Abstract:In order to improve the identification accuracy and reliability of Commensurate Fractional Order Model(CFOM)，a Separable Nonlinear Least Squares algorithm with Stable Constraints(SC-SNLS) was presented to optimize the mean square error evaluation criterion. Considering that the CFOM is linear in its numerator polynomial coefficients and are nonlinear in its common fractional derivative order and the denominator polynomial coefficients, the LS and LM algorithms were alternately and iteratively used to estimate the linear and non-linear parameters, respectively. Four unstable factors were revealed in the estimation procedure through perturbation analysis of the estimation of linear parameter. Then the stability and convergence of optimization procedure were improved through tackle the unstable factors. Simulation results showed that the proposed algorithm has a fast convergence speed and provides more accurate estimation compared to relative approaches.