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This paper presents a derivative and integral sliding mode controller in order to handle the stick-slip oscillation of rotary drilling system. The control method has induced integral of tracking error and the derivatives of tracking error are replaced by state variables, the developed controller uses the nonlinear derivative control for suppressing system oscillation and increasing system damping as error approximates to zero. Lyapunov principles have been carried out to verify the stability and robustness of system. The simulation results show that the controller has faster dynamic response, can further increase accurate rate of the control system, and can suppress stick-slip oscillation of rotary drilling system.