CN114035597A - Self-adaptive global sliding mode fault-tolerant control method based on Barrier function - Google Patents

Abstract

The invention discloses a novel Barrier function-based adaptive global sliding mode fault-tolerant control method. For four rotor unmanned aerial vehicle systems executor trouble takes place, combine together global sliding mode face with the self-adaptation sliding mode control based on Barrier function, omitted the approach process of traditional Barrier self-adaptation sliding mode motion stage one, promoted the rapidity and the accuracy of algorithm. Secondly, the Barrier function self-adaptive law is used for adjusting the gain of the switching item, so that the gain of the controller can be timely and accurately changed along with the change of the amplitude of the total disturbance, the over-estimation problem is avoided, and the buffeting of the control signal is reduced. The method is used for Barrier self-adaptive global sliding mode fault-tolerant control of the quad-rotor unmanned aerial vehicle with the actuator fault.

Description

Self-adaptive global sliding mode fault-tolerant control method based on Barrier function

Technical Field

The invention relates to a Barrier function-based adaptive global sliding mode fault-tolerant control method, and belongs to the technical field of nonlinear system fault-tolerant control.

Background

In recent years, because of the wide application of quad-rotor unmanned aerial vehicles in the aspects of agricultural production, data acquisition, logistics distribution and the like, research on quad-rotor unmanned aerial vehicles draws more and more attention. Compared with the traditional aircraft, the quad-rotor unmanned aerial vehicle has the advantages of light weight, simple structure, hovering property, easy maintenance and the like, and is the aircraft with the widest application range. However, control of quad-rotor drones remains a challenge because quad-rotor drones are typically non-linear systems and suffer from model uncertainty, external disturbances, and the like. In addition, four rotor unmanned aerial vehicle is possible to take place executor trouble in flight process, and this has more increased the degree of difficulty of controller design. The failure that unmanned aerial vehicle took place can reduce the performance of aircraft, even causes the failure of task, therefore design four rotor unmanned aerial vehicle's fault-tolerant control just seems to be very important.

Sliding mode control is widely used in fault tolerant control of various objects due to its insensitivity to external disturbances and parameter perturbations. For example, for an unmanned ship with signal quantization and time delay, the fault-tolerant control of the unmanned ship is realized by combining an adaptive sliding mode and a dynamic quantization parameter compensation strategy; some researchers propose a control strategy combining an adaptive fuzzy integral sliding mode and a disturbance observer, and apply the control strategy to the fault-tolerant control of the mechanical arm. However, to achieve accessibility to the sliding mode surfaces, a sufficiently high gain needs to be chosen to counter the total perturbation in the model, which is usually time-varying, and therefore when the total perturbation becomes small, strong control-law chatter is generated due to gain overestimation. In order to reduce buffeting, researchers have proposed a number of methods, the most common of which is boundary layer technology, namely, normal sliding mode control is adopted outside the boundary layer, and feedback control in a continuous state is adopted in the boundary layer, so that buffeting is effectively avoided or weakened, but the precision and the anti-disturbance capability of a controller are weakened. In the conventional sliding mode control, a large switching gain is often needed to eliminate the external disturbance and the uncertainty, so that a disturbance observer can be designed to estimate the external disturbance and the uncertainty in real time, thereby greatly reducing the gain of the switching term in the sliding mode controller and effectively eliminating buffeting. The switching function in the conventional sliding mode control method generally only depends on the system state and is irrelevant to control input, discontinuous items can be directly transferred to a controller, the switching function in the conventional sliding mode control method forms a new switching function through a differential link in the dynamic sliding mode method, the switching function is relevant to the first order or high order derivative of the control input of the system, the discontinuous items can be transferred to the first order or high order derivative of a control signal, a dynamic sliding mode control law which is essentially continuous in time is obtained, and buffeting is effectively reduced. In addition, a filtering technology is adopted to generate continuous equivalent control input to replace switching operation, but the influence of a filtering time constant on the system response is large, and the adjustment and the reference in practical application are difficult. Adaptive control is often used to adjust the control gain, which increases continuously when the sliding mode motion is in an approaching state; when the sliding mode surface is reached, the control gain remains unchanged. However, if the perturbation starts to decrement at a certain moment, this algorithm still has the problem of over-estimation. The scholars propose an improved adaptive sliding mode control, when the disturbance is reduced, the control gain is reduced, and the overestimation problem is avoided, however, the convergence error of the method depends on the disturbance amplitude, and the disturbance amplitude is unknown and is difficult to obtain in advance.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the research background, a novel Barrier function self-adaptive global sliding mode fault-tolerant control method for a pitching subsystem of a quad-rotor unmanned aerial vehicle is provided. The global sliding mode surface is combined with the self-adaptive sliding mode control based on the Barrier function, the approach process of the first motion stage of the traditional Barrier self-adaptive sliding mode is omitted, and the rapidity and the accuracy of the algorithm are improved. Secondly, the Barrier function self-adaptive law is used for adjusting the gain of the switching item, so that the gain of the controller can be timely and accurately changed along with the change of the amplitude of the total disturbance, the over-estimation problem is avoided, the buffeting of a control signal is reduced, and the control quality is improved.

