Control method and applications of robust trajectory linearization via nonlinear differentiators

Considering the lack of enough robustness against uncertainties in conventional trajectory linearization control (TLC) method, an improved robust control method was proposed, based on the design principle of nonlinear differentiators. Firstly, via introducing the concept of second-order linear differentiator (SOLD), it was indicated that peaking phenomenon which was similar with using high-gains in SOLD would emerge during the transient profile of differentiation of the nominal command in the existing TLC. And then, tracking differentiator (TD) was used to produce the nominal command and its derivative, peaking phenomenon was totally eliminated and the ability of adjusting the response speed of closed-loop system under the physical limitations was endowed simultaneously. Secondly, by constructing the desired tracking error dynamics of closed-loop system, the control law of the linear time-varying (LTV) system could be directly obtained, PD-spectrum theorem and real time tuning of the time varying bandwidth (TVB) of TLC were both avoided. Meanwhile, by utilizing the non-perturbation form of hybrid differentiator (HD) as the desired error dynamics of closed-loop system, the robustness of the system was thus enhanced. In addition, the boundedness of the tracking error in interference system was proved by Lyapunov theory. Finally, the proposed method was applied to the attitude tracking problem of hypersonic vehicle. The simulation results demonstrate the proposed method can still exhibit better control performance and anti-interference capability even if there exist large uncertainties in the aerodynamic parameters, thus the effectiveness and robustness of the control scheme is validated.