Parameter tuning of second-order sliding mode controllers for linear plants with dynamic actuators

Tuning of second-order sliding mode control (2-SMC) algorithms in linear systems with dynamic actuators is considered. By means of a describing function (DF) approach, it is investigated how the parameters of a 2-SMC algorithm (the so-called “generalized sub-optimal” algorithm) affect the frequency and the magnitude of the limit cycles that occur when the overall relative degree of the plant plus the actuator is three or more. Explicit formulas are given that allow for setting the parameters of the algorithm to obtain a periodic solution with the prescribed characteristics. By means of simulation examples, we show that the estimated chattering parameters are in good agreement with the actual ones. We also show that the proposed design procedure can also be useful when the local linearization of a nonlinear dynamics is sufficiently accurate.