An investigation of methodology for the control and failure identification of flexible structures

Abstract

This study examines the characteristics of four methods for the control of flexible structures and investigates the control performances of each method. The investigation is concerned with various control performance measures, such as control gain magnitude, settling time and overshoot in transient response, actuator phase and gain margins, and stability in the presence of actuator failure. In conjunction with the system performance, a systematic approach to the choice of weighting matrices for optimal control is presented. The approach shows a relation between the weighting matrices and the closed-loop eigenvalues. Since the approach is based on a set of independent second·order modal dynamics, the dimensionality of the system is no longer a problem in obtaining the optimal control law. The newly developed Minimum Gain Pole Placement (MGPP) is an optimal method in the sense that it minimizes an objective function, where the objective function is taken as control gain magnitudes with constraints of exact pole placement for any set of modes.

The robustness of Independent Modal Space Control (IMSC) is examined. In general, the parameters of the control system are usually approximated, so that the designed controller, based on a postulated model, will not perform on the actual system as expected. This study shows that when the IMSC method is used with collocated sensors and actuators, the modelling errors in the postulated system cannot lead to instability of the closed-loop system containing control modes and residual modes.However, in the case of coupled control (MGPP), this property cannot be shown. This points to the robustness of IMSC method with respect to modelling errors.

The IMSC method requires the same number of actuators as the number of control modes. The method can be extended to the cases of fewer actuator and more actuator by using the pseudo-inverse of modal particification matrix, an approach referred to as pseudo-independent modal-space control (PIMC). It is shown that PIMSC also yields some form of optimal control and that it is robust as well.

Modal filters are introduced to detect and identify failure of control components in large space structures. The failure mode is investigated in the modal space so that a simple failure detection and identification (FDI) based on modal dynamics is established. Moreover the information obtained from the modal analysis provides some guidelines for the identification of faulty components. The integral form of the modal filters provides the ability to mitigate the effects of noise, disturbances and parameter uncertainties pointing to the robustness of the method. The detection process proposed in this study reduces the computational effort and permits an assessment of the system stability.