Nonlinear two-mass system control with sliding-mode and optimised proportional–integral derivative controller combined with a grey estimator

The application of a sliding mode controller and an optimised proportional–integral–derivative (PID) controller to a nonlinear two-mass system is presented. Both of the proposed controller structures are strengthened with a grey estimator. A complete state-space mathematical model for a nonlinear two-mass system is first developed and numerically simulated. Then, an optimised PID controller and a sliding-mode controller are both designed to regulate the speed of the system. Finally, corresponding results are compared. The grey estimators of the torsional torque and the load machine speed are tested with open-loop and closed-loop control structure. The simulation results are confirmed by the experimental results.