Analysis of friction controlled motion

Control of motion through base excitation is considered for the unique circumstance where friction is the primary component of the interaction force. With a focus on the Dahl friction model, it is shown that the equations of motion can be divided into two cases: ‘large’ and ‘small’ friction. When analyzed in this manner, the corresponding models take two distinct forms, which subsequently lead to different approaches for control design and analysis. The case of large friction leads to a linear system with an unknown disturbance, the bound of which is related to constants of the friction model, thus allowing the application of standard linear control methods. The case of small friction is similar to the standard Coulomb model, and can be analyzed within the framework of sliding mode control. For both circumstances, relations between the friction constants and control variables are derived which guarantee position tracking performance in the absence of disturbance.