An adaptive neural network dynamic inversion with prescribed performance method is proposed for aircraft flight control. The aircraft nonlinear attitude angle model is analyzed. And we propose a new attitude angle controller design method based on prescribed performance which describes the convergence rate and overshoot of the tracking error. Then the model error is compensated by the adaptive neural network. Subsequently, the system stability is analyzed in detail. Finally, the proposed method is applied to the aircraft attitude tracking control system. The nonlinear simulation demonstrates that this method can guarantee the stability and tracking performance in the transient and steady behavior.
Flight control design for aircraft continues to be one of the most important problems in the world of automatic control. The problem is driven by the nonlinear and uncertain nature of aircraft dynamics. Traditionally, the solution to this problem is to design the linear controller using linearized aircraft models at multiple trimmed conditions. And this procedure is time consuming and expensive.
Control of aircraft by dynamic model inversion is well known and has been applied to the control of high angle of attack fighter aircraft [
The asymptotic tracking can be achieved using this method. However, the transient behavior of the output signals could be oscillatory when the tracking error magnitude is decreased by increasing the adaption rate. Several solutions [
It is very important for aircraft to track the attitude command with a desired transient and steady performance, when the aircraft finishes the special flight tasks, such as automated aerial refueling [
In this paper, we will investigate the aircraft attitude control problem of guaranteeing transient and steady performance in the adaptive compensation control system. By employing the prescribed performance bounds proposed in [
The paper is organized as follows: the problem and the control configuration are introduced in Section
The aircraft nonlinear attitude dynamic model can be presented as
Substituting (
Substituting (
The aircraft attitude model shown in (
The state tracking error is defined as
The proposed control architecture of the aircraft attitude control system is shown in Figure
Adaptive neural network dynamic inversion with prescribed performance architecture.
This section will show a brief introduction of dynamic inversion. And the readers could derive much more details from the reference [
We seek to linearize a nonlinear system through computing dynamic inversion to cancel the nonlinearities in the system. The aircraft dynamics are shown in (
The achieved system dynamics will match the chosen desired dynamics when there are no errors between the design model and real object. However, the model error is inevitable. So a new method is proposed to compensate the model error and guarantee the system performances in the transient and steady behavior.
A smooth function
For example, a performance function is
Then by satisfying the following condition:
According to (
By changing the parameters of performance function
To transform the original system with the constrained tracking error performance (in (
According to the first property in (
According to (
In addition, from the third property in (
Then (
Consider system in ( The system in ( Stabilization of the transformed system using (
In what follows, an adaptive neural network dynamic inversion method is proposed to stabilize the transformed system using (
The desired states
The states
We define the following error function
We define
The derivative of (
And the second derivative of (
Then we compute the time derivative of
And the pitch and yaw errors are derived by the similar method.
Substituting (
Then we can derive
To simplify the controller design progress, we linearize (
According to (
The formula
Because there are three channels in the attitude control and the form of each channel is the same, consider the following Theorem
Considering Assumption
The control input of roll channel is
The adaptive signal of roll channel is
The neural network weight update law of roll channel is
A suitable Lyapunov function of roll channel will be
Firstly, if
Substituting (
Considering (
Let the control input
Substituting (
By using the norms of the terms on the right side of (
In addition, the approximate error of neural network is bounded, so the following equation is satisfied:
The maximum weight of ideal neural network in the roll channel is
Substituting (
Considering (
If the system is stable, then
Next, if
Here the weight update law is
This completes the proof.
According to (
We define the model error
Then (
Substituting (
Comparing (
Therefore, the model error mainly depends on the different equilibrium points, attitude angles, actuator deflections, and so on.
The first step in determining the appropriate network structure is identifying the network inputs. Based on the analysis of model error sources described in Section
A Sigma-Pi neural network [
And a general description of the neural network is shown in Figure
Neural network structure.
And the basis function of roll channel
In this section, we consider the attitude angles control problem for a fixed-wing aircraft, and the initial flight state is the wings-level flight. Then the attitude angles commands in three channels will be tracked, respectively.
In the following simulation, the initial flight height and velocity are 6000 m and 190 m/s, and the initial attitude angles and angular rates including
The error transformation function [
The attitude angles commands of three channels are transformed into the desired attitude angles commands through the command filters. And the structure of command filter for the roll channel is shown in Figure
Command filter.
The command filter parameters are set as
Design the control inputs with prescribed performance for three channels through the procedures in Section
Performance parameters.
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−12° |
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−8° |
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−10° |
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−0.3° |
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−0.2° |
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−0.2° |
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0.7 |
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0.7 |
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0.7 |
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0.6 |
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0.5 |
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0.6 |
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1 |
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1 |
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1 |
Controller parameters.
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10 |
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10 |
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10 |
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200 |
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200 |
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50 |
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0.1 |
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0.1 |
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0.3 |
For the performance function
For the controller parameters, the adaptation gain
The design model I is derived at the trimmed flight condition of 6000 m and 190 m/s, and the model error is small.
The aircraft tracks the attitude angles commands from the initial flight state. And the attitude angles tracking responses and tracking errors are shown in Figures
Responses of the attitude angles.
Tracking errors of the attitude angles.
The two methods have achieved the attitude angles command tracking. Figure
In the real flight control system, there must be the model error. In order to verify that the similar tracking performance is also achieved when there is the large model error, we have conducted the following simulation study.
The flight condition is the same, and the initial flight height and velocity are 6000 m and 190 m/s. However, the design model II used to design the attitude angles controllers is derived at the trimmed flight condition of 4000 m and 150 m/s. Apparently, the model error is large.
And the attitude angles tracking responses and tracking errors are shown in Figures
Responses of the Attitude angles with model error.
Tracking errors of the attitude angles with model error.
Figures
The control actuators deflections for three channels are compared in Figure
Deflections of the control actuators in two design models.
Figure
The outputs of neural network in three channels.
Figure
In this paper, an adaptive neural network dynamic inversion with prescribed performance method is proposed for aircraft attitude control. By incorporating the adaptive neural network dynamic inversion with the prescribed performance concept, the proposed method guarantees the system tracking error satisfies the prescribed performance bound in the transient and steady behavior. The nonlinear simulation of the aircraft also verifies the effectiveness of the proposed approach.
Further investigation is needed for the situations in the presence of the external wind disturbance and unmodeled dynamics. And, these design parameters in this method should be decreased and optimized to achieve a real application.
This work was supported by the Program for New Century Excellent Talents in University (Grant no. NCET-10-0032) and by the National Natural Science Foundation of China (Grant no. 61175084).