Geometric nonlinear equivalence of frictional systems for compensation

Being a complex nonlinear phenomenon, friction is a difficult part to characterize and identify in a mechanical system. Friction is the result of interaction between one body over or along another and is dependent on many parameters, such as contact geometry, topography, surface materials, presence and type of lubrication and relative motion. The classical Coulomb friction has been widely used especially in the field of control engineering to compensate for the static force in a system. However, despite its simplicity, the effectiveness of the Coulomb model in capturing the frictional behavior in the presliding regime is relatively low. Further study shows that friction force exhibits strong (hysteretic) nonlinear relationship with sliding velocity, displacement and time, which makes the characterization become a difficult task to fulfill. As a consequence, an advanced control strategy, if necessary from the nonlinear class, is necessary to compensate for the effect of friction in high-precision positioning devices. This paper deals with the development of efficient (nonlinear) control structures, which are optimized based on the geometric nonlinear equivalent system that dynamically represents the nonlocal memory hysteresis friction in geometric form, i.e. an equivalent system with geometric damping and spring. The equivalent system is analyzed using the skeleton technique, which employs the instantaneous amplitude and frequency of the response output of the system under free vibration condition. The results show that the controllers are able to compensate for friction in the system, which also confirms that the equivalent system is efficient to mimic the dynamic behavior of the frictional system.