MATHEMATICAL MODELING AND CONTROL OF TWO-LINK FLEXIBLE MANIPULATORS WITH ACTUATOR DYNAMICS AND NONCOLLOCATED FEEDBACK

Modern applications in aerospace, biomedical and industry can make use of flexible-link robotic manipulators because they are lightweight, work fast and are energy efficient. Still, the inclusion of flexibility, special actuator dynamics and remote feedback makes it harder to model and control flexible linkages. A two-link flexible manipulator is mathematically modelled in this study using Euler-Bernoulli theory, Lagrangian mechanics and also includes second-order actuator dynamics with noncollocated sensors in the state-space version. Handling the resulting complexity and the issues of tracking states, a new Time-Varying Sliding Mode Controller (TSMC) is proposed. To ensure accurate movement and good vibration control, adaptive polynomial trajectories and disturbance rejection are applied by the controller. Simulations in MATLAB with a 0.02s time step and a duration of 80 seconds show that the proposed three-stage controller brings about both smooth joint movement and early damping of the cyclic deformations within the structure frame (d11–d22). The outcomes confirm that the controller functions well despite sensor delay, flexible buildings and unaccounted for dynamics. The framework as proposed is useful for controlling fast flexible manipulators and is simple to expand for use with experimental and AI solutions in future robotics.