Pitch Angle Control of an Airplane Using Fractional Order Direct Model Reference Adaptive Controllers

This paper deals with the longitudinal movement control of an airplane (pitch angle) using fractional order adaptive controllers (FOACs). It shows the improvements achieved in the plane’s behavior, in terms of the minimization of a given performance index. At the same time, less control effort is needed to accomplish the control objectives compared with the classic integer order adaptive controllers (IOACs). In this study, fractional order direct model reference adaptive control (FO-DMRAC) is implemented at the simulation level, and exhibits a better performance compared with the classic integer order (IO) version of the DMRAC (IO-DMRAC). It is also shown that the proposed control strategy for FO-DMRAC reduces the resultant system control structure down to a relative degree 2 system, for which the control implementation is simpler and avoids oscillations during the transient period. Moreover, it is interesting to note that this is the first time that an FOAC with fractional adaptive laws is applied to the longitudinal control of an airplane. A suitable model for the longitudinal movement of the airplane related to the pitch angle θ as the output variable with the lifter angle (δe) as the control variable, is first analyzed and discussed to obtain a reliable mathematical model of the plane. All of the other input variables acting on the plane are considered as perturbations. For certain operating conditions defined by the flight conditions, an FO-DMRAC is designed, simulated, and analyzed. Furthermore, a comparison with the implementation of the classical adaptive general direct control (relative degree ≥ 2) is presented. The boundedness and convergence of all of the signals are theoretically proven based on the new Lemma 3, assuring the boundedness of all internal signals ω(t).