The technical scheme is as follows: the utility model provides a novel Barrier function self-adaptation global sliding mode fault-tolerant control method to four rotor unmanned aerial vehicle every single move subsystems which characterized in that: aiming at the problem of control gain over-estimation in the traditional adaptive sliding mode control, the invention adopts the adaptive sliding mode fault-tolerant control based on the Barrier function, and the gain of the Barrier adaptive controller can be timely and accurately changed along with the change of the amplitude of the total disturbance, thereby avoiding the problem of gain over-estimation; aiming at the problem that control gain overestimation and robustness deterioration still exist in the approaching process of the traditional Barrier adaptive sliding mode control in the first stage, the global sliding mode surface is constructed and combined with the Barrier adaptive law, so that the sliding mode surface is in the small neighborhood of the zero point at the beginning, the approaching process of the traditional Barrier adaptive sliding mode motion stage I is omitted, and the rapidity and robustness of the algorithm are improved.

A Barrier function self-adaptive global sliding mode fault-tolerant control method for a pitching subsystem of a quad-rotor unmanned aerial vehicle comprises the following specific steps:

step 1) determining a mathematical model of a pitching subsystem of a quad-rotor unmanned aerial vehicle with an actuator fault:

wherein phi, theta and psi are respectively roll angle, pitch angle and yaw angle, J_xx，J_yy，J_zzRespectively the moment of inertia of three axes under the coordinate system of the machine body, J_rOmega is the difference between the rotating speed of the No. 2 and No. 4 motor and the rotating speed of the No. 1 and No. 3 motor, k is the air resistance coefficient, g_ΔTo control perturbation of gain, u_FFor pitch control input with fault, d (t) for external disturbance, let x for ease of controller design₁＝θ，

Equation (1) is written as the state space equation:

wherein x ═ x₁，x₂]^T∈R^2×1Is a variable of the state of the system,

it can be measured by a sensor or sensors,

is a non-linear function that is not known,

g_Δ(x) To control the gain perturbation, D (t) is the external time-varying perturbation, u is the actuator control input, F (x, t) is the actuator fault input, let D ═ F_Δ(x)+g₀F(x，t)+g_Δ(x)u+g_Δ(x) F (x, t) + d (t) is the total perturbation of the system, then (1) can be written as:

step 2) setting the expected signal of the system (1) as x_d＝(x_1d，x_2d)^T，

And x_2dCan lead, then error signal e ═ x₁-x_1d，

The following global sliding mode surfaces are designed:

wherein c > 0, e (0) and

for the error signal at the initial time, exp (·) is a natural exponential function, and equation (4) is derived and equation (3) is substituted to obtain:

let D equal to 0 to obtain the equivalent control law

In order to enable the system state to reach the pre-designed sliding mode surface, the following arrival control law is designed:

wherein

For Barrier adaptive parameters, the design is as follows:

finally, the self-adaptive control law of the obtained Barrier function is as follows:

u＝u₀+u₁ (9)

under the action of a control law (9), the closed loop of the whole system is stable, and the sliding mode surface defined by the formula (4) meets | s | ≦ epsilon in a limited time.

