On the noncollocated control of structures with optimal static output feedback: Initial conditions dependence, sensors placement, and sensitivity analysis

Abstract

It is well known that the linear quadratic regulator (LQR) exhibits significant frequency margins and reduced sensitivity properties. However, its application in real problems is restricted because it requires availability of all state variables of the controlled system to be measured. This problem is not satisfactorily overcome by state observers, because they are sensitive to spillover and their more complex structure can entail time delay. Another alternative to solve this problem is to use only linear combinations of measured signals for feedback, a technique known as optimal static output feedback (OSOF) or partial state feedback. In this paper, this method is studied considering additionally sensors locations as optimization variables. Necessary conditions of optimality are presented in order to highlight the dependence of the optimal solution on system initial conditions. A new approach to deal with this dependence, which is based on approaching the performances of OSOF and LQR for any initial condition, is developed and compared with the existing one. The method developed is tested on a simply supported plate modeled using the finite element method. The analyses of the results show that with a significantly reduced number of sensors, the OSOF controller has a performance equivalent to LQR. The developed methodology also provided the controlled system a relevant behavior to major problems of noncollocated control, such that it maintained stability and performance considering parameters variations and a large increase in frequency bandwidth.