CN113204192A - Tracking control method for preset performance of unmanned helicopter - Google Patents

Abstract

The invention discloses a method for controlling the preset performance of an unmanned helicopter, which comprises the following steps: 1. introducing system uncertainty and actuator faults into a nonlinear system model of the unmanned helicopter, and simultaneously converting inequality constraints of tracking errors into equality problems by adopting an error conversion function method for processing; 2. transforming the model established by the step 1, and approximating the system uncertainty by adopting a neural network method; meanwhile, an auxiliary system is constructed to solve the problem of failure fault of the actuator, so that the fault tolerance of the system is improved; 3. by combining the technologies 1 and 2, the robust fault-tolerant controller of the unmanned helicopter is designed under the framework of a backstepping method, and the tracking error of the system can be ensured to be changed in a set range all the time under the condition that the unmanned helicopter system faces complex environments such as system uncertainty, actuator faults and the like. The robust safe flight control scheme of the invention ensures that the tracking error of the unmanned helicopter can be converged within a set range under multiple factors such as system uncertainty, actuator fault and the like.

Description

Tracking control method for preset performance of unmanned helicopter

Technical Field

The invention belongs to the technical field of robust control of aircrafts, and particularly relates to a tracking control method for preset performance of an unmanned helicopter.

Background

An unmanned helicopter is an aircraft that performs a given task autonomously without human operators, using onboard sensors and automatic control systems, or by sending remote control commands via a radio remote control device. Compared with a fixed-wing unmanned aerial vehicle, the unmanned helicopter has the following characteristics: (l) The functions of fixed-point hovering, vertical take-off and landing, pivot turning, low altitude slow flight and the like can be completed; (2) the free flight can be realized in the severe environment in the field without a special airport and a runway. Due to the unique advantages, the unmanned helicopter lays a heavy military role and a wide civil prospect. In military operations, unmanned helicopters can carry various weapons such as small air-ground missiles and the like to attack targets on the ground, water surfaces and air. Meanwhile, the unmanned helicopter has great advantages in the aspect of carrier-based aircrafts compared with a fixed wing unmanned plane, and is very suitable for the actual needs of naval vessels because the unmanned helicopter can vertically take off and land in a small space. In modern operation, the unmanned helicopter can attack an enemy unmanned aerial vehicle flying close to the sea surface to capture the ultra-low-altitude airspace control right, and can also be matched with a naval vessel formation to land to execute a firepower support task. In the civil aspect, the unmanned helicopter can complete the work of topographic mapping, resource exploration, forest fire prevention, aerial photography, pesticide spraying and the like. When a serious natural disaster occurs, a rescue search task and the inspection of electric power, bridges and roads in a disaster area can be executed. Although the unmanned helicopter has such a huge application prospect and also obtains attention and research of numerous scientific organizations at home and abroad, due to the inherent characteristics of strong nonlinearity, complex dynamic characteristics, unstable open loop, underactuation and the like, the design of the unmanned helicopter control system still faces many practical problems to be explored and solved.

Firstly, the extensive military and civil values of unmanned helicopters determine that the unmanned helicopters often need to carry out various operations under different environments and different meteorological conditions, such as sea surfaces, urban areas, valleys and the like, so that the environment information for executing tasks is often not completely transparent. Meanwhile, the multivariable characteristics of the unmanned helicopter and the change of system parameters in the flight process can cause the existence of uncertainty problems such as modeling errors, and if the controller cannot timely cope with the problems, the performance of the control system can be reduced and even the control is out of control. Therefore, the analysis and the processing of the system uncertainty problems such as modeling errors and the like are important guarantees for the safe flight of the unmanned helicopter.

Secondly, the rotor structure makes the movable part in unmanned helicopter system obviously increase than the fixed wing aircraft, and this also leads to the probability that the system breaks down to be higher, for example the long-time high-speed rotation of rotor can cause the decline of control gain. In addition, the special military positioning of the unmanned helicopter requires that the unmanned helicopter often perform tasks in complex and variable environments, which puts higher requirements on the performance of the system, such as the requirement that the tracking error of the system is changed within a set range. In particular, for an unmanned helicopter system performing precise blows, the requirement of high precision performance is crucial to improving the task completion rate. However, most of the current researches on flight control of unmanned helicopters do not comprehensively analyze and consider the typical problems. Meanwhile, the coupling of uncertainty and other problems such as parameter change, modeling error and the like occurs, and a brand new challenge is brought to the design of the flight control system of the unmanned helicopter.

