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The present paper addresses an attitude tracking control problem of a ducted fan microaerial vehicle. The proposed indirect adaptive controller can greatly reduce tracking error in the initial stage of the adaptive learning process by using an error compensation strategy and can achieve good capability to eliminate the adverse effect of measurement noises on the convergence of adjustable parameters. Moreover, the learning rate adaptation strategy is proposed to further minimize the adverse effect of large learning rates on the convergence of adjustable parameters. The experimental tests have illustrated the effectiveness of the proposed adaptive controller.

Ducted fan microaerial vehicles (MAVs) are a kind of unmanned aerial vehicles with small sizes and compact structures, which are usually capable of low-speed flight in addition to the normal hover and vertical takeoff and landing capabilities. With both military and civilian applications, they have a great technological potential in arduous or hazardous mission like surveillance, inspection, exploration, intelligence reconnaissance, target acquisition, and signal relay [

Ducted fan aerodynamics has been widely explored on the piloted aerial vehicle platforms in the mid-20th century [

Great effort has been made for ducted fan MAVs, including optimal design [

Other existing methods include linear-quadratic regulator (LQR) and particle swarm optimization (PSO) [

This paper focuses on the attitude tracking control problem of a ducted fan MAV. An indirect adaptive control scheme is proposed in the presence of parametric uncertainties and measurement noises. The proposed adaptive control scheme is able to effectively reduce the tracking error in the initial stage of the adaptive learning process and eliminate the adverse effect of measurement noises on the convergence of adjustable parameters. Moreover, a learning rate adaptation strategy is proposed to further minimize the adverse effect of large learning rates on the convergence of adjustable parameters.

This paper is organized as follows. Section

This study is based on a small-size ducted fan VTOL MAV model shown in Figure

Ducted fan VTOL MAV.

For this ducted fan MAV, six-degree-of-freedom (6-DOF) nonlinear kinematic equations can be defined as follows:

The nonlinear system described by (

Apparently, the complexity of the control design mainly comes from the fact that

The goal of this study is to design a reliable and robust attitude controller for the ducted fan MAV in the presence of parametric uncertainties and measurement noises.

In general, the ducted fan MAV can be roughly regarded as a four-axis vehicle, that is, vertical, longitudinal, lateral, and directional axes. Each axis can then be controlled independently with interactions with others. In particular, the longitudinal and lateral axes have the same properties because the MAV is central symmetrical. To avoid repetition, the present study is focused on the longitudinal axis in the hovering flight condition to demonstrate the proposed control scheme, which, without loss of generality, can apply to other axes. Thus, referring to (

With respect to the ducted fan MAV, there exist

The schematic block diagram of the indirect adaptive attitude tracking controller is constructed, as shown in Figure

Control system block diagram.

Unlike most existing adaptive schemes, the mathematical model is regarded as the adjustable system substituting for the generalized plant in the abovementioned adaptive control scheme. The purpose is to eliminate the adverse effect of measurement noises on the convergence of adjustable parameters, which will be discussed in detail in the following sections. The error compensation module is introduced to reduce the tracking error especially in the initial stage of the adaptive learning process, but, on the other hand, this module also decreases adaptive learning rates because of the insignificant tracking error.

The generalized plant and the adjustable system model are given as follows:

From Figure

The system described by (

For this purpose, the indirect adaptive control laws are specified by

The adaptive control laws given by (

According to the Aeronautical Design Standard (ADS-33) Performance Specification, we assume that the ideal model is specified by the input-output relation

The output of the generalized plant can therefore track that of the ideal model based on the above adaptive strategies given by (

Denote

Thus,

However, if the generalized plant is regarded as an adjustable system substituting for the mathematical model in Figure

Although the indirect adaptive control strategy has been employed, the tracking error

Based on the a priori knowledge of the ducted fan MAV parameters, the proper choice of

Note that in (

To avoid this problem, the adaptive laws need to be improved through learning rate adaptation. The learning coefficient

In conclusion, the indirect adaptive control algorithm now proceeds as follows: first, adjust the adjustable parameters of the mathematical model using (

In this section the performance of the proposed indirect adaptive control strategy is demonstrated by a series of numerical simulations and flight tests, shown in Figure

Flight test.

