A guaranteed cost control method for aircraft with customized multi-index

Abstract

The present invention discloses a method for maintaining performance of aircraft for multi-index customization, and belongs to the field of aircraft descent control. The present invention constructs an aircraft dynamics model for controller design and obtains a tracking error dynamics model by subtracting the aircraft reference model designed artificially, and then realizes the constraint of the state quantity during the descent of the aircraft by designing a performance function with finite time constraints in the preset performance control, and designs the controller with the help of dynamic inverse control. With the help of online aerodynamic parameter identification, the controller is provided with real-time aerodynamic parameters of the aircraft, and at the same time, the extended state observer in the concept of self-disturbance rejection control is introduced to observe and compensate for the total disturbance of the system. The present invention designs the descent controller of the aircraft based on the requirements of multiple performance indicators, and comprehensively considers the problems such as complex environmental interference faced by the aircraft, effectively improving the control accuracy and robustness of the aircraft during the descent, and has long-term application prospects.

Description

Technical Field

[0001] The invention belongs to the field of aircraft descent control, and relates to a multi-index customized aircraft performance guaranteed control method. Background Art

[0002] Aircrafts have shown their irreplaceable multi-application status in today's society. With the increasing complexity of flight missions, the requirements for aircraft performance are also getting higher and higher, including challenges in speed, stability, accuracy, adaptability, etc. The continuous growth of this demand has greatly promoted the development of aircraft control system design, especially the controller design for engineering applicability indicators, to ensure that the aircraft can still perform tasks safely and efficiently in complex environments. The designed controller not only needs to meet the dynamic characteristics of the aircraft, but also needs to comprehensively consider the requirements of multiple performance indicators to achieve better control effects, and needs to have a certain anti-interference ability to external environmental disturbances, providing solid technical support for the widespread application and development of subsequent aircraft.

[0003] Considering that during the flight mission of an aircraft, the flight control system has extremely high requirements due to safety, stability and mission execution efficiency. Traditional control methods are difficult to meet the requirements of multiple performance indicators at the same time. Therefore, exploring and applying more advanced and efficient flight control technologies has become the key to improving the comprehensive performance of aircraft. Control methods based on advanced control theory can significantly improve the control performance of the control system, but they are basically limited to a single indicator requirement. For example, sliding mode control can significantly improve the robustness of the control system but will produce a certain overshoot phenomenon; backstepping control can make the system respond faster, but its controller design is complex and cannot guarantee the asymptotic convergence of parameter estimation to actual value. Therefore, it is necessary to design an aircraft control method that can meet the requirements of multiple performance indicators and realize an aircraft control method that can balance safety, stability, mission execution efficiency and controller design complexity.

[0004] Aircraft will be affected by complex environments during flight, which will not only change the real-time aerodynamic parameters of aircraft, but also directly affect the system control performance. When aerodynamic parameters are affected by external interference and show significant uncertainty fluctuations, high-precision attitude control will face huge challenges. Although advanced strategies such as sliding mode control and adaptive control can achieve high-precision control to a certain extent, they still rely on accurate aircraft models. In order to cope with complex and changing flight environments, higher requirements are placed on the anti-interference ability of the control system, that is, it is necessary to have stronger adaptability and robustness to effectively cope with the above challenges. In addition to improving the performance of the control system itself, the unknown disturbances can also be observed and compensated by designing observers to improve the system control performance.

[0005] Li Yu, Liu Xiaoxiong, Zhang Weiguo, et al. proposed an L1 adaptive dynamic inverse nonlinear fixed-wing aircraft flight control method based on an improved piecewise constant strategy in “A L1 adaptive dynamic inverse nonlinear fixed-wing aircraft flight control method” (CN202111536829). The conventional piecewise constant algorithm is improved by introducing enhancement factors and error information, and an adaptive law is constructed based on the improved piecewise constant algorithm; the tracking error is obtained according to the real-time angular velocity of the fixed-wing aircraft and the expected angular velocity output by the nonlinear reference model, and the influence caused by the sudden change of the center of gravity is solved by the adaptive law, and it is offset in the L1 adaptive dynamic inverse controller to ensure that the angular velocity response of the fixed-wing aircraft reaches the expected dynamics. However, L1 adaptive control has high requirements for aircraft system modeling, requires accurate system models and parameter estimation, and has high computational complexity, requiring a lot of computing resources and time.

