Six disadvantages of fal functions and traditional nonlinear extended state observers are summarized firstly. To solve these problems, a fal function with fixed time convergence is proposed, which has better convergence ability compared to traditional fal functions, and the upper bound of convergence time is independent of the initial error. Then the nonlinear extended state observer based on the proposed fal function, the exponential convergent extended state observer and the fixed time convergent extended state observer are designed. Finally, the simulation results show that the estimation errors of the three novel nonlinear extended state observers are respectively reduced by 15.4%, 16.9% and 93.8%, compared to the traditional nonlinear extended state observer, and the steady-state errors of the controlled states are reduced by 13.6%, 30.4% and 78.3% respectively.