficient. v M w M q , δ is the aerodynamic torque coefficient. c δ ε These are represented as collective pitch and elevator, respectively. y0 The initial moment of inertia is K = 11.24.

[0020] By selecting the state vector

[0021] X = [vwq θ] T ,

[0022] Obtain the state-space model

[0023]

[0024] where U=[δ c δ ε Matrix A and matrix B are shown below:

[0025]

[0026]

[0027] Because tiltrotor aircraft experience time delays and input saturation during the transition process,

[0028] Furthermore, the entire transition process is quite complex and difficult to describe clearly using a single state function. Therefore, the flight dynamics state-space model of the transition process needs to be modeled as a switching system in the following general form:

[0029]

[0030] Where: X(t) represents the state vector at time t, and U(t) represents the control input at time t. σ(t): [0,+∞)→M={1,2,...,M} represents the switching signal, and M represents the number of modes. A σ(t) Bσ(t) These are the tiltrotor nacelle tilt angles I and I. n The state matrix and control input matrix at different angles, C σ(t) It is a constant matrix with appropriate dimensions. sat(·) denotes the unit saturation function. It is a continuous initial function. The time-varying delay d(t) satisfies the following form:

[0031]

[0032] Among them, h1, h2 and d max It is a normal number.

[0033] Step 3: Lyapunov-Krasovskii functional design;

[0034] The Lyapunov-Krasovskii functional is designed as follows.

[0035] V σ(t) (t)=V 1σ(t) (t)+V 2σ(t) (t)+V 3σ(t) (t)+V 4σ(t) (t)+V 5σ(t) (t)

[0036] V 1σ(t) (t)=x T (t)P σ(t) x(t);

[0037]

[0038]

[0039]

[0040]

[0041] Where: P σ(t) Q 1σ(t) Q 2σ(t) D 1σ(t) D 2σ(t) R 1σ(t) R 2σ(t) Z σ(t) Indicates positive determination

[0042] A symmetric matrix, where α is a positive constant and h 12 =h2-h1.

[0043] Step 4: Design of the state feedback controller;

[0044] Design the following state feedback controller

[0045] U(t) = K σ(t) X(t)

[0046] K σ(t) It is the gain of the controller, and

[0047]

[0048] Where D j It is an m×m diagonal matrix, where all diagonal elements are either 0 or 1. I is the identity matrix, K σ(t) H σ(t) ∈R m×m symbol R m×m This represents an m×m dimensional real matrix.

[0049] Step 5: Establish the state-space model of the closed-loop system;

[0050] Substituting the designed state feedback controller into the state-space model of the flight dynamics of the transient process, the following closed-loop system state-space model is obtained.

[0051]

[0052] Further simplification yields the following closed-loop system state-space model.

[0053]

[0054] Step 6: Stability analysis of the closed-loop system;

[0055] V σ(t) The derivative of (t) with respect to time is

[0056]

[0057] Substituting the conditions of the linear matrix inequality, we can further obtain...

[0058]

[0059] In turn, one can obtain

[0060]

[0061] Where c and λ are positive constants, t0 is the initial time, and X(0) is any initial state. This demonstrates that the closed-loop system is exponentially stable.

[0062] This invention addresses the longitudinal motion flight control system of a tiltrotor aircraft with actuator saturation by designing a state feedback controller to avoid actuator saturation. By constructing a Lyapunov-Krasovskii functional with a triple integral term and fully utilizing the lower bound information of the time delay, a less conservative stability criterion is obtained, expanding the system's stable operating region. Given a lower bound of the time delay, this invention improves the maximum upper bound of the time delay that guarantees stable system operation. Detailed Implementation

[0063] A state feedback control method for the longitudinal motion flight control system of a tiltrotor aircraft, the method specifically includes the following steps:

[0064] Step 1: Establish the longitudinal dynamic model of the tiltrotor aircraft.

