The significant challenges seen with the mathematical modeling and control of spatial parallel manipulators are its difficulty in the kinematic formulation and the inability to real-time control. The analytical approaches for the determination of the kinematic solutions are computationally expensive. This is due to the passive joints, solvability issues with non-linear equations, and inherent kinematic constraints within the manipulator architecture. Therefore, this article concentrates on an artificial neural network–based system identification approach to resolve the complexities of mathematical formulations. Moreover, the low computation time with neural networks adds up to its advantage of real-time control. Besides, this article compares the performance of a constant gain proportional–integral–derivative (PID), variable gain proportional–integral–derivative, model predictive controller, and a cascade controller with combined variable proportional–integral–derivative and model predictive controller for real-time tracking of the end-effector. The control strategies are simulated on the Simulink model of a 6-degree-of-freedom 3-PPSS (P—prismatic; S—spherical) parallel manipulator. The simulation and real-time experiments performed on the fabricated manipulator prototype indicate that the proposed cascade controller with position and velocity compensation is an appropriate method for accurate tracking along the desired path. Also, training the network using the experimentally generated data set incorporates the mechanical joint approximations and link deformities present in the fabricated model into the predicted results. In addition, this article showcases the application of Euler–Lagrangian formalism on the 3-PPSS parallel manipulator for its dynamic model incorporating the system constraints. The Lagrangian multipliers include the influence of the constraint forces acting on the manipulator platform. For completeness, the analytical model results have been verified using ADAMS for a pre-defined end-effector trajectory.
An integrated continuous downstream process with real‐time control: A case study with periodic countercurrent chromatography and continuous virus inactivation
