Time maximum disturbance switch curve and isochrones of linear second-order systems with numerator dynamics

It has been established recently that the most stressful bounded (time maxi mum) disturbance for stabilized second-order systems with numerator dynamic s is of bang-bang type. This bang-bang disturbance can be implemented with a switch curve that is constructed by using isochrones as the level sets fo r the disturbance index in a state-space setting. Tn this paper, the isochr ones of linear second-order systems with numerator dynamics are shown to ha ve a closed analytic form. This closed analytic form requires less computat ional effort and gives an intuitive feeling of just how the isochrones chan ge with the other parameters of the system. Simulation results show how the isochrones evolve and approach a maximum limit cycle with different dampin g coefficients and finite zero locations. Furthermore, these isochrones cou ld be utilized directly in synthesizing the time maximum disturbance and th erefore, the ideas can be readily extended to higher order systems. (C) 200 0 The Franklin Institute. Published by Elsevier Science Ltd. All rights res erved.