A method based on non-linear regression has been proposed by Toh and Devanathan (1996) to perform closed-loop process identification under naturally occurring load disturbances. The significance of this method includes relaxation of an important assumption on the knowledge of the input excitation source, given a stable controller which is to be improved. While not aiming to identify a precise model as in classical design, this method uses an approximate process model for on-line identification. This serves as a basis for controller refinement, without having to interrupt the process operation for identification test. In this paper, we present a refined formulation and then perform convexity analysis and quasiconvexity analysis on this refined formulation. We show that these results can be utilized to obtain convergence independent of the initial estimates. Applicability of the identification for controller tuning is also demonstrated using a process with an unknown model.