[0065] Tiltrotor aircraft have a bilaterally symmetrical structure. Based on the condition of horizontal, sideslip-free flight, simplified to a longitudinal dynamic model, the entire external pod can tilt from 0° to 90° in the entire longitudinal plane. Assuming the fuselage and blades are rigid bodies; and assuming no other motion occurs during the transition, the product of inertia I... xy ,I zy The value is 0; the atmospheric density remains constant, and the compressibility of air and the interference of the rotor downwash on the fuselage are not considered.

[0066] Under the above assumptions, the longitudinal dynamic model of the tiltrotor aircraft is as follows:

[0067]

[0068] Where v, w, q, and θ represent the forward velocity, vertical velocity, pitch rate, and pitch angle, respectively. m is the mass of the aircraft, I y For pitch rotation inertia, F x F is the component of the net force acting on the body along the x-axis of the body. z M is the component of the net force acting on the body along the z-axis. y The pitching moment is generated by the resultant force. v0, w0, and g represent the initial forward velocity, initial vertical velocity, and gravitational acceleration, respectively.

[0069] Step 2: Establish the state-space model of the tiltrotor aircraft

[0070] The aerodynamic characteristics of tiltrotor aircraft are

[0071]

[0072]

[0073] Aircraft torque characteristics are

[0074]

[0075] Nacelle Incline I n During the transition, it can change from 0° to 90°. As the nacelle inclination angle changes, I... y It will also change, and can be approximated by a linear formula as I. y =I y0 -KI n In the formula: X v X w X q , Z v Z w Z q , M is the aerodynamic coefficient. v M w M q , δ is the aerodynamic torque coefficient. c δ ε These are represented as collective pitch and elevator, respectively. y0 The initial moment of inertia is K = 11.24.

[0076] By selecting the state vector

[0077] X = [vwq θ] T ,

[0078] Obtain the state-space model

[0079]

[0080] where U=[δ c δ ε Matrix A and matrix B are shown below:

[0081]

[0082]

[0083] Because tiltrotor aircraft experience time delays and input saturation during the transition process,

[0084] Furthermore, the entire transition process is quite complex and difficult to describe clearly using a single state function. Therefore, the flight dynamics state-space model of the transition process needs to be modeled as a switching system in the following general form:

[0085]

[0086] Where: X(t) represents the state vector at time t, and U(t) represents the control input at time t. σ(t): [0,+∞)→M={1,2,...,M} represents the switching signal, and M represents the number of modes. A σ(t) B σ(t) These are the tiltrotor nacelle tilt angles I and I. n The state matrix and control input matrix at different angles, C σ(t) It is a constant matrix with appropriate dimensions. sat(·) denotes the unit saturation function. It is a continuous initial function. The time-varying delay d(t) satisfies the following form:

[0087]

[0088] Among them, h1, h2 and d max It is a normal number.

[0089] Step 3: Lyapunov-Krasovskii Functional Design

[0090] The Lyapunov-Krasovskii functional is designed as follows.

[0091] V σ(t) (t)=V 1σ(t) (t)+V 2σ(t) (t)+V 3σ(t) (t)+V 4σ(t) (t)+V 5σ(t) (t)

[0092] V 1σ(t) (t)=x T (t)P σ(t) x(t);

[0093]

[0094]

[0095]

[0096]

[0097] Where: P σ(t) Q 1σ(t) Q 2σ(t) D 1σ(t) D 2σ(t) R 1σ(t) R 2σ(t) Z σ(t) Let h denote a positive definite symmetric matrix, where α is a positive constant and h is a positive definite symmetric matrix. 12 =h2-h1.

[0098] Step 4: Design of the State Feedback Controller

[0099] Design the following state feedback controller

[0100] U(t) = K σ(t) X(t)

[0101] K σ(t) It is the gain of the controller, and

[0102]

[0103] Where D j It is an m×m diagonal matrix, where all diagonal elements are either 0 or 1. I is the identity matrix, K σ(t) H σ(t) ∈R m×m symbol R m×m This represents an m×m dimensional real matrix.

[0104] Step 5: Establish the state-space model of the closed-loop system.

[0105] Substituting the designed state feedback controller into the state-space model of the flight dynamics of the transient process, the following closed-loop system state-space model is obtained.

