Optimal control and design of flexible manipulators based on LQR output feedback

The construction of lightweight manipulators with a larger speed range is one of the major goals in the design of well-behaving industrial robotic arms. Their use will lead to higher productivity and less energy consumption than is common with heavier, rigid arms. However, due to the flexibility involved with link deformation and the complexity of distributed parameter systems, modeling and control of flexible manipulators still remain a major challenge to robotic research. Mechatronic design is a global optimization of the overall system. As a flexible manipulator, the overall system is the integration of link dynamics, DC motor equation, measuring sensors and the selected controller. The optimization process will result in an optimal link geometric distribution, an optimal controller structure subject to the performance requirement. A rectangular beam is considered and divided into N segments equally along with the beam spatial coordinate. Case studies based on LQR formula are considered. The LQR feedback is as an inner loop followed by an Adaptive Iterative algorithm (IHR) as an outer loop searching for the beam width distribution. The mechatronic design procedure is addressed through detailing the integration of the inner loop with the outer loop. Also, The responses for step-type disturbance and step input are carried out to show the system robustness.