[0006] In “Research on “Magic Carpet” Landing Technology for Carrier-Based Aircraft” (see Nanjing University of Aeronautics and Astronautics, 2020 Master’s Thesis, pages 49-61), Zhu Yulian proposed a landing control method based on the architecture of “magic carpet” landing and based on auto-disturbance rejection control. Auto-disturbance rejection control is used to resolve the contradiction between rapidity and overshoot in the classic PID, and the interference can be automatically observed and compensated. For carrier-based aircraft landing missions with many interference factors, the trajectory can be quickly and accurately corrected during the landing mission. However, this method does not comprehensively consider multiple performance indicators such as overshoot and rise time, and auto-disturbance rejection control will cause “peaking” due to the initial state error.

[0007] In “A method for determining the control strategy of a fixed-wing UAV based on reinforcement learning” (CN202410239788), Liu Hao, Liu Deyuan, Ren Ziming, etc. derived the expression of the Bellman equation and the optimal control strategy based on the augmented system and the value function, and then reconstructed the augmented system based on the policy iteration method in reinforcement learning, and then determined the policy iteration equation by combining the value function, the reconstructed augmented system, the Bellman equation and the expression of the optimal control strategy; the initial control strategy and the initial reference signal were applied within a predetermined time period, the tracking error was statistically calculated, and the initial control strategy and the tracking error were substituted into the policy iteration equation to solve the optimal strategy for fixed-wing UAV control. However, this method needs to interact with the environment, requires a lot of training time, and the control performance may be affected when the environment changes. At the same time, reinforcement learning is difficult to explain its decision-making process and behavior, which limits the reliability and acceptability of its application. Summary of the invention

[0008] In order to solve the above problems, the present invention proposes a multi-index customized aviation vehicle guaranteed performance control method. The tracking error dynamics model is obtained by constructing an aircraft model and a model that meets the requirements of multiple performance indicators. Then, the performance function with finite time constraints in the preset performance control is designed to realize the constraints on various state quantities during the descent of the aircraft, thereby improving the maneuverability control performance. Based on the idea of ​​the self-resistance control method, an extended state observer is designed to observe and compensate for unknown disturbances in the aircraft system, cope with the interference effects during the flight of the aircraft, and improve the robustness of the flight control system. Finally, the control law is designed through dynamic inverse control to reduce the complexity of the controller design.

[0009] The technical solution of the present invention is as follows:

[0010] A multi-index customized guaranteed performance control method for an aircraft includes the following steps:

[0011] Step (1) Establishing aircraft dynamics modeling for controller design

[0012] In order to clarify the flight state of the aircraft during the descent, the aircraft kinematics and dynamics model is expressed as follows:

[0013] (1)

[0014] Where: They are respectively the aircraft body in the body coordinate system Velocity components on three axes; They are the roll angular rate, yaw angular rate and pitch angular rate of the body axis system respectively; They are roll angle, pitch angle and yaw angle respectively; They are forward flight distance, flight altitude and lateral distance respectively; the superscript " ” denotes derivative; is the airspeed in the velocity coordinate system; Angle of attack; is the sideslip angle. is the maximum thrust of the aircraft engine; is the throttle opening; In the body coordinate system Aerodynamic force components on three axes; is the acceleration due to gravity; is the mass of the aircraft; Respectively represent the body on the body coordinate system The moment of inertia of the three axes, Represents the entire cross section of the body relative to the body coordinate system Axis and The moment of inertia of the axis; They represent rolling moment, yaw moment, and pitch moment respectively.

[0015] In order to meet the needs of subsequent controller design, the aircraft kinematics and dynamics in step (1) are processed to obtain the longitudinal model expression as shown below:

[0016] (2)

[0017] Where: are flight resistance and aircraft lift respectively, and the aerodynamic force / torque expression can be fitted as:

[0018] (3)

[0019] Where: is the atmospheric density; is the wing reference area; is the average starting chord length of the aircraft; for elevator and flap commands respectively; is the constant term of the drag coefficient; The coefficient relationships between drag and squared angle of attack, angle of attack, elevator and flap are respectively; is the lift coefficient constant term; They are the coefficient relationships of lift angle of attack, elevator and flap respectively; is the constant term of the pitching moment coefficient; They are the coefficient relationships between the pitch moment and the angle of attack, elevator and flap, respectively.

