Robust Linear Control of Nonlinear Flat Systems

Asymptotic estimation of external, unstructured, perturbation inputs, with the aim of exactly, or approximately, canceling their influences at the controller stage, has been treated in the existing literature under several headings. The outstanding work of professor C.D. Johnson in this respect, under the name of Disturbance Accommodation Control (DAC), dates from the nineteen seventies (see Johnson (1971)). Ever since, the theory and practical aspects of DAC theory have been actively evolving, as evidenced by the survey paper by Johnson Johnson (2008). The theory enjoys an interesting and useful extension to discrete-time systems, as demonstrated in the book chapter Johnson (1982). In a recent article, by Parker and Johnson Parker & Johnson (2009), an application of DAC is made to the problem of decoupling two nonlinearly coupled linear systems. An early application of disturbance accommodation control in the area of Power Systems is exemplified by the work of Mohadjer and Johnson in Mohadjer & Johnson (1983), where the operation of an interconnected power system is approached from the perspective of load frequency control. A closely related vein to DAC is represented by the sustained efforts of the late Professor Jingqing Han, summarized in the posthumous paper, Han Han (2009), and known as: Active Disturbance Estimation and Rejection (ADER). The numerous and original developments of Prof. Han, with many laboratory and industrial applications, have not been translated into English and his seminal contributions remain written in Chinese (see the references in Han (2009)). Although the main idea of observer-based disturbance estimation, and subsequent cancelation via the control law, is similar to that advocated in DAC, the emphasis in ADER lies, mainly, on nonlinear observer based disturbance estimation, with necessary developments related to: efficient time derivative computation, practical relative degree computation and nonlinear PID control extensions. The work, and inspiration, of Professor Han has found interesting developments and applications in the work of Professor Z. Gao and his colleagues ( see Gao et al. (2001), Gao (2006), also, in the work by Sun and Gao Sun & Gao (2005) and in the article by Sun Sun (2007)). In a recent article, a closely related idea, proposed by Prof. M. Fliess and C. Join in Fliess & Join (2008), is at the core of Intelligent PID Control(IPIDC). The mainstream of the IPIDC developments makes use of the Algebraic Method and it implies to resort to first order, or at most second order, non-phenomenological plant models. The interesting aspect of this method resides in using suitable algebraic manipulations to 20