A deep stall recovery control method and system based on hybrid model predictive control

Abstract

The application discloses a deep stall recovery control method and system based on a hybrid model predictive control, relates to the technical field of flight control and flight safety, and solves the problem that an airplane is difficult to recover after entering a deep stall and exceeding a stall angle of attack by establishing a quadratic objective function of post-predictive control attitude stability, using a hybrid system and a quadratic objective function predictive control strategy, on-line solving a mixed integer quadratic programming, obtaining a current optimal control input and state estimation, and then through rolling optimization, obtaining a final stall recovery control sequence.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of flight control and flight safety, more particularly, to a deep stall recovery control method and system based on hybrid model predictive control. BACKGROUND

[0002] At present, many aviation accidents are caused by stall, and deep stall refers to the phenomenon that the horizontal tail of an airplane is exposed in the turbulent flow region of the wing at a large angle of attack, resulting in an increase in the angle of attack, and when the angle of attack exceeds the stall angle of attack, the angle of attack is locked, at this time, even if the pilot pushes the stick to the bottom and the elevator is deflected to the maximum, it is also impossible to obtain sufficient moment, at this time, the elevator loses its effectiveness. Whether in adverse weather conditions or human intervention, the problem of deep stall is difficult to avoid. Deep stall recovery can be achieved by generating a lateral pitching moment through a certain roll angle and yaw angle. Although entering deep stall often depends on the pilot to recover, research on automatic recovery strategies can also guide the pilot to safely and effectively recover.

[0003] In fact, the flight model of deep stall can be regarded as a hybrid system, which is a combination of continuous systems and discrete systems, including continuous systems such as dynamic models, and discrete event-driven discrete systems. For such a system, the optimal control needs to be estimated to make it recover as much as possible and drop to a small height. Due to the limitation of control quantity, the control quantity is discretized, and the discrete sequence is dynamically optimized, so an advanced hybrid system predictive control algorithm needs to be designed to provide an effective tool for flight control system and flight guidance.

[0004] Therefore, how to solve the problem of elevator losing effectiveness after the airplane enters deep stall is a problem that needs to be solved by those skilled in the art. SUMMARY

[0005] Therefore, the present application considers that most of the existing airplane accidents are caused by stall, in order to solve the above problems, a deep stall recovery control method and system based on hybrid model predictive control are provided to provide a reference for flight control strategy.

[0006] In order to achieve the above purpose, on the one hand, the present application provides a deep stall recovery control method based on hybrid model predictive control, comprising the following steps:

[0007] Step 1, using the piecewise affine model in the hybrid system theory to linearize the nonlinear dynamic model of the airplane, and using differential equations to establish the linearized flight dynamic model under multiple states;

[0008] Step 2, determining variable constraints of each state variable in the flight dynamics model and determining a quadratic objective function used by the model predictive control;

[0009] Step 3, using the hybrid system and the quadratic objective function based predictive control strategy, solving the mixed integer quadratic programming on line to obtain the current optimal control input and state estimation, and through rolling optimization, obtaining the final stall recovery control sequence.

[0010] Optionally, the linear modeling method in step 1 is to describe the nonlinear dynamics model of the aircraft by using the following dynamic equation,

[0011]

[0012] u = [thrust, ail, rud] ;

[0013]

[0014] In the formula, is the differential quantity of the aircraft state at the next time, f and g are transfer functions of the nonlinear dynamics model of the aircraft, the control quantity u includes the engine thrust thrust, the elevator deflection ele, the aileron deflection ail, and the rudder deflection rud, and the state quantity includes the north-east ground coordinates npos, epos, alt, the roll angle φ, the pitch angle θ, and the yaw angle the flight total speed v, the angle of attack α, the sideslip angle β, the roll angular velocity p, the pitch angular velocity q, and the yaw angular velocity r.

[0015] Optionally, the specific process of establishing the linearized flight dynamics model of the aircraft in multiple states by using the differential equation in step 1 is as follows:

[0016] Linear expansion is performed at each working point to obtain n+2 linear models of the nonlinear dynamics model of the aircraft,

[0017]

[0018] Simplifying,

[0019]

[0020] In the formula,

[0021]

[0022] x i , y i , and u i respectively represent the input quantity, the output quantity, and the control quantity of the linearization of the nonlinear model of the aircraft at the working point.

