In order to verify the performance

In order to verify the performance of the proposed controller, i.e, AFISMC-DO, we compare it with other stateof-the-art controllers such as PID, computed torque control (CTC), nonsingular fast terminal sliding mode controller (NFTSMC), which has been recently proposed for FTC systems [8], [24]. The design of the NFTSMC is described in Appendix A. The design of the CTC and PID are omitted in this paper since they are well-known methods and can be easily found in the literature. TABLE I depicts the selection of parameters of the controllers. It is notice that most of the gains of the proposed AFISMC-DO, i.e., Ko;K1;K2; ; ; , are proportional gains, so the effects of these parameters are quite obvious. For instance, if bigger values of the gains are selected, the convergence rate of the system is quicker, but the oscillatory is bigger, and vice versa. The parameters used in this simulation are selected based on trial and error procedure or based on experience to obtain a compromise between the convergence speed and oscillatory. The set of membership functions of the fuzzy logic used in the AFISMC-DO are selected as follows: