Efficient reaching law for SMC with PID surface applied to a manipulator

Robotic manipulators are employed in various applications like pick and place, painting and welding etc. In these applications it is required to track a predefined trajectory. For the same an efficient controller is required as the manipulator is a nonlinear complex and coupled system. Due to nonlinearities and coupling effect, the design of an ideal controller has been a challenging task. This paper presents a comparative study of sliding mode control (SMC) with proportional, integral, and derivative sliding surface with three different reaching laws, namely, constant rate, exponential and power rate reaching law to control a two-link robotic manipulator. All the three cases for different reaching laws are investigated for trajectory tracking, disturbance rejection and mass uncertainty. The control parameters for SMC and boundary layer are tuned with Genetic Algorithm optimization technique. Simulation results show that the power rate reaching law offers better performance than the other two laws for disturbance rejection and mass uncertainties, whereas all the three laws performed equally well for set-point tracking.