Robust Force Control of a One-Link Flexible Arm

In this paper we consider robust force control of a one-link flexible arm. Since the tip of the flexible arm contacts with a given constraint surface, a constraint condition should be satisfied. By using Lagrange multiplier method and Hamilton's principle, we derive dynamic equations of the joint angle (an ordinary differential equation), the vibration of the flexible arm (a partial differential equation), and the constraint force. The boundary condition of the derived distributed parameter system is nonhomogeneous. We introduce a new variable and derive a homogeneous boundary condition. By solving an eigenvalue problem, eigenvalues and corresponding eigenfunctions are derived. On the basis of the eigenfunction expansion we derive a finite dimensional modal model. To compensate the spillover instability an optimal controller with low-pass property and a robust H∞ controller are constructed. The stability of the direct force feedback and the compliance control considering uncertainty of the arm flexibility is analyzed. To demonstrate the validity of the derived model and the effectiveness of the proposed controllers, a set of experiments has been carried out. Experimental results confirm that the robust controllers perform well.