[0020] The present invention designs a controller for aircraft trajectory control. In addition to the above modeling, it is also necessary to build an aircraft state space model and select the aircraft pitch angle. and pitch rate As a state quantity, x = [ θ q ] T , the elevator is used as the control quantity, that is According to the small disturbance linearization equation, when the aircraft's glide path angle is small, the system state space expression is:

[0021] (4)

[0022] Where: ; .

[0023] In order to allow the control law to take into account the real-time flight status of the aircraft, the present invention uses the widely used recursive least squares technology to perform online identification of the aircraft. The recursive least squares algorithm can be expressed as:

[0024] (5)

[0025] Where: is the least squares estimate at the current moment; is the gain vector at the current moment; is the covariance matrix at the current moment; is the information vector formed by the observation data at the current moment; is the unit matrix; is an artificially set constant. This algorithm is used to calculate the pitch moment The various coefficients are identified, and then the system is provided with the real-time aerodynamic parameters of the aircraft for control law design to improve control accuracy.

[0026] Step (2) Establishing a reference model of the longitudinal channel of an aircraft

[0027] When an aircraft performs maneuvers to perform related flight missions, the tracking of target commands reflects the control performance of the controller. In order to achieve a controller that meets the index requirements, a second-order system with expected overshoot, rise time and stability margin is designed as a reference model, which is shown in the following form:

[0028] (6)

[0029] Where: is the Laplace operator; is the natural frequency; is the damping ratio; are the expected pitch angle command and the pitch angle output by the reference model respectively.

[0030] Based on the second-order system transfer function, the overshoot and rise time can be obtained:

[0031] (7)

[0032] (8)

[0033] According to the flight performance index requirements of aircraft, the natural frequency and damping ratio are designed to obtain a reference model that meets human requirements.

[0034] Step (3) Construction of model tracking error dynamics model

[0035] In order to distinguish the actual aircraft system from the artificially designed reference model system, the pitch angle response value is defined and the pitch rate response value As the reference model state quantity, x m = [ θ m q m ] T , expected pitch angle command As control input , we get the following reference model state space equation:

[0036] (9)

[0037] in: , .

[0038] By jointly constructing the system state space equation (4) and the reference model state space equation (9), the model tracking error dynamics model can be obtained as:

[0039] (10)

[0040] In the formula, are the actual aircraft system state quantities The state response of the reference model The tracking error between .

[0041] Step (4) Design of extended state observer for total disturbance observation compensation of the system

[0042] In addition to the influence of interference, modeling inaccuracy will also affect the control performance during the control process of aircraft. Therefore, it is necessary to observe and compensate for the system disturbance. The extended state observer in the self-disturbance rejection control can observe the object as an integral series link containing uncertain disturbances when the model of the controlled object is unknown. The expanded state in the observed signal is used to observe the uncertain disturbance, and its feedback is used as real-time compensation for the disturbance, so that the object is approximately an integral series link, eliminating its uncertainty and making the closed-loop control have a better control effect.

[0043] Based on the second-order system state space equation of equation (4), the extended state observer based on active disturbance rejection control is designed. For the actual system, there are unknown disturbances caused by environmental interference and the inability to obtain accurate true values ​​of parameters, which can be expressed in the state space equation as follows:

[0044] The second-order active disturbance rejection control system model is defined as:

[0045] (11)

[0046] Where: It is the total disturbance including external disturbance, time-varying part and inaccurate estimation of the inherent parameters of the aircraft.

[0047] The total disturbance function Expand to a new state variable, let , the system state space equation of equation (11) can be further expressed as follows:

[0048] (12)

[0049] In order to facilitate the subsequent derivation and design, the above formula (12) is organized into the following format:

[0050] (13)

[0051] in, Q = [ 0 1 0 0 0 1 0 0 0 ] ; W = [ 0 A 0 ] ; E = [ 0 0 1 ] ; C = [ 1 0 0 ] , Output for the system.

[0052] Design an observer for system (13). The standard form of the observer construction is as follows:

[0053] (14)

[0054] Where: are the state and output of the system observed by the observer, is the error feedback gain matrix of the extended state observer, L = [ β 1 β 2 β 3 ] T ,in , , is the adjustable parameter of the extended state observer; in formula (14) As part of the disturbance, it can be attributed to the total disturbance Therefore Item can be omitted.

[0055] If the initial state of the system and the controlled object are the same, under the same input (control quantity u), there is an observed state vector = Actual state vector ; However, the setting of the system initial conditions can only be estimated, and the initial state of the controlled object is unknown, so the estimated state Between the actual state There must be errors .

