Parameter Identification of Vibrating MIMO Mass-Spring-Damper Mechanical Systems with Coulomb Friction - KangSok Wi; KonKi Ri; KwangIl Ri; YongIl Ri (International Journal of Mechanical Dynamics and Systems Analysis, 2025)
This study presents a time-domain method for identifying parameters in multi-degree-of-freedom (DOF) linear mass-spring-damper systems that include Coulomb friction, where the friction coefficient varies within a limited range, using measurements of position and control force. For mass identification in single-degree-of-freedom (DOF) vibrating mechanical systems with stiffness and no damping but Coulomb friction, the friction term is eliminated by first derivative processing. In addition, the identification of the coefficient of friction is not considered, and friction is treated as measurement noise by reference trajectory search control. A method of implementing online algebraic parameter identification by measuring position and control force in the time domain for MIMO (Multiple-Input, Multiple-Output) mass-spring-damper systems with limited Coulomb friction is proposed. The results of the mathematical model and study of the differential flatness of an n-DOF mass-spring-damper system with friction were obtained. An output feedback control scheme for trajectory tracking tasks considering Coulomb friction was obtained. The friction coefficient and parameters of mass, stiffness, and damping coefficient have been algebraically estimated from real-time position and input control force measurements to extend the application range of the online algebraic parameter identification method. By determining the velocity sign in two short time intervals when Coulomb friction exists and by processing the friction term in the manner of linearizing the sign function, in the case of an integral near a singular point, the reference trajectory tracking problem is realized. Based on this, a six-DOF mechanical system, for example, mass, stiffness, and damping factor without friction, was identified in real-time, and mass, stiffness, damping factor, and Coulomb friction coefficient in the presence of friction were identified. When friction exists and does not, parameter identification of a six-DOF vibrating mechanical system and reference trajectory tracking have been realized correctly. The method is of great help in realizing the static motion control of multi-DOF MIMO mechanical systems, including robot manipulators, medical devices, and precision tracking mechanisms. As a result, control costs are reduced.
Keywords: Coulomb friction; control force measurements; parameter identification; vibrating mechanical systems; vibration control