Has the advantages that: for four rotor unmanned aerial vehicle systems executor trouble takes place, combine together global sliding mode face with the self-adaptation sliding mode control based on Barrier function, omitted the approach process of traditional Barrier self-adaptation sliding mode motion stage one, promoted the rapidity and the accuracy of algorithm. Secondly, the Barrier function self-adaptive law is used for adjusting the gain of the switching item, so that the gain of the controller can be timely and accurately changed along with the change of the amplitude of the total disturbance, the over-estimation problem is avoided, and the buffeting of the control signal is reduced. Overall, the following specific advantages are provided:

firstly, aiming at the problem that the control gain of a general self-adaptive sliding mode fault-tolerant algorithm is over-estimated, a self-adaptive gain based on a Barrier function is adopted, and the self-adaptive gain can change along with the change of a total disturbance amplitude value, so that the over-estimation problem of the control gain is avoided;

the traditional self-adaptive sliding mode control based on the Barrier function is divided into two stages, a rapidly-increased high-gain self-adaptive law adopted in the first stage also has the problem of overestimation, and the first stage is in the approaching process of a sliding mode surface, so that the robustness of the controller is reduced, and the global sliding mode surface is adopted, so that a sliding mode variable is fixed near a zero point at the initial moment, the approaching process of the traditional Barrier self-adaptive sliding mode is omitted, the overestimation problem is avoided in the whole process, and the robustness of a control strategy is improved;

the fault-tolerant control method for the four-rotor unmanned aerial vehicle system aiming at actuator faults has certain practical value, is easy to realize, good in real-time performance and high in accuracy, can effectively improve the fault-tolerant performance of the control system, is strong in operability, saves time, is higher in efficiency, and can be widely applied to actuator fault-tolerant control of the four-rotor unmanned aerial vehicle system.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a plot of Qdrone quad-rotor drone pitch angle;

fig. 3 is a plot of Qdrone quad-rotor drone pitch rate;

fig. 4 is a graph of the control signal u.

Detailed Description

The invention is further explained below with reference to the drawings.

As shown in fig. 1, for the problem of overestimation of the control gain of a general adaptive sliding mode fault-tolerant algorithm, an adaptive gain based on a Barrier function is adopted, and the adaptive gain can change along with the change of the total disturbance amplitude, so that the problem of overestimation of the control gain is avoided; aiming at the traditional self-adaptive sliding mode control based on the Barrier function, the self-adaptive sliding mode control is divided into two stages, the problem of overestimation possibly exists in a fast-growing high-gain self-adaptive law adopted in the first stage, the first stage is in the approach process of a sliding mode surface, the robustness of the controller is reduced, a global sliding mode surface is adopted, a sliding mode variable is fixed near a zero point at the initial moment, the approach process of the traditional Barrier self-adaptive sliding mode is omitted, the overestimation problem is avoided in the whole process, and the robustness of a control strategy is improved, and the method specifically comprises the following steps:

step 1) determining a mathematical model of a pitching subsystem of a quad-rotor unmanned aerial vehicle with an actuator fault:

wherein phi, theta and psi are respectively roll angle, pitch angle and yaw angle, J_xx，J_yy，J_zzRespectively the moment of inertia of three axes under the coordinate system of the machine body, J_rOmega is the difference between the rotating speed of the No. 2 and No. 4 motor and the rotating speed of the No. 1 and No. 3 motor, k is the air resistance coefficient, g_ΔTo control perturbation of gain, u_FFor pitch control input with fault, d (t) for external disturbance, let x for ease of controller design₁＝θ，