[0056] From the output observation equation of the controlled object, we can know the error This will inevitably lead to an error in the output of the controlled object. , the output of the controlled object can be measured by the sensor, so the error can be obtained, the error Negative feedback to Control Approaching 0, Approaching 0, the observation of the state vector x is realized, and the expanded state observer equation is expanded as follows:

[0057] (15)

[0058] By inputting the controlled object output y and the control variable u into the extended state observer through formula (15), the output of the extended state observer can be calculated. The system state variables are The observed value can be used to generate a deviation signal; the expanded state The total disturbance can be unknown Make good estimation observations and lay the foundation for subsequent total disturbance compensation.

[0059] Step (5) Design a control algorithm with multiple control performance index constraints

[0060] When performing a glide maneuver, an aircraft needs to accurately track the preset glide trajectory. Therefore, a preset performance control strategy with a finite time constraint is designed to set the flight pitch angle error within an acceptable envelope. The specific process is as follows:

[0061] First, the preset performance function of the finite time constraint Designed, the expression is as follows:

[0062] (16)

[0063] Where: are the initial and terminal errors of the performance function, respectively; The terminal time for the set error stabilization; , is the set error convergence speed constant. The above performance function satisfies , , , and has an exponential convergence rate.

[0064] The aircraft state error constraints need to satisfy:

[0065] (17)

[0066] Where: is the overshoot constraint constant of the lower error boundary, is the overshoot constraint constant of the upper error boundary, is the vehicle tracking error , is the unconstrained variable after mapping, As the error conversion function, the normalized variable is introduced , the unconstrained variable form obtained by the logarithmic mapping function is as follows:

[0067] (18)

[0068] Towards new unconstrained variables , the benchmark control law is designed through dynamic inverse control, as follows:

[0069] The dynamic inverse control algorithm needs to be based on the system state space equation for control law design. For conventional aircraft state space equations, it can be expressed as follows:

[0070] (19)

[0071] Where: , and They are the state quantity, output quantity and control quantity of the system respectively; is the system matrix; is the control matrix; is the output matrix.

[0072] The system output differential equation can be expressed as:

[0073] (20)

[0074] In the formula, Function Along The first-order Lie derivative of is defined to facilitate subsequent derivation. .

[0075] By transforming equation (20), the following control law can be obtained by inverting the system:

[0076] (twenty one)

[0077] In the formula, is the desired dynamic characteristic of the system. From the above formula (21), we can know that the control quantity to achieve the desired output can be obtained by solving the inverse system , the control amount By inputting it into the original system, the expected output that meets multiple index requirements can be achieved.

[0078] Beneficial effects of the present invention:

[0079] 1. Considering the strong nonlinearity, strong coupling, and fast time-varying characteristics of aircraft, a weak model-dependent control algorithm is designed to reduce the dependence on the precise model in the control process and improve the control method's adaptability to model uncertainty.

[0080] 2. The controller design is carried out by comprehensively considering control performance indicators such as control overshoot, rise time, and stability margin, and a control method customized for control performance indicators is formed to ensure that the control performance of the aircraft meets the mission requirements.

[0081] 3. The present invention provides the controller with real-time aerodynamic parameters of the aircraft with the help of online aerodynamic parameter identification, and adopts an expanded state observer to observe and compensate for unknown disturbances, which effectively improves the accuracy and robustness of the aircraft during the descent process, has good descent control performance, and has long-term application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a block diagram of the overall control method of an aviation vehicle;

[0083] Figure 2 It is a flow chart of the guaranteed performance control method for aviation vehicles customized for multiple indicators;

[0084] Figure 3 It is a simulation curve diagram of pitch angle tracking of an aircraft;

[0085] Figure 4 It is the aircraft pitch angle error-error envelope time curve diagram;

[0086] Figure 5 It is a simulation curve diagram of aircraft altitude tracking;

[0087] Figure 6 It is an aircraft speed tracking simulation curve. DETAILED DESCRIPTION

[0088] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0089] The overall control architecture of the present invention is as follows Figure 1 As shown, a multi-index customized aviation vehicle guaranteed performance control method of the present invention is as follows Figure 2 As shown, the implementation steps are:

[0090] Step 1: Establish a control-oriented aerospace vehicle dynamics model; Establish an aerospace vehicle dynamics model to lay the foundation for subsequent control method design and controller application.