[0023] Optionally, the variable constraint in step 2 is:

[0024]

[0025]

[0026] where (x ε ,μ ε ) is the equilibrium pair, which actually means the state and control variables of the aircraft when it is flying horizontally at the current altitude, t is the current time, x(t) is the current state variable, u is the control command, x_0 is the initial state of the system when t=0, μ0 T-1 ={μ(0),μ(1),…,μ(T-1)} is the optimal control sequence of the future k time periods obtained at t, λ i >0 is a hyperparameter, μ0 k-1 ={μ(0),μ(1),…,μ(k-1)} is the optimal control sequence of the future k time periods obtained at t, represents a segmented affine model based on the model of the system, the differential quantity at the next time under the action of x(t) and μ0 k-1 at t; T represents the prediction length of the model predictive control, J is the final optimization target, i.e., the cost function, i represents the i-th subsystem in the segmented affine model, x min , x max are the hard constraints of the input variables of the aircraft nonlinear model, y min , y max are the hard constraints of the output variables of the aircraft nonlinear model and the control variables, u min , u max are the hard constraints of the control variables of the aircraft nonlinear model.

[0027] Optionally, step 2 further comprises introducing a stall warning angle of attack and a stall angle of attack to describe different flight states and switching between different flight states, and decomposing the initial flight state into multiple hybrid system models according to the different initial flight states, and determining the hybrid system model through a state lookup table.

[0028] In another aspect, the application provides a deep stall recovery control system based on hybrid model predictive control, comprising the following modules:

[0029] A linear modeling module that uses a segmented affine model in hybrid system theory to linearly model the nonlinear dynamics model of the aircraft;

[0030] A differential equation modeling module that uses differential equations to establish linearized flight dynamics models in multiple states;

[0031] A quadratic objective function construction module determines variable constraints of each state variable in the flight dynamics model and determines a quadratic objective function used by the model predictive control;

[0032] A stall recovery control sequence solving module uses a hybrid system and a quadratic objective function predictive control strategy to solve a mixed integer quadratic programming online to obtain a current optimal control input and state estimation, and further obtains a final stall recovery control sequence through rolling optimization.

[0033] Optionally, the system further comprises a variable constraint construction module configured to determine the constraint values of each state variable in the flight dynamics model.

[0034] According to the above technical solution, compared with the prior art, the application provides a deep stall recovery control method and system based on hybrid model predictive control, which comprehensively uses hybrid system theory and model predictive control technology, regards the control input and disturbance as system input, regards the actual state of the aircraft as system output, and converts the stall dynamics model recovery control problem into a constrained linear hybrid system rolling optimization problem. The problem of difficult recovery after the aircraft enters deep stall and exceeds the stall angle of attack is solved. The control sequence obtained by the solution can also be used as flight guidance to guide the pilot to re-enter the flight envelope and stabilize the aircraft attitude after the rudder loses effect, and complete the stall recovery. BRIEF DESCRIPTION OF DRAWINGS

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of the provided drawings.

[0036] Figure 1 is a hybrid model predictive control recovery flowchart under deep stall;

[0037] Figure 2 is a flight dynamics model diagram under deep stall;

[0038] Figure 3 is a hybrid system model structure diagram of the present application. DETAILED DESCRIPTION

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] This invention discloses a deep stall recovery control method based on hybrid model predictive control, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0041] Step 1: Linearize the nonlinear dynamics model of the aircraft using the piecewise affine model in hybrid systems theory, and establish the linearized flight dynamics model under various states using differential equations.

[0042] Step 2: Determine the variable constraints of each state variable in the flight dynamics model and determine the quadratic objective function used by the model predictive control;

[0043] Step 3: Using a hybrid system and predictive control strategy based on a quadratic objective function, solve the mixed integer quadratic programming problem online to obtain the current optimal control input and state estimate. Then, through rolling optimization, obtain the final stall recovery control sequence.

[0044] In one specific embodiment, the linearization modeling method in step 1 involves describing the nonlinear dynamics model of the aircraft using the following dynamic equations.

