Reduced order design of active suspension control

Exact decomposition of the algebraic Riccati equation of deterministic multimodeling optimal control problems

“…In addition, the results of this paper are extended in [24] to the Kalman filtering multimodeling structure. Those results are successfully applied to a passenger car under unevenness of the road disturbances model of [19] in the context of the singularly perturbed multiparameter Kalman filtering problem [24].…”

“…This is obvious from the application of the nonsingular state transformation (Chang) to (9), which will replace zero matrices in (9) by nonzero elements. This will cause coupling between the fast state-costate variables in (19). Having obtained coupled state-costate variables in (19) produces coupled fast algebraic Riccati equations in (22).…”

“…This will cause coupling between the fast state-costate variables in (19). Having obtained coupled state-costate variables in (19) produces coupled fast algebraic Riccati equations in (22). That is why in this paper we have used a much more complex transformation of [21] that in addition of extracting independent slow state-costate variables also completely decouples fast state-costate variables of the fast subsystems corresponding to the time scales induced by parameters 1 and 2 .…”

“…The fast subsystems are strongly connected to the slow subsystem and weakly connected (or not connected) among themselves. Such large scale systems describe dynamics of several real physical systems, for example, power systems [1] and automobiles [13], [19]. The corresponding multimodeling representation of [1] is defined by…”

Spindle position regulation for wind power generators

“…For manufacture automation, flexible robot links have been frequently employed and analyzed by singular perturbation technique [19]. Suspension of quarter-car model has been studied by two-time-scale approach [20]. Moreover, multiple-time-scale singularly perturbed systems were discovered in engineering applications [21,22].…”