[0106]

[0107] Further simplification yields the following closed-loop system state-space model.

[0108]

[0109] Step 6: Stability analysis of the closed-loop system

[0110] V σ(t) The derivative of (t) with respect to time is

[0111]

[0112] Substituting the conditions of the linear matrix inequality, we can further obtain...

[0113]

[0114] In turn, one can obtain

[0115]

[0116] Where c and λ are positive constants, t0 is the initial time, and X(0) is any initial state. This demonstrates that the closed-loop system is exponentially stable.

Claims

1. A state feedback control method for the longitudinal motion flight control system of a tiltrotor aircraft, characterized in that: The method specifically includes the following steps: Step 1: Establish the longitudinal dynamic model of the tiltrotor aircraft; Step 2: Establish the state-space model of the tiltrotor aircraft; Step 3: Lyapunov-Krasovskii functional design; specifically: in: , , , , , , , Indicates positive determination Symmetric matrix For positive integers, , , It is a positive number; Step 4: Design of the state feedback controller; Design the following state feedback controller. It is the gain of the controller, and in yes A diagonal matrix, where all diagonal elements are either 0 or 1. , , , ; It is the identity matrix. ,symbol express 3D real matrix; Step 5: Establish the state-space model of the closed-loop system Substituting the designed state feedback controller into the state-space model of the flight dynamics of the transient process, the following closed-loop system state-space model is obtained. in, , These are the tiltrotor nacelle tilt angles. The state matrix and control input matrix at different angles, It is a constant matrix with appropriate dimensions; Represents a unit saturation function. It is a continuous initialization function; This represents the state vector at time t. This represents the control input at time t; Indicates a switching signal. Represents the number of modes; Further simplification yields the following closed-loop system state-space model. Step Six: Stability Analysis of the Closed-Loop System The derivative with respect to time is Substituting the conditions of the linear matrix inequality, we get... And thus obtain in and It is a positive number. It is the initial moment. It can be any initial state.

2. The state feedback control method for the longitudinal motion flight control system of a tiltrotor aircraft according to claim 1, characterized in that: The longitudinal dynamic model of the tiltrotor aircraft is established as follows: Tiltrotor aircraft have a bilaterally symmetrical structure. By simplifying the flight model to a longitudinal dynamic model under horizontal, sideslip-free flight conditions, the entire external pod can achieve zero speed across the entire longitudinal plane. ◦ ~90 ◦ The tilting; assuming the fuselage and propeller blades are rigid bodies; assuming no other motion occurs during the transition, therefore the product of inertia... , The value is 0; the atmospheric density remains constant, and the compressibility of air and the interference of the rotor downwash on the fuselage are not considered. Under the above assumptions, the longitudinal dynamic model of the tiltrotor aircraft is as follows: in, , , , , respectively, represent forward velocity, vertical velocity, pitch rate, and pitch angle; For the mass of the aircraft, For pitch rotation inertia, This represents the component of the net force acting on the organism along the x-axis. This represents the component of the net force acting on the organism along the z-axis. The pitching moment is the resultant force. , , These are represented as the initial forward velocity, the initial vertical velocity, and the gravitational acceleration, respectively.

3. The state feedback control method for the longitudinal motion flight control system of a tiltrotor aircraft according to claim 1, characterized in that: Establish the state-space model of the tiltrotor aircraft, specifically as follows: The aerodynamic characteristics of tiltrotor aircraft are Aircraft torque characteristics are Nacelle Incline From 0 during the transition process ◦ Convert to 90 ◦ As the nacelle inclination angle changes, It will also change, and can be approximated by a linear formula as follows: In the formula: , , , , , , , , , For aerodynamic coefficients, , , , , The aerodynamic torque coefficient, , These are represented as collective pitch and elevator, respectively. Let the initial moment of inertia be... ; By selecting the state vector Obtain the state-space model in Matrix A and matrix B are shown below: The flight dynamics state-space model of the transition process is modeled as a switching system in the following general form: Among them: time-varying time delay It meets the following form: in, , and It is a normal number.

Images