Consider the planar three-degrees-of-freedom 4RRRparallel manipulator shown in Figure 3.32 and described in Problems 3.5 and 4.4. Consider the dynamic formulation with the geometrical and inertial parameters and the typical trajectory used in Problem 5.5.
a. For this manipulator, design a decentralized PD controller in the task space, and implement the required force distribution in terms of the mechanism Jacobian matrix. Develop a program in MATLAB to simulate the closed-loop tracking performance of the mechanism. Find proper choices for the controller gains to obtain suitable tracking performance with a limited control effort.
b. Improve the performance by a feed forward control scheme. Simulate the closed-loop behavior and consider %10 perturbation in all geometrical and inertial parameters. Tune the controller gains to reach a suitable tracking performance with a limited control effort.
c. Design an inverse dynamics controller for the mechanism and consider %10 perturbation in all geometrical and inertial parameters. Simulate the closedloop performance and tune the controller gains to reach a suitable tracking performance with a limited control effort.
d. Consider a partial feedback linearization in the IDC control and consider %10 perturbation in all geometrical and inertial parameters. Simulate the closedloop performance and use the controller gains considered in full IDC.
e. Plot and analyze motion trajectories, tracking errors, and the Cartesian and actuator forces versus time for different controllers and compare the results.
