^{1, 2}

^{3}

^{1, 2}

^{3}

^{1}

^{2}

^{3}

This paper presents a novel robust attack angle control approach, which can effectively suppress the impacts from system uncertainties and servo-loop dynamics. A second-order linear model of electromechanical servo loop is considered in the modeling and design processes. With regard to the block-structure models facing attack angle control, the multiple robust surfaces and dynamic surface control (DSC) approaches are both employed. By means of Lyapunov function method, the stability conditions of attack angle control systems are, respectively, given without/with considering the servo-loop dynamics in design process. Computer simulation results present that, compared with the attack angle control scheme which does not consider the servo-loop dynamics in design process, the proposed scheme can guarantee that the whole attack angle control system possesses the better comprehensive performances. Moreover, it is easy to be realized in engineering application.

In aircraft attitude control system, the existing system uncertainties, including modeling errors, parameter perturbations, and external disturbances, can badly affect the flight performances and even lead to the failure of flight task [

With regard to the aircraft flight system, the multiple robust surfaces method combined with backstepping method is generally employed [

The remainder of this paper is organized as follows. Section

Only considering the pitching channel of aircraft, the attitude motion equations are shown as follows [

Subsequently, when the servo-loop dynamics is not considered in the design period, the design model facing attack angle control is obtained as follows:

For DC electromechanical servo system, it is usually simplified into a second-order linear model, which is shown as follows:

In fact, (

Therefore, when the servo-loop dynamics is considered in the design period, the design model facing attack angle control will be transformed into

The establishment of design models (

With regard to a class of system with strict feedback form, just as system (

Owing to the simple design and strong robust property of SMC, it will be introduced in the design process of subsystem control. Furthermore, the reaching law approach [

The following two assumptions are useful in the next design and analysis.

The uncertainty terms in system are all bounded; that is,

When the DSC method is applied, the filter output

Aiming at the two-layer design model (

When the servo-loop dynamics is not considered, by means of Steps A1–A5, the actual attack angle

Choose a Lyapunov function as follows:

According to (

Substituting (

In similar, according to (

Substituting (

Obviously, the derivation of Theorem

In this subsection, aiming at the three-layer design model (

When the servo-loop dynamics is considered, by means of Steps B1–B8, the actual attack angle

Choose a Lyapunov function as follows:

According to (

Subsequently, as similar with the proof process of Theorem

According to (

According to (

In order to avoid the high-frequency chattering at control input, which resulted from the signum term in control laws, the following saturation function will be employed to replace the signum function:

It can be proved that if the signum functions are replaced by the saturation functions, the Lyapunov asymptotic stability presented in Theorems

Until now, the attack angle control laws have been finished without/with considering the servo-loop dynamics. These two control schemes will be verified and compared by means of computer simulations in the next section.

In this section, the simulation results of the proposed control scheme are compared with those of conventional control scheme, which is designed without considering the servo-loop dynamics.

In simulation, the parameters of researched aircraft are shown as follows: ^{2}. The nominal aerodynamic parameters are shown as follows:

In the selection process of control coefficients, the coefficients of low-pass filters and saturation functions can be first obtained. In concrete, the filter coefficients are selected based on the compromise between estimation accuracy on virtual command and suppression effect on “explosion of terms”; meanwhile the saturation function coefficients are selected based on the compromise between robust property of control system and smooth property of control output. As a result, we first select

When the servo-loop dynamics is not considered, the coefficients of attack angle control law are chosen as follows:

When the servo-loop dynamics is considered, the coefficients of attack angle control law are chosen as follows:

The step response of servo loop is illustrated in Figure

Step response curve of servo loop.

As seen from Figure

With computer simulation on the whole pitching control system, the comparison curves of attack angles under the two control schemes are shown in Figure

Curves of attack angles under the two control schemes.

As seen from Figure

Next, the outputs of servo loops under the two control schemes are shown in Figure

Output curves of servo loops under the two control schemes.

As seen from Figure

At this time, the control coefficients of the conventional scheme are chosen the same as with the proposed scheme; that is,

Tracking curve of attack angle under the conventional control scheme.

As seen from Figure

With consideration of second-order dynamics of electromechanical servo loop, this paper puts forward a robust attack angle control approach. By means of sliding mode control and dynamic surface control theories, the multiple subsystems of control plant are effectively connected, and the robust property of control system is also guaranteed. The stability analysis on attack angle control systems is given by using Lyapunov function method. From simulation results, we can see that the proposed scheme can guarantee that the attack angle control system possesses more satisfactory performances, compared with the conventional one which did not consider the servo-loop dynamics in design period. Moreover, the structure of the proposed control scheme is simple; therefore it is easy to be realized in engineering application. In addition, the proposed method in this paper can be extended to explore the robust whole-channel attitude control approaches, which will be carried out in future works.

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

This work is supported by the National Nature Science Foundation of China (Grant no. 61403355).