[0091] Step 2: Establish a reference model of the longitudinal channel of an aircraft; consider performance indicators such as system response overshoot, rise time, and stability margin, use a second-order oscillation system to design a reference model of the longitudinal channel of an aircraft, and construct a state-space equation model.

[0092] The third step: model tracking error dynamics construction and error conversion; obtain the real-time aerodynamic parameters of the aircraft through online identification technology, and get the aviation aircraft dynamics model that reflects the real-time flight status. The aviation aircraft dynamics model is subtracted from the designed aircraft reference model to obtain the model tracking error dynamics model, and then the preset performance function is designed to limit the error within the artificially specified envelope, so as to constrain the tracking transient and steady-state performance.

[0093] Step 4: Design of an extended state observer for observing and compensating the total disturbance of the system; in view of the influence of modeling inaccuracy and unknown disturbances, the extended state observer is used to observe and compensate the total disturbance of the system.

[0094] Step 5: Design of performance-guaranteed control laws for aircraft that are customized for multiple indicators; design of aircraft controller based on dynamic inverse control method based on new variables processed by preset performance and observed total disturbance, so that the control performance meets the requirements of multiple performance indicators set by humans.

[0095] The specific steps are as follows:

[0096] Step 1: Establish a control-oriented aircraft dynamics model

[0097] For the subsequent controller design requirements, the longitudinal model of the aircraft is expressed as follows:

[0098] (twenty two)

[0099] Where: They are respectively the aircraft body in the body coordinate system Velocity components on the axis; is the body axis pitch rate; is the pitch angle; the superscript “ ” denotes derivative; is the flight altitude of the aircraft; is the airspeed in the velocity coordinate system; Angle of attack; is the maximum thrust of the aircraft engine; is the throttle opening; is the acceleration due to gravity; is the mass of the aircraft; The body-to-body coordinate system The moment of inertia of the shaft; They represent the pitching moment respectively. They are flight resistance, aircraft lift and pitch moment respectively. The aerodynamic force and moment expressions can be fitted as follows:

[0100] (twenty three)

[0101] Where: is the atmospheric density; is the wing reference area; is the average aerodynamic chord length of the aircraft; for elevator and flap commands respectively; is the constant term of the drag coefficient; The coefficient relationships between drag and squared angle of attack, angle of attack, elevator and flap are respectively; is the lift coefficient constant term; They are the coefficient relationships of lift angle of attack, elevator and flap respectively; is the constant term of the pitching moment coefficient; They are the coefficient relationships between the pitch moment and the angle of attack, elevator and flap, respectively.

[0102] Step 2: Establish a reference model of the longitudinal channel of an aircraft

[0103] When an aircraft executes relevant maneuvering instructions, a second-order system with expected overshoot, rise time and stability margin is designed as a reference model, which is shown as follows:

[0104] (twenty four)

[0105] Where: is the Laplace operator; is the natural frequency; is the damping ratio; are the expected pitch angle command and the pitch angle output by the reference model respectively.

[0106] Based on the above second-order system, the overshoot can be obtained and rise time :

[0107] (25)

[0108] (26)

[0109] According to the model capability of the aircraft and the expected performance, the natural frequency and damping ratio are designed to obtain a reference model that meets the requirements.

[0110] Step 3: Model tracking error dynamics construction and error conversion

[0111] The present invention designs a controller for aircraft trajectory control. In addition to the modeling in the first and second steps, it is also necessary to build an aircraft state space model, select the aircraft pitch angle and pitch rate As a state quantity, x = [ θ q ] T , the elevator is used as the control quantity, that is According to the small disturbance linearization equation, when the aircraft's glide path angle is between 0 and 6°, the system state space equation is expressed as:

[0112] (27)

[0113] Where: ; .

[0114] The present invention uses the widely used recursive least squares technique to perform online identification of aircraft. The recursive least squares algorithm can be expressed as:

[0115] (28)

[0116] Where: is the least squares estimate at the current moment; is the gain vector at the current moment; is the covariance matrix at the current moment; is the information vector formed by the observation data at the current moment; is the unit matrix; An artificially set constant.

[0117] Based on the recursive least squares algorithm, the real-time aerodynamic parameters of the aircraft during flight are identified. , , and , which lays the foundation for the subsequent control law design. In order to distinguish the actual aircraft system from the artificially designed reference model system, the pitch angle response value is defined and the pitch rate response value As the reference model state quantity, x m = [ θ m q m ] T , expected pitch angle command As control input , we get the following reference model state space equation:

[0118] (29)

[0119] in: , .

