A behavioral approach to inversion-based control. (September 2018)

• Record Type: Journal Article
• Authors: Costalunga, Alessandro; Piazzi, Aurelio
• Is Part Of: Automatica. Volume 95(2018)
• Page Start: 433
• Page End: 445
• Publication Date: 2018-09
• Subjects: Inversion-based control -- Feedforward -- Behavioral approach -- Stable inversion -- Nonminimum-phase systems -- Linear systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.06.008
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: A new simplified behavior theory is proposed to address inversion-based control for linear, nonminimum-phase SISO systems. The chosen space of signals is the set of piecewise C ∞ -functions and input–output pairs (as weak solutions) satisfy a differential–integral equation with additional smoothness requirements. A related key result is the output–input (or inverse) representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded, noncausal desired outputs are allowed. It is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one. When this straightforward condition is satisfied, a closed-form expression provides the inverse input. Then, an analysis on preaction and postaction control follows. Two examples are included showing the relevance of output signal design in control applications.