Dynamic Modeling and Inverse Optimal PID with Feed-forward Control in H _∞ Framework for a Novel 3D Pantograph Manipulator

This paper affords dynamic modeling and control for a new 3D pantograph manipulator. The new manipulator possesses pure decoupled translational motions and it is characterized by large workspace to size ratio, high speed, rigidity, and accuracy. Euler-Lagrange first type method is used to get the dynamic model. However, the resulted dynamic model is too complex to be used in model-based control techniques. Therefore, a simplified nominal plant is proposed. It allows the inverse dynamic solution efficiently. However, an explicit form of the nominal Coriolis and centrifugal matrix cannot be obtained due to the complicated kinematic terms. Considering these dynamic characteristics as well as the required robust trajectory tracking performance of the manipulator, a new controller is proposed. The new controller is called inverse optimal PID with Feed-Forward Control which is designed in H_∞ framework. The new controller has the following merits; robustness, optimality, simple implementation, and efficient execution without the need of explicit forms of dynamic matrices. The extended disturbance in the proposed controller is smaller than that in the inverse optimal PID control (IPID) and contains one type of error contrary to the nonlinear robust motion controller (NRIC). The performance of the proposed controller is compared with those of IPID and NRIC controllers for different trajectories and payloads. The dynamic simulation results via co-simulation of MSC-ADAMS® and MATLAB®/Simulink software prove the robustness of the proposed controller against speed/payload variations. The proposed controller is found to have higher performance compared with IPID and NRIC controllers. These results assure the feasibility of the 3D pantograph manipulator with the proposed controller for pure translational tracking applications.