In previous studies, an excretion care support robot has been developed for the bedridden people. To improve the motion performance for the robot, a digital acceleration controller has been designed to deal with the problem of uncertain and unbounded nonlinear friction. The motion performance of the digital acceleration control system is not sufficient because the design of the digital acceleration controller need the exact values of the plant parameters of the robot. However, these values are variable due to center-of-gravity shifts and load changes. In this paper, to address these issues, a discrete-time system identification method using recursive least squares(RLS) algorithm is proposed to identify the parameters of the plant online. This method is effective to deal with the problem of center-of-gravity shifts and load changes. Simulations are conducted, the results demonstrate the feasibility and effectiveness of the proposed control method by comparing it with the digital acceleration controller without RLS.