Equation (1) is written as the state space equation:

wherein x ═ x₁，x₂]^T∈R^2×1Is a variable of the state of the system,

it can be measured by a sensor or sensors,

is a non-linear function that is not known,

g_Δ(x) To control the gain perturbation, D (t) is the external time-varying perturbation, u is the actuator control input, F (x, t) is the actuator fault input, let D ═ F_Δ(x)+g₀F(x，t)+g_Δ(x)u+g_Δ(x) F (x, t) + d (t) is the total perturbation of the system, then (1) can be written as:

step 2) setting the expected signal of the system (1) as x_d＝(x_1d，x_2d)^T，

And x_2dCan lead, then error signal e ═ x₁-x_1d，

The following global sliding mode surfaces are designed:

wherein c > 0, e (0) and

for the error signal at the initial time, exp (·) is a natural exponential function, and equation (4) is derived and equation (3) is substituted to obtain:

let D equal to 0 to obtain the equivalent control law

In order to enable the system state to reach the pre-designed sliding mode surface, the following arrival control law is designed:

wherein

For Barrier adaptive parameters, the design is as follows:

finally, the self-adaptive control law of the obtained Barrier function is as follows:

u＝u₀+u₁ (9)

under the action of a control law (9), the closed loop of the whole system is stable, and the sliding mode surface defined by the formula (4) meets | s | ≦ epsilon in a limited time.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

The effectiveness of the implementation is illustrated in the following by a practical case simulation.

The selected simulation object is a Qdrone quadrotor unmanned aerial vehicle developed by Quanser in Canada, and the rationality and the effectiveness of the design scheme are verified on the aircraft. The whole set of experiment system comprises an optitrack motion sensing system, a ground station, a wireless router and a QDrone quad-rotor unmanned aerial vehicle. The OptiTrack space positioning system utilizes a plurality of infrared cameras arranged around a room to position, has high precision and is suitable for indoor environment. The simulation laboratory selects 12 OptiTrack Flex-3 motion capture cameras, and is matched with an OptiTrack Tools software system provided by the American Natural Point company and used for a 3D real-time positioning and tracking solution, so that the high-precision positioning of an indoor target can be realized. The motion capture cameras are used to obtain the position (X, Y, Z) and yaw angle ψ of the drone, while the roll angle Φ and pitch angle θ are obtained by the IMU unit on the drone. The ground workstation comprises a high-performance host and a wireless network adapter, wherein the PC host is used for realizing the detection and control of the whole four-rotor flight fault-tolerant experiment simulation system, and is provided with a QUARC real-time fault-tolerant control system developed based on Matlab simulation software. In the experiment, the simulation platform compiles and links a control algorithm of the PC host and transmits the control algorithm to the unmanned aerial vehicle through a wireless network, and then sends the position information of the four rotors, which is acquired by the OptiTrack motion capture camera, back to the PC host, so that the next control quantity is implemented, meanwhile, a nonlinear state function can be set at a ground station, and command parameters such as disturbance and fault and the like can remotely change corresponding parameter variables in the four rotor controller in real time, so that the verification of the control algorithm is realized. The main physical parameters of the Qdrone quad-rotor drone are shown in table 1.

TABLE 1 Qdrone Main parameters

Parameter(s)	Physical significance of parameters	Value of
			Jxx	Rotational inertia of rolling motion	0.01kg.m2
Jyy	Moment of inertia of pitching motion	0.0082kg.m2
			Jzz	Moment of inertia of yawing motion	0.0148kg.m2
M	Quality of	1.121kg

The mathematical model of the quad-rotor unmanned aerial vehicle pitching subsystem with the unknown nonlinear state function, controller perturbation, actuator fault and external disturbance is as follows:

wherein x ═ x₁，x₂]^T∈R^2×1Is a variable of the state of the system,

it can be measured by a sensor or sensors,

is a non-linear function that is not known,

g_Δ(x) To control gain perturbation, d (t) is the external time-varying disturbance, u is the actuator control input, and F (x, t) is the actuator fault input. In this case, the relevant model parameters are set as: f. of_Δ(x)＝0.03cos(t)sin(t)，g_Δ(x)＝0.5sin(x₁ ²)，d(t)＝＝0.5(x₁+x₂)cos(t)+0.1x₂exp(-5t)，

Indicating that an actuator failure occurred in second 10. The controller parameters are selected as follows: epsilon is 0.002, c is 5 and lambda is 10. System desired state x_d＝[0.1sin(t)，0.1cos(t)]^TInitial state x₀＝[-0.01，0.05]^T。

