A decisive question about control and diagnosis tasks is how to carry them out using only few measurements or using easy practicable and less expensive measurements. For real applications these requirements are given due to practical restrictions caused by construction of the considered device or the aim to limit the expenses for measurement equipment. This problem can be solved by applying observers. Observers provide the capability to gain enhanced information about a system by processing available measurements. The commonly used Luenberger observer achieves this estimation task for linear systems. By the use of a linear system model and measured outputs of the system this method offers the possibility to receive estimations of all states of the system. But, in considering nonlinear or disturbed systems this approach is not applicable since this approach depends on the quality of the linear model and does not take any extra information into account. Hence, the error equation is affected by the additional influence directly. To overcome those difficulties, without assuming any knowledge about the nonlinear part, the Proportional-Integral Observer can be applied. The Proportional-Integral Observer (PIO) acts as an extension of the classical observer approach. The PIO makes it possible to determine the states even in presence of nonlinearities, disturbances, or model inaccuracies. Moreover, the PIO is also able to estimate those additional influences acting on the system. This approach offers a great variety of usage possibilities for the replacement of real sensors and for the validation of measurements or models. Furthermore, by its capability to reconstruct the disturbances, the PIO is also predestined to fault detection.
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