[0045]

[0046] u = [thrust,ail,rud];

[0047]

[0048] In the formula, Let f and g be the differential components of the aircraft's state at the next moment, and f and g be the transfer functions of the aircraft's nonlinear dynamics model. The control variables u include engine thrust, elevator deflection ele, aileron deflection ail, and rudder deflection rud. The state variables include the NE coordinates npos, epos, alt, roll angle φ, pitch angle θ, and yaw angle. Total flight speed v, angle of attack α, sideslip angle β, roll rate p, pitch rate q, yaw rate r.

[0049] In one specific embodiment, the specific process of establishing a linearized flight dynamics model under multiple states using differential equations in step 1 is as follows:

[0050] Considering the warning angle of attack α when entering stall.sw Based on their different entry states, they are divided into n categories, denoted by α. SW-1 ,α SW-2 ,…,α SW-n The stall angle of attack is denoted as α. stall , where α stall >α sw-n If the value is greater than 0, the running state is divided into n+2 regions, i.e.

[0051] X1={α|α>α stall},X 2n ={α|α stall >α>α sw-n},X3={α|α sw-n >α>0};

[0052] Linear expansion is performed at each operating point to obtain n+2 linearized models of the aircraft's nonlinear dynamics model.

[0053]

[0054] Simplifying, we get

[0055]

[0056] In the formula,

[0057]

[0058] x i y i u i These represent the linearized input, output, and control quantities of the aircraft nonlinear model at the operating point, respectively.

[0059] like Figure 2 As shown, the system is divided into three affine systems based on the range of angles of attack. When the aircraft enters a deep stall state due to certain factors, the angle of attack exceeds the set stall angle of attack, i.e., α. stall <α, it starts from X1, at which point the stall subsystem in the system takes effect. Simultaneously, it acquires the stall warning trigger angle given by the stall warning system before entering deep stall. As the control action increases, its angle of attack moves closer to the flight envelope. When the angle of attack α SW-n <α<α stall At this time, α∈X 2n When the system switches, the stall alarm subsystem activates, and so on until the system finally stabilizes at the equilibrium point, thus achieving the control objective.

[0060] In one specific embodiment, the variable constraint in step 2 is:

[0061]

[0062]

[0063] where (x ε ,μ ε ) is the equilibrium pair, which actually means the state and control variables of the aircraft when it is flying horizontally at the current altitude, t is the current time, x(t) is the current state variable, u = [thrust,ail,rud] is the control command, x_0 is the initial state of the system when t = 0, and μ0 T-1 = {μ(0),μ(1),…,μ(T-1)} is the optimal control sequence of the future T time steps, λ i > 0 is the hyper parameter, and μ0 k-1 = {μ(0),μ(1),…,μ(k-1)} is the optimal control sequence of the future k time steps obtained at time t, represents the differential of the system based on the model of the system at time t under the action of state x(t) and μ0 k-1 , T represents the prediction length of the model predictive control, J is the final optimization objective, i.e., the cost function, i represents the i-th subsystem in the piecewise affine model, x min , x max are the hard constraints of the input variables of the nonlinear model of the aircraft, y min , y max are the hard constraints of the output variables of the nonlinear model of the aircraft and the control variables, u min , u max are the hard constraints of the control variables of the nonlinear model of the aircraft.

[0064] In one specific embodiment, step 2 further comprises introducing a stall warning angle of attack and a stall angle of attack to describe different flight states and switching between different flight states, and decomposing the initial flight state into a plurality of hybrid system models according to different initial flight states, as shown in Figure 3 , and determining the hybrid system model by means of state table lookup.

[0065] In one specific embodiment, the specific process of step 3 is as follows: assuming that the optimal control sequence μ0 According to the principle of the receding horizon control, the first element of the optimal control sequence is applied to the system

[0066]

[0067] The other elements of the control sequence are discarded At time t + 1, according to the measured state information x(t + 1), the above process is repeated, and the final stall recovery control sequence is obtained.

[0068] In one embodiment, a deep stall modification control system based on hybrid model predictive control is provided, comprising the following modules:

[0069] A linearization modeling module linearizes a nonlinear dynamic model of an aircraft using a piecewise affine model in hybrid system theory;

[0070] A differential equation modeling module establishes a linearized dynamic model of an aircraft in multiple states using differential equations;

[0071] A quadratic objective function construction module determines variable constraints of each state variable in the dynamic model of the aircraft and determines a quadratic objective function used in model predictive control;

[0072] A stall modification control sequence solving module solves a mixed integer quadratic programming on-line using a hybrid system and based on a quadratic objective function predictive control strategy to obtain a current optimal control input and state estimation, and further obtains a final stall modification control sequence through rolling optimization.

