This chapter presents a tool for analysis of robust stability, consisting of a graphical method based on the construction of the value set of the characteristic equation of an interval plant that is obtained when the transfer function of the mathematical model is connected with a feedback controller. The main contribution presented here is the inclusion of the time delay in the mathematical model. The robust stability margin of the closed-loop system is calculated using the zero exclusion principle. This methodology converts the original analytic robust stability problem into a simplified problem consisting on a graphic examination; it is only necessary to observe if the value-set graph on the complex plane does not include the zero. A case of study of an internal combustion engine is treated, considering interval uncertainty and the time delay, which has been neglected in previous publications due to the increase in complexity of the analysis when this late is considered.
Part of the book: Robust Control
A Lagrangian formalism is used to model a PVTOL in order to obtain an aircraft model. The Euler‐Lagrange model of the PVTOL is used to develop an algorithm for fault diagnosis. Diagnosis implies the detection, isolation and identification of a fault. The considered approach is based on the knowledge of a system model as well as the model of the possible faults. The idea is to use non‐linear decoupling approach to derivate a set of subsystems, each related to a specific fault or a set of faults. An observer‐based residual generation is designed for each subsystem, this structure allows the fault detection and isolation stage, for fault identification a kind of approximated inversion algorithm to meet the different diagnostic levels. The results are obtained taking advantage of the structure given by the Euler‐Lagrange modelling of the PVTOL as well as from recent results related to observer design and fault identification.
Part of the book: Lagrangian Mechanics