Tip position control of flexible single-link manipulators in the frequency domain without model reduction

This article develops the fundamentals of the tip position control of flexible single-link robotic manipulators in the frequency domain without approximating the model. Analytic transfer functions of the hub angle and tip position are derived without any model order reduction. Conditions for the stability of the transfer functions are presented by considering the payload mass change as an uncertain parameter. Using the D-decomposition method, a simple procedure is introduced to design an output feedback controller which guarantees the stability and a desired tracking performance. The introduced design method leads to less conservatism comparing with design methods established upon model reduction. The controller structure includes two proportional-derivative and integral loops and needs only two measurements of joint angle and tip position which are easily implementable. A numerical example is provided to demonstrate the merit of the achieved results.