Based on the technical scheme, high-quality flight control research is carried out on the unmanned helicopter with important strategic position in military, various factors threatening the flight safety of the unmanned helicopter are comprehensively analyzed, and the research significance and the practical value are important for ensuring the survival capability and task completion of the unmanned helicopter in battlefield environment.

Disclosure of Invention

The invention aims to provide a control method for the preset performance of an unmanned helicopter, which ensures that the tracking error of the unmanned helicopter can be converged within a set range under multiple factors such as system uncertainty, actuator fault and the like.

In order to achieve the purpose, the technical scheme of the invention is as follows:

a control method for preset performance of an unmanned helicopter specifically comprises the following steps:

(1) firstly, introducing system uncertainty and actuator faults into a nonlinear system model of the unmanned helicopter, and simultaneously converting inequality constraints of tracking errors into equality problems by adopting an error conversion function method for processing;

(2) and (3) transforming the model established in the step (1), and approximating the system uncertainty by adopting a neural network method. Meanwhile, an auxiliary system is constructed to solve the problem of failure fault of the actuator, so that the fault tolerance of the system is improved;

(3) and (3) combining the technologies in the step (1) and the step (2), designing the robust fault-tolerant controller of the unmanned helicopter under the framework of a backstepping method, and ensuring that the tracking error of the system can be changed in a set range all the time under the condition that the unmanned helicopter system faces complex environments such as system uncertainty, actuator faults and the like.

Further, in step (1), the attitude height composite model representing the vertical take-off and landing movement of the unmanned helicopter can be described as follows:

wherein g represents gravitational acceleration, m and J_fRespectively representing mass and moment of inertia, Z, of the unmanned helicopter_gAnd w_fRepresenting the altitude and velocity of the unmanned helicopter in the vertical direction, Λ_f＝[φ,θ,ψ]^TRepresenting the attitude angle vector (roll, pitch and yaw, respectively), omega_f＝[p,q,r]^TRepresenting the attitude angular rate vector, H, in a collective coordinate system_fRepresenting the attitude change matrix, T_mrSum-sigma_f＝[Σ_xf,Σ_yf,Σ_zf]^TRespectively, the control force and the moment acting on the unmanned helicopter.

In step (1), the failure fault of the unmanned helicopter actuator can be modeled as

u_f＝ρ_fu

Wherein

Is the control input vector, p, to be designed_f＝diag{ρ₁,ρ₂,ρ₃,ρ₄}，ρ_i(i 1.., 4) is the ith^thUnknown residual control efficiency of each actuator and satisfies 0 < rho_i≤1。

Definition of

And (3) combining the steps (1) to (3) and simultaneously considering the influence of system uncertainty, rewriting the altitude and attitude combined dynamic model of the unmanned helicopter into the following form:

y＝M_f

wherein Δ F (N)_f) Representing the total uncertainty of the system and y is the system output.

In step (1), the purpose of the preset performance is to guarantee the tracking error e_y＝y-y_dTransient and steady state performance. If the tracking error e_yThe preset performance can be guaranteed by varying all the time within the following preset ranges:

-λ_f1iχ_fi(t)＜e_yi＜λ_f2iχ_fi(t),i＝1,2,3,4

wherein e_y＝[e_y1,e_y2,e_y3,e_y4]^T，λ_f1iAnd λ_f2iIs a parameter to be designed and satisfies lambda_f1i∈(0,1]，λ_f2i∈(0,1]。χ_fiIs a performance function.

To accomplish control performance, the inequality constraint is transformed into an equality form using an error transfer function as follows:

wherein beta is_fiIs a transition error variable, Q (-) is an increasing function and has the following properties:

i)Q(·):(-λ_f1i,λ_f2i)→(-∞,∞),ii)

in step (1), an error transformation function β of the form_fi(i-1, 2,3,4) to ensure e_yiThe preset performance of (2):

for convenience, let α_i＝α(e_yi(0)/χ_fi(0)). The error transfer function can then be rewritten as

For beta is_iDerived with respect to time t

Wherein

Definition of beta_f＝[β_f1,β_f2,β_f3,β_f4]^T，χ_f＝diag{χ_f1,χ_f2,χ_f3,χ_f4H and Π_f＝diag{Π_f1,Π_f2,Π_f3,Π_f4Is obtained by

Considering e_y＝y-y_dAnd y ═ M_fThe above equation can be further written as

Combining the converted error dynamic equation with the unmanned helicopter attitude height model to obtain:

in step (2), the composite unmanned helicopter dynamic model is rewritten into

Wherein I_f＝diag{1,1,1,1}，U_f1＝G_fU_f。

In step (2), in order to cope with actuator faults and compensate for their negative effects, an auxiliary system is constructed with the same dimensions as the system as follows:

wherein P is_f1∈R^4×4And P_f2∈R^4×4For positively determined symmetrical matrices to be designed, ζ_f1∈R⁴And ζ_f2∈R⁴To assist the internal state of the system.

