Modeling Dry Friction in Multibody Mechanical Systems and Its Applications to the Underactuated Control of an Overhead Crane-Payload System

This paper presents a comprehensive analysis of dry friction modeling for conducting reliable computer simulations in the MATLAB and SIMULINK environments. In particular, this investigation highlights practical issues relevant to studying underactuated multibody systems and implementing control strategies suitable for this family of mechanical systems within the SIMSCAPE MULTIBODY framework. Another significant contribution of this study is the development of a novel nonlinear control algorithm that combines feedforward and feedback approaches. This enables the control of underactuated dynamical systems, which are typically found in mechanical engineering applications, such as an overhead crane-payload system, serving as the case study analyzed in this work. Beginning with the preliminary analysis of a benchmark problem, a demonstrative example, and a control example, this paper presents several scenarios that consider dry friction and the feedforward plus feedback controller both separately and in combination. To further explore the performance of the adopted control strategy for the case study, critical remarks are provided on the performance of the control policy developed in this study under wind gust conditions, which serve as random disturbances for the crane-payload system. The numerical results presented in this paper for all examined dynamical systems emphasize the importance of accurate dry friction modeling in the overall nonlinear motion control of underactuated multibody mechanical systems.