Input-Output Jumps of Scalar Linear Systems. Issue 17 (2019)

• Record Type: Journal Article
• Authors: Kavaja, Juxhino; Piazzi, Aurelio
• Is Part Of: IFAC-PapersOnLine. Volume 52:Issue 17(2019)
• Page Start: 13
• Page End: 18
• Publication Date: 2019
• Subjects: Linear continuous-time systems -- single-input/single-output systems -- input-output jump discontinuities -- initial conditions -- control systems education; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2019.11.019
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In the classic control systems analysis a known difficulty is to determine a transient output response when non-zero (discontinuous) initial conditions are present. This difficulty is overcome by means of the presented input-output jump relations. For a system with order n and relative degree r = n - m, these relations relate the jump discontinuities of the input and its derivatives up to the order m - 1 to the jump discontinuities of the output and its derivatives up to the order n - 1. A simplified behavior theory is used in deducing these straightforward relations. A simple, complete solution to the initial conditions problem that uses neither generalized derivatives nor ad hoc assumptions is then presented. A detailed example illustrating this solution is included.