To demonstrate the modified ISMC in

To demonstrate the modified ISMC in this section, consider the same illustrative example with the same settings as that in Section II. The construction of the control law follows the steps in Section II except the filtering constant μ in (21) is set to be 0.1. Simulation trajectories are shown in Fig. 3, where the state vector x follows its desired signal xd under a smooth control input u. However, although the sliding variable s still keeps near to 0 from t = 0, its time derivative ˙ s demonstrates serious chattering resulting in a large phase lag in the estimation of h eventhesettingof μ =0.1issmall.Theseresultsareconsistent with the results of [14, Fig. 8.18]. Further decreasing μ is not suggested as it may introduce serious chattering at u.