[0073] In one embodiment, a variable constraint construction module is further included for determining the constraint values of each state variable in the dynamic model of the aircraft.

[0074] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts of each embodiment can be referred to each other. For the apparatus disclosed in the embodiments, the description is relatively simple because it corresponds to the method disclosed in the embodiments. The relevant parts can be referred to the description of the method.

[0075] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A deep stall recovery control method based on hybrid model predictive control, characterized in that, Includes the following steps: Step 1: Linearize the nonlinear dynamics model of the aircraft using the piecewise affine model in hybrid systems theory, and establish the linearized flight dynamics model under various states using differential equations. Step 2: Determine the variable constraints of each state variable in the flight dynamics model and determine the quadratic objective function used by the model predictive control; Step 3: Using a hybrid system and predictive control strategy based on a quadratic objective function, solve the mixed integer quadratic programming online to obtain the current optimal control input and state estimate. Then, through rolling optimization, obtain the final stall recovery control sequence. The variable constraints mentioned in step 2 are: ； ； In the formula, For the purpose of balance, its practical meaning is the state and control variables of the aircraft during horizontal flight at the current altitude. t For the current moment, As the current state variable, when the control command is ,when t When =0, Define the initial state of the system. , For hyperparameters, In order to be in t The optimal control sequence for the next k time segments is obtained at each step. This represents a system-based model. t Always in the zone as well as Under the influence of , the differential component at the next moment; T represents the prediction time of the model predictive control, J is the final optimization objective, i.e., the cost function, and i represents the i-th subsystem in the piecewise affine model. , Hard constraints on the input quantities of the aircraft nonlinear model. , Hard constraints and control variables are used to define the output of the aircraft's nonlinear model. , This is a hard constraint on the control variables of the aircraft's nonlinear model.

2. The deep stall recovery control method based on hybrid model predictive control according to claim 1, characterized in that, The linearization modeling method described in step 1 involves using the following dynamic equations to describe the nonlinear dynamics model of the aircraft. ； ； ； In the formula, This is a differential component representing the aircraft's state at the next moment. , The transfer function of the nonlinear dynamics model of the aircraft, and its control variables Including engine thrust elevator deflection Aileron deflection rudder deflection Its state quantities include northeast coordinates Roll angle Pitch angle Yaw angle Total flight speed Angle of attack Sideslip angle Roll angular velocity Pitch angular velocity yaw rate .

3. The deep stall recovery control method based on hybrid model predictive control according to claim 1, characterized in that, The specific process of establishing linearized flight dynamics models under various states using differential equations in step 1 is as follows: Linear expansion is performed at each operating point to obtain n+2 linearized models of the aircraft's nonlinear dynamics model. ； Simplifying, we get ； In the formula, ; ； , , These represent the linearized input, output, and control quantities of the aircraft nonlinear model at the operating point, respectively.

4. The deep stall recovery control method based on hybrid model predictive control according to claim 1, characterized in that, Step 2 further includes introducing stall warning angle of attack and stall angle of attack to describe different flight states and the switching between different flight states, and decomposing them into multiple hybrid system models according to the different initial flight states, and then determining the hybrid system model by state lookup table.

5. A deep stall recovery control system based on hybrid model predictive control, characterized in that, The deep stall recovery control method based on hybrid model predictive control according to any one of claims 1-4 includes the following modules: The linearization modeling module uses a piecewise affine model from hybrid systems theory to linearize the nonlinear dynamics model of the aircraft. The differential equation modeling module uses differential equations to establish linearized flight dynamics models under various conditions; The quadratic objective function construction module determines the variable constraints of each state variable in the flight dynamics model and determines the quadratic objective function used by the model predictive control. The stall recovery control sequence solving module uses a hybrid system and predicts the control strategy based on a quadratic objective function. It solves the mixed integer quadratic programming online to obtain the current optimal control input and state estimate. Then, through rolling optimization, it obtains the final stall recovery control sequence.

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