In this paper, an adaptive sliding mode tracking control scheme is developed for the medium-scale unmanned autonomous helicopter with system uncertainties and external unknown disturbances. A simplified mathematical model is established, which is divided into position subsystem and attitude subsystem. The uncertainty term of the system is handled by the inherent approximation ability of the neural network. The sliding model control scheme under the backstepping frame is developed for tackling disturbances. The stability of the simplified system is proved by using the Lyapunov theory, and the tracking errors are guaranteed to be uniformly bounded. Numerical simulation results show that the proposed control strategy is effective.
The unique flight capabilities of unmanned autonomous helicopters (UAHs), such as vertical take-off and landing, hovering, low-altitude flying, make them have an irreplaceable position in military and civil fields. The UAHs are widely used in battlefield reconnaissance, information collection, earthquake relief, and fire detection [
Recently, some efficient control methods have been explored and utilized for the UAH [
SMC has the advantages of fast response, insensitivity to system parameter changes, good adaptability to unmodeled dynamics and external disturbances, and the design is simple and easy to implement [
On the other hand, NNs have been widely used as universal approximators to compensate the unmodeled dynamics of the system [
In [
This paper is motivated by the tracking control of the UAH with the effect of unknown uncertainties and disturbances. The adaptive SMC scheme based on the NN is developed for tracking reference trajectory.
The rest of this paper is organized as follows: in Section
In this paper, the medium-scale UAH is regarded as a rigid-body model. Then, the simplified nonlinear dynamic model of the 6 degrees of freedom (DOF) can be expressed as follows [
Considering the system uncertainties and external disturbances, system (
Define
In view of the problem of handling the UAH robust trajectory tracking control, the relevant assumptions and lemmas are described as follows.
[
[
[
[
[
The continuous function
Borrowing the backstepping control method, the inner-outer-loop control scheme is adopted in this section. The position loop is considered as an outer loop; then, the attitude loop is considered as an inner loop.
In this section, an adaptive SMC based on RBFNN will be established for the UAH position system.
Consider (
Differentiating
Consider the Lyapunov function candidate
Its time derivative is
Choose the following virtual control law as
Substituting (
Consider the second equation in (
Substituting (
Differentiating
Define the sliding surface as
Then, the time derivative of
Choose the Lyapunov function candidate
Its time derivative is
Choose the Lyapunov function candidate
The time derivative of
Choose the following SMC law as
Substituting (
The time derivative of
Then, we obtain
The updated law of the NN is designed as
Substituting (
Consider the following inequality:
Substituting (
It is well known that the control input
Define
The inequality (
Considering the underactuated characteristics of the UAH, it is necessary to calculate the reference roll angle and the reference pitch angle of the attitude subsystem with the virtual control input of the position subsystem.
Define
Considering
Similar to the position system, the control law based on SMC and RBFNN will be designed to achieve the purpose of tracking the reference attitude signal.
Consider (
Differentiating
Choose the Lyapunov function candidate
Its time derivative is
Choose the following virtual control law
Substituting (
Similar to the position subsystem,
Substituting (
Differentiating
Define the sliding surface as
Then, the time derivative of
Choose the Lyapunov function candidate
Its time derivative is
Consider the Lyapunov function candidate
The time derivative of
Choose the following virtual control law as
Substituting (
The time derivative of
The updated law of the NN is designed as
Substituting (
Considering the following inequality:
Substituting (
Similar to the position loop, the approximation function is used to replace a symbolic function, the proof is the same as before (
Consider the Lyapunov function candidate of the overall closed-loop system
Consider (
From (
In this section, the simulation results are presented to investigate the effectiveness of the proposed adaptive SMC scheme for the medium-scale UAH with model uncertainties and external unknown disturbances. The parameters of the medium-scale UAH are given as
In order to illustrate the effectiveness of the proposed control scheme, two different simulation cases are studied based on these state conditions.
The initial state conditions are assumed as
Figure
The initial state conditions are assumed as
Tracking result of the position control for Case
Tracking result of the attitude control for Case
The control inputs of thrust and moments for Case
Tracking result of the position control for Case
Tracking result of the attitude control for Case
The control inputs of thrust and moments for Case
It can be observed from tracking results for two cases that the position and the attitude angles can track the desired trajectory in a satisfactory way in the presence of system uncertainties and external unknown disturbances. We note that the system has strong robustness. From Figures
In this paper, an adaptive sliding controller has been developed for the UAH system on the basis of the neural network and backstepping, which can make the UAH tracks the desired trajectory accurately even if it has the parameter uncertainties and the external disturbances. Firstly, a mathematical model has been established and simplified appropriately. Then, an adaptive sliding mode controller has been designed for tackling the unknown disturbances. In addition, the RBFNN has been utilized to estimate the UAH system uncertainty. Finally, the proposed control scheme can ensure that all signals of the closed-loop system are uniformly bounded by using the Lyapunov analysis method. The effectiveness of the method has been verified by simulation.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported in part by the National Natural Science Foundation of China under Grant no. 61533008, in part by the Natural Science Foundation of Jiangsu Province of China (BK20171417), and in part by the Aeronautical Science Foundation of China under Grant no. 20165752049.