Limit cycle oscillations in high performance robot drives

Analysis and design of high performance robot drives require that elastic modes and nonlinear friction are considered. A control law based on linear state feedback and an observer can be used to provide active damping of the resonant modes. The achievable bandwidth is limited by the appearance of limit cycle oscillations at zero speed. The limit cycles are caused by the Coulomb friction in the drive motor, and their appearance is related to the stability of the regulator. It is shown that an unstable linear regulator is a sufficient condition for limit cycle oscillations in this type of system. This, in combination with the inherent windup problem, leads to the conclusion that unstable regulators should be avoided when designing flexible servo control systems. The stability of the regulator depends mainly on a dimensionless quantity, which includes the load inertia, the spring constant of the elastic modes and the closed loop natural frequency. Analytic expressions have been derived from which approximate values of the stability limit can be calculated with good accuracy. All results have been verified experimentally on a simple prototype system