This paper proposes an improved method of integral backstepping for real time control of a laboratory helicopter with variable speed rotors known as the Two-Rotor Aero-dynamic System (TRAS). The coupled system is decomposed into the horizontal subsystem (HS) and the vertical subsystem (VS) and traditional backstepping, augmented with direct integral action is designed for each subsystem. The transient response to both constant and time varying references is then simultaneously improved by modifying an already proposed method called dual boundary conditional integration. A switching technique is also employed to enhance the tracking response of the undamped HS for its bi-directional motor which exhibits jerking effects. Experimental results show that the proposed approach yields improved transient and tracking performance when compared to previously proposed methods exploiting conditional integration earlier proposed for improving the transient response of controlled nonlinear systems with integral action. The results also show the robustness of the proposed method in the presence of the coupling effects and additional external disturbance applied to the system in the form of a wind gust.
In this paper, the energy efficiency of the widespread application of backstepping control to a class of nonlinear motion systems is investigated. A Switched Step Integral Backstepping Control (SSIBC) scheme is introduced to improve immunity to measurement noise and to increase the energy efficiency of conventional backstepping in practice. The SSIBC is realized by switching between two candidate controllers obtained at different steps of the iterative backstepping design process. A bi-state dependent hysteresis rule is developed to supervise stable switching between the different regimes in the presence of noise. The proposed method is experimentally verified on a MIMO twin rotor laboratory helicopter involving coupled nonlinear dynamics, inaccessible states and uncertainties. Experimental results show that in addition to a reduction in power consumption, the SSIBC reduces saturation of the control signal and visible motor jerking in contrast with conventional backstepping. Additional comparisons with a previously proposed optimized decoupling PID controller also show significant improvement in precision achieved with higher energy efficiency. Experimental results obtained with the introduction of an external disturbance into the system also show the robustness of the proposed SSIBC.