Simple finite-time sliding mode control approach for jerk systems

Abstract

This article describes an easy way to apply active control upon all jerk systems for which the linear part of the third-order differential jerk equation strongly depends on acceleration and velocity. The kernel of that methodology is to rewrite the jerk equation as a single implicit first-order differential equation escorted with a sliding variable. It is shown that, for such a jerk class, the fast terminal sliding convergence based on Lyapunov stability is achieved with a first-order sigmoid sliding surface. Various numerical simulations have been conducted on Sprott simple jerk class as well as on the single op-amp jerk system. For experiment, we synchronize two Sprott circuits with nonlinearity being the absolute value of position. Experimental results match well with numerical simulations.