In step (2), the radial basis function neural network of the form_f1(ρ_f-I_f)U_f1The approximation is carried out and the result is obtained,

wherein

For the matrix to be designed, W₁ ^*The ideal weight matrix is represented by a matrix of weights,

to satisfy

And c is₁A gaussian function of > 0 and a high frequency,

is an approximation error and satisfies

The control design is driven by a practical auxiliary system of the form:

wherein

Is W₁ ^*An estimate of (d).

In step (3), an error variable is defined as

z_f1＝β_f-ζ_f1

z_f2＝N_f-N_fd-ζ_f2

Wherein N is_dIs a virtual control law to be designed.

In step (3), a virtual control law N is designed_fdIs composed of

Wherein

Is a matrix of designs.

In step (2), Δ F (N) due to system uncertainty_f) Is unknown, and is approximated by constructing a radial basis function neural network of the form

Wherein

For a matrix to be designed, the matrix

The ideal weight matrix is represented by a matrix of weights,

is at c₂When is greater than 0, satisfy

The function of the gaussian function of (a) is,

is at the same time

When it is satisfied with

The error is approximated by the neural network.

In step (3), the adaptive robust fault-tolerant controller is designed as

Wherein

For the matrix to be designed, the matrix is,

represents W₂An estimate of (d).

Because of U_f1＝G_fU_fThen the actual control input is

In step (3), design

And

is the parameter update law of

Wherein

And

is a constant to be designed.

Adopt the beneficial effect that above-mentioned technical scheme brought:

the invention adopts an error conversion method to process inequality constraints of output performance, and simultaneously approaches system uncertainty by combining a radial basis function neural network method. In addition, an auxiliary system is constructed to solve the problem of actuator failure, and the fault tolerance of the system is improved. Finally, the designed robust fault-tolerant control scheme based on the preset performance can enable the unmanned helicopter to safely and intelligently fly, and meanwhile, the output tracking error is always changed within the set range.

Drawings

FIG. 1 is a flow chart of the system control of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention will be described in further detail with reference to embodiments, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The vertical take-off and landing modality considered by the present invention is the typical motion of an unmanned helicopter as distinguished from a fixed wing aircraft. The unmanned helicopter belongs to a high-precision system, and as the structure and the task of the unmanned helicopter become more and more complex, the control performance requirement of the unmanned helicopter becomes stricter, so that the limit of the output performance considered by the invention is based on the actual engineering requirement.

The invention discloses a preset performance control method of an unmanned helicopter, which simultaneously considers system uncertainty and actuator faults. Firstly, introducing an error conversion function to release inequality constraint conditions of tracking errors; then, in order to improve the robustness of the system, a neural network method is adopted to approximate the uncertainty of the system; meanwhile, an auxiliary system is constructed to solve the problem of failure faults of the actuator; and finally, a robust fault-tolerant controller is designed by combining a preset performance method to ensure the safe flight of the unmanned helicopter, and the tracking error is always changed within a set range.

Referring to FIG. 1, the present invention will be described in further detail with reference to the accompanying drawings and detailed description.

1. System model and related lemmas and assumptions

The vertical take-off and landing movement is a typical characteristic of unmanned helicopters as distinguished from fixed-wing aircraft. As a representative motion mode of the unmanned helicopter, the motion equation can be described as follows:

wherein g represents gravitational acceleration, m and J_fRespectively representing mass and moment of inertia, Z, of the unmanned helicopter_gAnd w_fRepresenting the altitude and velocity of the unmanned helicopter in the vertical direction, Λ_f＝[φ,θ,ψ]^TRepresenting the attitude angle vector (roll, pitch and yaw, respectively), omega_f＝[p,q,r]^TRepresenting the attitude angular rate vector, H, in a collective coordinate system_fRepresenting the attitude change matrix, T_mrSum-sigma_f＝[Σ_xf,Σ_yf,Σ_zf]^TRespectively, the control force and the moment acting on the unmanned helicopter.

Actuator failure problems often occur in practice due to long-term operation of the actuator and mechanical wear. Actuator failure faults, common in unmanned helicopter systems, are considered herein and may be modeled as

u_f＝ρ_fu (2)

Wherein

Is the control input vector, p, to be designed_f＝diag{ρ₁,ρ₂,ρ₃,ρ₄}，ρ_i(i 1.., 4) is the ith^thUnknown residual control efficiency of each actuator and satisfies 0 < rho_i≤1。

Definition of

And (3) combining the steps (1) to (3) and simultaneously considering the influence of system uncertainty, rewriting the altitude and attitude combined dynamic model of the unmanned helicopter into the following form:

wherein Δ F (N)_f) Representing the total uncertainty of the system and y is the system output.

