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This paper presents a new improved nonlinear tracking differentiator (INTD)with hyperbolic tangent function in the state space system. The stability andconvergence of the INTD are thoroughly investigated and proved. Through theerror analysis, the proposed INTD can extract differentiation of any piecewisesmooth nonlinear signal to reach a high accuracy. the INTD has the requiredfiltering features and can cope with th nonlinearities caused by the niose.Through simulations, the INTD is implemented as signal derivative generator forthe closed loop feedback control system with a nolinear PID controller for thenonlinear Mass Spring Damper system and showed that it could achieve the signaltracking and differentiation faster with a minimum mean square error.

On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design