**7. Conclusions**

In this study, a sliding mode control scheme with a bounded region and its convergence analysis are explained to the finest detail. In particular, it can easily be said that the work done here is a field study that specifically gives the relevant subject with such meticulous detail. It is our claim that this study has a guiding identity for the researchers who are interested in this control method or want to present it with the intelligent and modern control methodologies with its understandability and clarity targeted here. In this regard, the design of SMC including its finite-time convergence is handled by using Lyapunov's direct method. The tracking error vector converges exponentially to the bounded region once in the

*An In-Depth Analysis of Sliding Mode Control and Its Application to Robotics DOI: http://dx.doi.org/10.5772/intechopen.93027*

boundary layer as proven analytically. Two examples were used for simulation studies to demonstrate the feasibility and effectiveness of the proposed control problems, i.e., the position control of a dc motor subject to a varying external disturbance, and a two-link robot manipulator. Simulations show that a fast convergence rate, and hence quick response, the ability to reject the varying external disturbances, and the robustness against the model uncertainty assumed to be unbounded and fast-varying have all achieved its purpose entirely. Chattering is eliminated by using the boundary layer whose attractiveness and invariance properties of the boundary layer were also introduced. This study also examines the advantages of SMC and PID comparably. Although, in the comparisons given in the literature, the pros and cons of both strategies are mentioned, it is generally observed that SMC performs better than PID. Nevertheless, PID control can still be used as an alternative to SMC. When the PID control strategy does not work well under unknown disturbances and payload changes, SMC provides robustness against parameter uncertainties and unmodeled disturbances so long as the observed undesirable chattering effect is overcome through some modifications as described in the text. Robustness analysis has been performed and successfully applied to the two-link rigid planar robotic manipulator. We have not observed any performance degradation of the trajectory to be maintained in the sliding surface. The results given here do not contradict the view that one can use it instead of the other without losing too much performance. Finally, a two-step simulation has been carried out, testing all the features mentioned above, and the results have confirmed the success of the presented approach. However, it is meaningful and challenging to develop new SMC theories and methods for nonlinear systems due to its broad application potentials in today's world.
