Input-Output Jumps of Scalar Linear Systems

作     者：Juxhino Kavaja Aurelio Piazzi 

作者机构：Department of Engineering and Architecture University of Parma Parco Area delle Scienze 181/A - 43124 Parma Italy 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2019年第52卷第17期

页      面：13-18页

主　　题：Linear continuous-time systems single-input/single-output systems input-output jump discontinuities initial conditions control systems education 

摘      要：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.