The simulation result of the case shows that the Barrier adaptive global sliding mode fault-tolerant control algorithm of the quad-rotor unmanned aerial vehicle system for actuator faults, which is designed by the invention, can well process the fault problem, obtain a good control effect, and well solve the problem of gain over-estimation of a controller, thereby well inhibiting buffeting of a control law. Compared with the traditional fault-tolerant control algorithm, the four-rotor aircraft body has better control performance under the action of the control method designed by the simulation of the scheme. As shown in fig. 2 and 3, both control algorithms enable tracking of the desired angle and the desired angular velocity, and the actual signal fits the desired signal again very quickly even after a failure. Because the algorithm designed by the method adopts the global sliding mode surface, the method is superior to the algorithm of the traditional method in rapidity and accuracy. In the control signal of fig. 4, the algorithm of the present disclosure adopts Barrier adaptive control law, which effectively avoids over-estimation of control gain, so that the control signal of the present disclosure greatly reduces buffeting compared with the conventional method. To more intuitively illustrate the advantages of the control algorithm herein, we enumerate three quantitative indicators, i.e., the settling time of the tracking signal, the mean square error, and the buffeting peak value of the control signal, as shown in table 2.

TABLE 2 comparison of the two methods

In conclusion, for a quad-rotor unmanned aerial vehicle system with actuator failure, the simulation control method is effective.

Claims (1)

1. A novel adaptive global sliding mode fault-tolerant control method based on a Barrier function is characterized in that: considering the problem of overestimation of control gain of a general adaptive sliding mode fault-tolerant algorithm, the adaptive gain based on the Barrier function is adopted, and can change along with the change of the total disturbance amplitude value, so that the overestimation problem of the control gain is avoided; considering that the traditional self-adaptive sliding mode control based on the Barrier function is divided into two stages, the problem of overestimation may exist in a fast-growing high-gain self-adaptive law adopted in the first stage, and the first stage is in the approaching process of a sliding mode surface, the robustness of the controller is reduced, a global sliding mode surface is adopted, so that a sliding mode variable is fixed near a zero point at the initial moment, the approaching process of the traditional Barrier self-adaptive sliding mode is omitted, the overestimation problem is avoided in the whole process, the robustness of a control strategy is improved, and the novel self-adaptive global sliding mode fault-tolerant control method based on the Barrier function comprises the following specific steps:

step 1) determining a mathematical model of a pitching subsystem of a quad-rotor unmanned aerial vehicle with an actuator fault:

wherein phi, theta and psi are respectively roll angle, pitch angle and yaw angle, J_xx，J_yy，J_zzRespectively the moment of inertia of three axes under the coordinate system of the machine body, J_rOmega is the difference between the rotating speed of the No. 2 and No. 4 motor and the rotating speed of the No. 1 and No. 3 motor, k is the air resistance coefficient, g_ΔTo control perturbation of gain, u_FFor pitch control input with fault, d (t) for external disturbance, let x for ease of controller design₁＝θ，

Equation (1) is written as the state space equation:

wherein x ═ x₁，x₂]^T∈R^2×1As system state variables，

It can be measured by a sensor or sensors,

is a non-linear function that is not known,

g_Δ(x) To control the gain perturbation, D (t) is the external time-varying perturbation, u is the actuator control input, F (x, t) is the actuator fault input, let D ═ F_Δ(x)+g₀F(x，t)+g_Δ(x)u+g_Δ(x) F (x, t) + d (t) is the total perturbation of the system, then (1) can be written as:

step 2) setting the expected signal of the system (1) as x_d＝(x_1d，x_2d)^T，

And x_2dCan lead, then error signal e ═ x₁-x_1d，

The following global sliding mode surfaces are designed:

wherein c > 0, e (0) and

for the error signal at the initial time, exp (·) is a natural exponential function, and equation (4) is derived and equation (3) is substituted to obtain:

let D equal to 0 to obtain the equivalent control law

In order to enable the system state to reach the pre-designed sliding mode surface, the following arrival control law is designed:

wherein

For Barrier adaptive parameters, the design is as follows:

finally, the self-adaptive control law of the obtained Barrier function is as follows:

u＝u₀+u₁ (9)

under the action of a control law (9), the closed loop of the whole system is stable, and the sliding mode surface defined by the formula (4) meets | s | ≦ epsilon in a limited time.

Images