Model-free Adaptive Control in Frequency Domain: Application to Mechanical Ventilation

Abstract

Looking back at the history of control engineering, one finds that technology and ideas combine themselves until they reach a successful result, over the timeline of several decades (Bernstein, 2002). It is such that before the computational advances during the so-called Information Age, a manifold of mathematical tools remained abstract and limited to theory. A recent trend has been observed in combining feedback control theory and applications with well-known, but scarcely used in practice, mathematical tools. The reason for the failure of these mathematical tools in practice was solely due to the high computational cost. Nowadays, this problem is obsolete and researchers have grasped the opportunity to exploit new horizons. During the development of modern control theory, it became clear that a fixed controller cannot provide acceptable closed-loop performance in all situations. Especially if the plant to be controlled has unknown or varying dynamics, the design of a fixed controller that always satisfies the desired specifications is not straightforward. In the late 1950s, this observation led to the development of the gain-scheduling technique, which can be applied if the process depends in a known or measurable way on some external, measurable condition (Ilchmann & Ryan, 2003). The drawback of this simple solution is that only static (steady state) variations can be tackled, so the need for dynamic methods of controller (re)tuning was justified. One can speak of three distinct features of the standard PID controller tuning: auto-tuning, gain scheduling and adaptation. Although they use the same basic ingredients, controller auto-tuning and gain scheduling should not be confused with adaptive control, which continuously adjusts controller parameters to accommodate unpredicted changes in process dynamics. There are a manifold of auto-tuning methods available in the literature, based on input-output observations of the system to be controlled (Bueno et al., 1991; Astrom & Hagglund, 1995; Gorez, 1997). The tuning methods can be classified twofold: • direct methods, which do not use an explicit model of the process to be controlled; these can then be either based on tuning rules (Astrom & Hagglund, 1995), either on iterative search methods (Astrom & Wittemark, 1995; Gorez, 1997). • indirect methods, which compute the controller parameters from a model of the process to be controlled, requiring the knowledge of the process model; these can be based on