This article presents a compensated positive position feedback strategy for active control of flexible structures with piezoelectric actuators. In the proposed compensated positive position feedback method, a negative feedback compensator is involved to remedy the deficiency of traditional positive position feedback and to introduce roll-off characteristic at low frequencies. Thus, compensated positive position feedback controllers can be developed with minimal influences on lower order modes and cause no steady-state error to the controlled system. For demonstration purpose, the design processes and the effectiveness of the compensated positive position feedback method are illustrated by active control of a cable net structure with integrated piezoelectric stacked actuators. The numerical simulations demonstrate that compared to the conventional positive position feedback method, the proposed compensated positive position feedback approach overcomes the fundamental defects of frequency shift and spillover into lower order modes and achieves the goal of step-tracking with zero steady-state error. These comparative results confirm the efficacy and superiority of the proposed compensated positive position feedback methodology in active control of flexible structures.

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The quadrotor, as a kind of Unmanned Aerial Vehicles (UAVs), has become a hot research topic, due to its small size, easy configuration, good stealthy characteristics, etc. It is a typical nonlinear system with coupling multi-variables. Therefore, it is difficult to optimize trajectory in real-time and its trajectory optimization research is limited so far. In this paper, we firstly establish a quadrotor dynamic model by Newton-Euler equations and simplify it properly. Then a Gauss Pseudospectrum Method (GPM) with the hp-adaptive mesh refinement algorithm is proposed to solve the problem which is a nonlinear optimal control problem with path and boundary constraints. The results verify that the method can effectively generate satisfied optimal trajectories for the aircraft and it provides mathematical foundation for the further engineering applications.

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