This paper presents a systematic modelling technique for a nonholonomic underactuated mechanical system from input-output data and implement conventional controllers to achieve desire control performance. The main objective of this modelling approach is to derive the parametric modelling of real dynamic systems from input output data by using the system identification process. A nonlinear couple multivariable system namely wheeled mobile robot (WMR), a popular laboratory-based test bed pose challenges for several modelling techniques have been considered as a candidate system to estimate the state-space modelling and implement PID and state feedback control law to achieve the stability of the system. The quality of the identified modeling has been verified in the simulation environment.