[0120] By subtracting the constructed system state space equation and the reference model state space equation, the model tracking error dynamics model can be obtained as:

[0121] (30)

[0122] Taking into account the control system errors and preset performance constraints:

[0123] (31)

[0124] In the formula, is the overshoot constraint constant of the lower error boundary, is the overshoot constraint constant of the upper error boundary, is the unconstrained variable after mapping, is the error transfer function, It is the preset performance function.

[0125] The designed preset performance function form is as follows:

[0126] (32)

[0127] Where: are the initial and terminal errors of the performance function, respectively; The terminal time for the set error stabilization; , is the set error convergence speed constant. The above preset performance function satisfies , , , and has an exponential convergence rate.

[0128] With the help of the error conversion function, the constrained control problem can be converted into an unconstrained problem, and the obtained unconstrained variable form is:

[0129] (33)

[0130] Where: is the normalized variable, is the flight attitude angle tracking error.

[0131] In order to simplify the derivation writing process, etc. , taking the derivative of the above formula (33) we can get:

[0132] (34)

[0133] Where: , Then further derive the above formula (34) to obtain:

[0134] (35)

[0135] Where: .

[0136] Therefore, a new second-order system state equation with unconstrained variables as state quantities can be established. We can get:

[0137] (36)

[0138] Combining equations (35) and (36) to simplify, we can obtain:

[0139] (37)

[0140] Where:

[0141] Step 4: Design of extended state observer for total disturbance observation compensation

[0142] In order to improve the control performance of the controller and suppress the influence of external disturbances and related parameter estimation errors, an extended state observer is designed based on active disturbance rejection control to achieve observation and compensation of the total disturbance. Its form is as follows:

[0143] (38)

[0144] In the formula, is the adjustable coefficient of the extended state observer, Respectively and the observed value of the total disturbance.

[0145] Step 5: Design of guaranteed cost control law for multi-index customized aircraft

[0146] According to the derivation of the system state equation and the designed extended state observer, the attitude tracking control law can be designed for:

[0147] u =− ( RA ) − 1 [ k κ 2 + N + z 3 ] (39)

[0148] In the formula, The reference model is designed for multiple performance index requirements. The control law is designed based on the system error between the actual aircraft system and the artificially designed reference model, which can make the control performance of the actual aircraft system close to the artificially designed reference model. In this way, the deflection of the attitude control rudder surface of the aircraft that meets the requirements of multiple performance indicators can be obtained, thereby achieving the attitude control task.

[0149] A simulation experiment is carried out based on the designed control law: first, the aircraft maintains level flight at an altitude of 500m with a trim angle of attack of 12.05°, and then performs a flight maneuver at a target pitch angle of 8.05°, with the speed reference set to 80m / s.

[0150] Table 1 shows the aircraft data and status data:

[0151] Table 1 Simulation parameters.

[0152]

[0153] The results are as follows Figure 3-Figure 6As shown. It can be seen that under the action of the multi-index customized aircraft guaranteed performance control method proposed in the present invention, the pitch angle, altitude and speed of the aircraft are effectively tracked, and the speed change range is within ±1m / s, meeting the engineering flight quality standards, such as Figure 3 , Figure 5 , Figure 6 In addition, Figure 4 The tracking error of the pitch angle command is given in the figure. Its rise time is 1.8s and the overshoot is 9.47%, which meets the expected system response performance index requirements. The pitch angle error is always within the performance envelope of the artificially set finite time constraint, which can significantly improve the attitude angle tracking control capability and anti-interference ability, while meeting multiple performance index requirements.

