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Theory and Modern Applications

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