Adaptive nonlinear control of one-link flexible arm

When a flexible arm is rotated by a motor about an axis through the arm´s fixed end, transverse vibration may occur. The motor torque should be controlled in such a way that the motor rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested at the end of rotation. In this paper, the authors propose deterministic and adaptive control laws for one-link flexible arm. Using the fact that matrix dD(δ)/dt-2C(θ, θ˙, δ, δ˙) is skew symmetric, controllers which have a simplified structure with less computational burden are proposed by using Lyapunov stability theory