All flight tests begin with the trim conditions given as follows:

ideal model:

error compensator:

proportional and differential coefficients:

initial values:

learning rates:

Three different tests have been conducted to demonstrate the advantages of the indirect adaptive controller. The performance of the proposed controller is also compared with other existing controllers designed with the same assumptions.

The numerical simulation uses a model of the MAV, as proposed by Ning [

Numerical simulation results.

Pitch angle

Tracking error with noise

The noise-free tracking error (

Parameter learning process for

Parameter learning process for

The proposed controller is now demonstrated by using the full MAV dynamics. The performances of the controller with error compensation are shown in Figure

Flight test results with error compensation.

Pitch angle

Tracking error

Parameter learning process for

Parameter learning process for

Compared with the above numerical simulation results, adjustable parameters exhibit considerable variation because the complete model with actuator dynamics and the saturation constraints on the inputs have been incorporated during the flight test. However, adjustable parameters converge fast because the significant tracking error can accelerate the adaptive learning rates. Note that the tracking performance and the convergence of adjustable parameters deteriorate if the learning rate adaptation method is not employed.

The experimental results without error compensation are shown in Figure

Flight test results without error compensation.

Pitch angle

Tracking error

Parameter learning process for

Parameter learning process for

The experimental results of the existing adaptive controller without any noise reduction strategy in [

Flight test results of the existing adaptive controller in [

Pitch angle

Tracking error

Parameter learning process for

Parameter learning process for

The results also demonstrate that the existing controller lacks robustness in the presence of measurement noises, though the adaptive algorithm uses a combination of low- and high-pass filters.

The experimental results show that the indirect adaptive controller effectively solves the unbiased and convergent problem of adjustable parameters caused by the measurement noises and therefore achieves satisfactory tracking performance. Figure

This paper presents the detailed design of the indirect adaptive attitude tracking controller for the ducted fan MAV. The proposed indirect adaptive controller is stable and robust and shows significant improvement in performance over the existing adaptive controllers in the presence of measurement noises. It is able to effectively reduce the tracking error in the initial stage of the adaptive learning process because of the error compensation strategy and overcome the effect of measurement noises on the convergence of adjustable parameters. Moreover, the learning rate adaptation strategy can further minimize the effect of large adaptive learning rates on the convergence of adjustable parameters. The experimental results have verified the proposed adaptive controller.

System matrix

Plant parameters

Adjustable model parameters

Control matrix

Characteristic polynomial of

Expectation

Equivalent trim disturbance

Estimate errors of trim input and trim state vectors

Tracking error

Nonlinear kinematic function

Adjustable parameter vector

Adjustable parameters

Coefficients of error compensator

Aerodynamic parameter

Aerodynamic parameter vector

Linearized roll, pitch, and yaw rates, deg/s

Roll, pitch, and yaw rates, deg/s

System input and its linearized version

Trim input and nominal trim input

Linearized forward, lateral, and vertical velocities, m/s

Forward, lateral, and vertical velocities, m/s

State vector and its linearized version

Trim state and nominal trim state

Increment or difference

Equivalent input disturbance

Input disturbance vector

Linearized pitch, roll, yaw, and throttle control, deg

Plant input, deg

Adjustable system input, deg

Manipulated input, deg

Pitch, roll, yaw, and throttle control, deg

Generalized error with noise

Noise-free generalized error

Unknown input disturbance

Positive constant

Uncertain aerodynamic parameter set

Linearized pitch, roll, and yaw angles, deg

Unknown true value of pitch angle, deg

Adjustable system output, deg

Pitch derivative and its unknown true value, deg/s

Pitch, roll, and yaw angles, deg

Adaptive learning rate

Differential or proportional coefficient

Measurement noise.

Adjustable model parameters

Pitch

Pitch rate

Roll

Throttle

Forward velocity

Vertical velocity

Yaw

Roll cyclic

Main rotor collective

Generalized error

Input disturbance

Pitch angle

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study was supported by the Fundamental Research Funds for the Central Universities under Grant no. NS2013032. The authors would like to thank two anonymous reviewers for helpful comments.