Claims

1. A method for guaranteed performance control of an aircraft for multi-index customization, the specific steps are as follows: Step 1: Establish a control-oriented aircraft dynamics model For the controller design requirements, the longitudinal model of the aircraft is expressed as follows: (1) Where: They are respectively the aircraft body in the body coordinate system Velocity components on the axis; is the body axis pitch rate; is the pitch angle; superscript " ” denotes derivative; is the flight altitude of the aircraft; is the airspeed in the velocity coordinate system; Angle of attack; is the maximum thrust of the aircraft engine; is the throttle opening; is the acceleration due to gravity; is the mass of the aircraft; The body-to-body coordinate system The moment of inertia of the shaft; denote the pitching moment respectively; They are flight resistance, aircraft lift and pitch moment respectively. The aerodynamic force and moment expressions are fitted as follows: (2) Where: is the atmospheric density; is the wing reference area; is the average aerodynamic chord length of the aircraft; for elevator and flap commands respectively; is the constant term of the drag coefficient; The coefficient relationships between drag and squared angle of attack, angle of attack, elevator and flap are respectively; is the lift coefficient constant term; They are the coefficient relationships of lift angle of attack, elevator and flap respectively; is the constant term of the pitching moment coefficient; are the coefficient relationships between pitch moment and angle of attack, elevator and flap respectively; Step 2: Establish a reference model of the longitudinal channel of an aircraft When an aircraft executes relevant maneuvering instructions, a second-order system with expected overshoot, rise time and stability margin is designed as a reference model, which is shown as follows: (3) Where: is the Laplace operator; is the natural frequency; is the damping ratio; are the desired pitch angle command and the pitch angle output by the reference model respectively; Based on the above second-order system, the overshoot is obtained and rise time : (4) (5) According to the model capability and expected performance of the aircraft, the natural frequency and damping ratio are designed to obtain a reference model that meets the requirements; Step 3: Model tracking error dynamics construction and error conversion Designing a controller for aircraft trajectory control requires building an aircraft state space model in addition to the modeling in the first and second steps, and selecting the aircraft pitch angle. and pitch rate As a state quantity, , the elevator is used as the control quantity, that is According to the small disturbance linearization equation, when the aircraft's glide path angle is between 0 and 6°, the system state space equation is expressed as: (6) Where: ; ; The recursive least squares technique is used for online identification of aircraft. The recursive least squares algorithm is expressed as: (7) Where: is the least squares estimate at the current moment; is the gain vector at the current moment; is the covariance matrix at the current moment; is the information vector formed by the observation data at the current moment; is the unit matrix; To set constants artificially; Based on the recursive least squares algorithm, the real-time aerodynamic parameters of the aircraft during flight are identified. , , and , laying the foundation for the subsequent control law design; In order to distinguish the actual aircraft system from the artificially designed reference model system, the pitch angle response value is defined and the pitch rate response value As the reference model state quantity, , expected pitch angle command As control input , we get the following reference model state space equation: (8) in: , ; By subtracting the constructed system state space equation and the reference model state space equation, the model tracking error dynamics model is obtained as: (9) Taking into account the control system errors and preset performance constraints: (10) In the formula, is the overshoot constraint constant of the lower error boundary, is the overshoot constraint constant of the upper error boundary, is the unconstrained variable after mapping, is the error transfer function, is a preset performance function; The designed preset performance function form is as follows: (11) Where: are the initial and terminal errors of the performance function, respectively; The terminal time for the set error stabilization; , is the set error convergence speed constant; the preset performance function satisfies , , , and has an exponential convergence rate; The error conversion function is used to transform the constrained control problem into an unconstrained problem, and the unconstrained variable form is obtained as follows: (12) Where: is the normalized variable, is the flight attitude angle error; In order to simplify the derivation writing process, Abbreviated as , taking the derivative of the above formula (12) we can get: (13) Where: , Then further derive the above formula (13) to obtain: (14) Where: ; Therefore, a new second-order system state equation with unconstrained variables as state quantities can be established. We can get: (15) Combining equation (14) and equation (15) to simplify, we can get: (16) Where: Step 4: Design of extended state observer for total disturbance observation compensation In order to improve the control performance of the controller and suppress the influence of external disturbances and related parameter estimation errors, an extended state observer is designed based on active disturbance rejection control to achieve observation and compensation of the total disturbance. Its form is as follows: (17) In the formula, is the adjustable coefficient of the extended state observer, Respectively and the observed value of the total disturbance; Step 5: Design of guaranteed cost control law for multi-index customized aircraft According to the derivation of the system state equation and the designed extended state observer, the attitude tracking control law is designed. for: (18) In the formula, is an adjustable control parameter; The reference model is designed for multiple performance index requirements. The control law is designed based on the system error between the actual aircraft system and the artificially designed reference model, so that the control performance of the actual aircraft system is close to that of the artificially designed reference model. In this way, the deflection of the attitude control rudder surface of the aircraft that meets the requirements of multiple performance indexes is obtained, thereby achieving the attitude control task.

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