To facilitate robust fault tolerant control scheme design for unmanned helicopter systems, the following assumptions and reasoning are given to achieve the desired control objectives.

Assume that 1: desired track signal y_dAnd its derivative are bounded. Furthermore, all of the closed loop systemsThe states are both measurable and usable.

Assume 2: the roll and pitch angles of the helicopter satisfy inequality constraints, i.e.

And

introduction 1: as a linear parameterized neural network, radial basis function neural networks are often used to approximate an arbitrary unknown continuous function v (Z), which can be expressed in terms of its form

Wherein Z ∈ RⁿAnd

respectively representing the estimated values of the input vector and the weight matrix of the neural network, gamma is the approximation error of the radial basis function neural network,

is a vector of the basis functions,

is usually selected as

Where i ═ i1, i2]^TAnd ζ_iThe center and width of the gaussian function, respectively.

Based on the above analysis, the radial basis function neural network can approximate any smooth continuous function v (Z) on the tight set to

Wherein W^*Is an ideal weight matrix, and W^*Is to satisfy

The error of the approximation of (a) is,

next we give a definition of the preset properties. The purpose of the preset performance is to guarantee the tracking error e_y＝y-y_dTransient and steady state performance. If the tracking error e_yThe preset performance can be guaranteed by varying all the time within the following preset ranges:

-λ_f1iχ_fi(t)＜e_yi＜λ_f2iχ_fi(t),i＝1,2,3,4 (8)

wherein e_y＝[e_y1,e_y2,e_y3,e_y4]^T，λ_f1iAnd λ_f2iIs a parameter to be designed and satisfies lambda_f1i∈(0,1]，λ_f2i∈(0,1]。χ_fiIs a performance function expressed as

χ_fi(t)＝(χ_fi0-χ_fi∞)exp(-δ_fit)+χ_fi∞,i＝1,2,3,4 (9)

Wherein, delta_fi> 0 and χ_fi0＞χ_fi∞> 0 is a normal number. According to chi_fi(t) definition, it can be seen that ×,/_fi(0)＝χ_fi0，

At the same time, let us know chi_fi(t) is a positive, smooth, bounded monotonically decreasing function.

To accomplish control performance, the inequality constraint is transformed into an equality form using an error transfer function as follows:

wherein beta is_fiIs a transition error variable, Q (-) is an increasing function and has the following properties:

i)Q(·):(-λ_f1i,λ_f2i)→(-∞,∞),ii)

2, leading: for error variable e_yiAnd a conversion error variable beta_fiIf beta is_fiAnd bounded, the preset performance (8) is satisfied for all t ≧ 0.

2. Safety flight control scheme design based on preset performance

2.1 error transfer function design

Taking into account the increasing nature of the smoothing function Q (-) an error transformation function β of the form_fi(i-1, 2,3,4) to ensure e_yiThe preset performance of (2):

wherein α (e)_yi(0)/χ_fi(0) Is satisfied with

For convenience, let α_i＝α(e_yi(0)/χ_fi(0)). The error transfer function (11) can then be rewritten as

For beta is_iDerived with respect to time t

Definition of beta_f＝[β_f1,β_f2,β_f3,β_f4]^T，χ_f＝diag{χ_f1,χ_f2,χ_f3,χ_f4H and Π_f＝diag{Π_f1,Π_f2,Π_f3,Π_f4Is obtained by

Considering e_y＝y-y_dAnd y ═ M_fEquation (15) can be further written as

Combining the converted error dynamics equation (19) with the unmanned helicopter system (3) yields:

due to the variable χ_f，Π_fAnd e_yAre known and can therefore be applied directly to control designs. And then, under the framework of backstepping control, a self-adaptive neural network fault-tolerant control scheme is designed for the converted system (17), the designed controller can ensure the safety and stability of the original unmanned helicopter system (3), and the output error is changed within a set range all the time.

2.2 virtual controller design

For the purpose of analysis, the composite unmanned helicopter dynamic model (17) is rewritten to

Wherein I_f＝diag{1,1,1,1}，U_f1＝G_fU_f。

To cope with actuator faults and compensate for their negative effects, an auxiliary system is constructed with the same dimensions as (18) as follows:

wherein P is_f1∈R^4×4And P_f2∈R^4×4For positively determined symmetrical matrices to be designed, ζ_f1∈R⁴And ζ_f2∈R⁴To assist the internal state of the system.

