Stable Torsion Torque Control Based on Friction-Backlash Analogy for Two-Inertia Systems with Backlash

Torsion torque control (TTC) has been studied in applications ranging from industrial robots to electric vehicles. However, its performance is severely compromised when there is joint backlash, causing limit cycles and inducing unstable behavior. This study proposes a stable TTC scheme for two-inertia systems with joint backlash based on an analogy between static friction and backlash phenomena. First, a transformation of the joint torsion dynamics into a first-order system is applied, and a proportional torsion torque controller is proposed. Then, an analogy between the transformed joint torsion dynamics with backlash and one-mass systems with static friction is established. Based on this analogy, a combination of a switched disturbance observer and an impact torque suppression controller is proposed, ensuring rapid control over backlash and stable reengagement with reduced gear collision impact. The effectiveness of the proposed method is verified through simulation and experimental results.