Transient performance improvement of linear systems using a split-path nonlinear integrator

In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot (i.e., improves transient performance). The resulting closed-loop dynamics can be described by a continuous-time switched dynamical system, for which we will provide sufficient conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in simulation examples.