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Table 1 Comparison between the results of the FISMC (20) and FTSM (21)

From: A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

Comparison items The result of this paper The result in [62]
Control methodology Fractional integral sliding mode control (FISMC) Fast terminal sliding mode (FTSM)
Design parameters Overall, 4n + 2 parameters should be selected Overall, 6n + 1 parameters should be selected
Chattering and convergence The FISMC seems to has a chattering free control procedure and a fast convergence to equilibrium point The FTSMC seems to has chattering in control procedure and needs a long time for convergence to equilibrium point
Magnitude of oscillations Normal range (based on the behavior of the error system) Out of range (based on the behavior of the error system)
Conclusions The advantages of the proposed FISMC: (1) higher robustness; (2) the controller is easier to design and may be more convenient for practical use; (3) chattering-free; (4) higher convergence accuracy The advantages of the FTSM: (1) it has many parameters that may be difficult to use; (2) it is effectively working when the states of the systems are known; (3) it is applicable for the vast area of systems