Design of a robust controller for a gearboxconnected two-mass system based on a hybrid model

Backlash is a common nonlinear phenomenon in mechanical systems, producing undesired behavior such as inaccuracies and oscillations. Instability thereby may limit the speed and position in industrial robots, automotive, and other applications. In this paper, a two-mass system connected by a gearbox is modeled as a hybrid system based on a two modes approach. First, the size of the backlash gap is assumed known; thus, when the motor and load are in negative or positive-contact, the system becomes an equivalent system (rigid body) and can be modeled as one degree of freedom, which is described as a second-order system, this mode is called Contact Mode. Second, when the motor reverses its direction, the system behaves as two separated subsystems so that each subsystem can be modeled as one degree of freedom; this mode is called Backlash Mode. A sliding mode controller (SMC) has been proposed for the above two modes in this work. Hence, two sliding mode controllers are designed, one for the contact mode to achieve tracking position performance, while the other is for the backlash mode to achieve stability. Finally, the two controllers are connected by designing a switching control mode based on the gap conditions and size. The proposed control system is tested considering two different desired references. The simulation result proved the ability and robustness of the designed SMC controllers to force the load position to track the desired reference position and overcome the nonlinearities and drawbacks of SMC, such as chattering.