This paper proposes a control algorithm based on the sliding mode (SM) control law with an exponential term which improves the convergence to the origin. Such convergence to the origin is compared with other existing results such as the super-twisting (ST) and an SM controller with exponential terms. To compensate for unknown but bounded disturbances, a discontinuous function through an integral action has been employed. The presented algorithm with the exponential term, or exponential SM control algorithm, has been employed to a nonlinear system that can be represented into a block controllable form to follow an admissible trajectory. Finally, a real-time experiment and a numerical simulation have been carried out on a direct current motor to show effectiveness of the proposed control law. Numerical simulations have been compared with the ST control law and with a predefined-time controller with expon0ential terms.
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