Due to actuator failure factor ρ_fUnknown, hence the coupling term (p)_f-I_f)U_f1It cannot be used directly. Thus, based on theorem 1, the radial basis function network takes the form of_f1(ρ_f-I_f)U_f1Performing an approximation of the form:

wherein

For the matrix to be designed, W₁ ^*The ideal weight matrix is represented by a matrix of weights,

to satisfy

And c is₁A gaussian function of > 0 and a high frequency,

is an approximation error and satisfies

In combination with (19) - (20), a practical auxiliary system of the form:

wherein

Is W₁ ^*An estimate of (d).

According to the proposed assistance system (21), an error variable is defined as

z_f1＝β_f-ζ_f1 (22)

z_f2＝N_f-N_fd-ζ_f2 (23)

Wherein N is_dIs a virtual control law to be designed.

To z_f1The derivation is carried out and the calls (18), (19) and (21) are obtained

Design virtual control law N_fdIs composed of

Wherein

Is a matrix of designs.

Substituting (25) into (24) to obtain

2.3 robust fault tolerant flight control scheme design

Considering (18) and (23), z can be obtained_f2Is a derivative of

Due to system uncertainty Δ F (N)_f) Is unknown, and the following form of radial basis function neural network is constructed and approximated by combining the theorem 1, and the following form of radial basis function neural network can be obtained

Wherein

For a matrix to be designed, the matrix

The ideal weight matrix is represented by a matrix of weights,

is at c₂When is greater than 0, satisfy

The function of the gaussian function of (a) is,

is at the same time

When it is satisfied with

The error is approximated by the neural network.

Substituting (28) into (27) to obtain

Wherein

Representing the approximation error.

Designing an adaptive robust fault-tolerant controller as

Wherein

For the matrix to be designed, the matrix is,

represents W₂An estimate of (d).

Because of U_f1＝G_fU_fThen the actual control input is

Substituting equation (30) into (29) can result in

Wherein

Indicating the estimation error.

Choosing a Lyapunov function as:

wherein

And

is a parameter to be designed.

Considering (21), (26) and (31), and taking the derivative of (33) to obtain

In combination with the Young's inequality, equation (34) may be further written as

Design of

And

is the parameter update law of

Wherein

And

is a constant to be designed.

Considering (36) and (37), the following inequality can be obtained:

substituting the inequality into (35) can obtain:

the parameter to be designed satisfies K_f2≥I_fAnd 2P_f2≥I_fAt the same time have

2.4 stability analysis

The above analysis design process can be summarized as theorem 1 as follows:

theorem 1: the method comprises the step of considering a vertical take-off and landing mode system model of the unmanned helicopter, wherein the vertical take-off and landing mode system model simultaneously has system uncertainty and actuator faults. The error transfer function is chosen as (11), the auxiliary system is designed as (21), and the parameter adaptation law is chosen as (36) - (37). Under the action of the robust fault-tolerant controller (30), the overall closed-loop system signal is bounded. At the same time, the tracking error e_yAlways varying within a preset performance range (8).

And (3) proving that: from equation (38), the adaptive control scheme (30) is designed to ensure the bounding of all closed loop system signals. Further, from (38) can be obtained

Considering the Lyapunov function V_fCan be given by

This means that when t → ∞ the tracking error z_f1Satisfy the requirement of

Also, we can get

Due to beta_f1＝z_f1+ζ_f1Thus obtaining

From equation (41) and theorem 2, the tracking error e can be derived_yRemain within the preset performance (8).

The present invention has been described in terms of specific examples, which are provided to aid understanding of the invention and are not intended to be limiting. Any partial modification or replacement within the technical scope of the present disclosure by a person skilled in the art should be included in the scope of the present disclosure.

Claims (1)

1. A preset performance control method of an unmanned helicopter is characterized by comprising the following steps:

(1) introducing system uncertainty and actuator faults into a nonlinear system model of the unmanned helicopter, and simultaneously converting inequality constraints of tracking errors into equality problems by adopting an error conversion function method for processing;

(2) transforming the model established in the step (1), and approximating the system uncertainty by adopting a neural network method; meanwhile, an auxiliary system is constructed to solve the problem of failure fault of the actuator, so that the fault tolerance of the system is improved;

(3) and (3) combining the technologies in the step (1) and the step (2), designing the robust fault-tolerant controller of the unmanned helicopter under the framework of a backstepping method, and ensuring that the tracking error of the system can be changed in a set range all the time under the condition that the unmanned helicopter system faces complex environments such as system uncertainty, actuator faults and the like.

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