Scheduled control for robust attenuation of non-stationary sinusoidal disturbances with measurable frequencies

• Published in: Automatica (Oxford) Vol. 47; no. 3; pp. 504 - 514
• Main Authors: Köroğlu, Hakan, Scherer, Carsten W.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2011; Elsevier
• Subjects: [formula omitted] synthesis; Applied sciences; Asymptotic (output) regulation; Asymptotic properties; Attenuation; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Differential equations; Disturbance rejection/attenuation; Disturbances; Exact sciences and technology; Ground, air and sea transportation, marine construction; Linear matrix inequalities (LMI); Linear parameterically varying (LPV) methodologies; Marine and water way transportation and traffic; Mathematical analysis; Mathematical models; On-line systems; Optimization-based controller synthesis; Regulators; Synthesis; Asymptotic (output) regulation; Linear matrix inequalities (LMI); ℋ 2 synthesis; Linear parameterically varying (LPV) methodologies; Optimization-based controller synthesis; Disturbance rejection/attenuation; Disturbance rejection; H2 control; Differential equation; Control synthesis; H; Linear parameter varying system; Non stationary process; Modeling; Optimization; Bounded solution; Uncertain system; Indirect method; Linear matrix inequality; Off line; Matrix equation; synthesis; Transient response; Linear parameterically varying (LPV); Existence theorem; Operator equation; methodologies; H infinite control; Matrix inequality; Steady state; Robust control; Symmetric matrix; Asymptotic approximation; Ship; State dependence; Solvability; Output feedback
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2011.01.017

Attenuation of sinusoidal disturbances with uncertain yet online measurable frequencies is considered. The disturbances are modeled as the outputs of an undisturbed parameter-dependent exogenous system with a skew-symmetric system matrix, obtained in response to nonzero initial conditions. The problem is formulated for a parameter-dependent plant as the synthesis of a parameter-dependent controller in a way to ensure internal stability as well as a desired level of steady-state disturbance attenuation in the face of all admissible parameter variations. The solvability of this problem is first related to the existence of bounded solutions to a matrix differential regulator equation subject to an asymptotic norm constraint. Reformulating this as a parameter-dependent state-feedback like synthesis, based on which suitable solutions to the differential regulator equation can be obtained online, tractable solvability conditions are then provided in the form of parameter-dependent matrix inequalities. Controllers that solve the generalized asymptotic regulation problem are also parameterized in terms of the suitable solutions of the differential regulator equation and some free parameter-dependent matrices that are to be designed off-line to ensure stability. A procedure is then developed to design the free parameters in a way to achieve desirable transient behavior. The use of the developed synthesis procedure is illustrated on a simplified version of the course control problem in ship steering.