This paper intends to study and implement recent state observation techniques of the ultra-local model used in model-free control approach in two different methodologies, through an ultra-local model-based algebraic estimator and using an ultra-local model-based derivative estimator. The estimation is based on Taylorâs expansion coefficients for an arbitrary order. This research serves a discrete implementation details of the proposed approach using operational calculus and finite impulse response filters. A comparative study between algebraic and derivative estimators is presented. Different tests have been verified on a position trajectory control scheme of a DC motor that is subjected to disturbances and uncertainties. The used ultra-local model design is independent of initial conditions and stands in need only to measure the systemâs input and output values. This study shows that the proposed design reduces the nonlinearities and increases the robustness to disturbances resulting from Coulomb friction effects. Moreover, the algebraic and derivative estimation process is computed in real-time. The evidence of the recommended approaches has been examined by numerical simulation and compared with other strategies.