Modal analysis and control of a rotating Euler-Bernoulli beam part I: Control system analysis and controller design

Control of the vibration modes become critical when one wants to push the state of the art with faster, lighter, and more accurate flexible link. There are three steps which are necessary for the control of the flexible link. First, a good design based model of the plant must exist. Second, a good controller which is also realizable must be designed. Third, input to the controller must be constructed using knowledge of the system dynamic response. In this paper, involving a complete control strategy, pertaining to design based model, control, and dealing with the shaping of system input is presented. In Part I, a single-input single-output transcendental transfer function, pole-zero pattern, controllability, observability, and system type for distributed parameter system is illustrated by application to feedback control of an Euler-Bernoulli beam. The eigenfunctions, orthogonality condition, and mode summation method have been investigated in order to get the system analytical solution. A new control scheme, which depends on the pole-zero plot of the infinite-dimensional system and uses a realizable actuator and sensor without involving truncation of the higher-frequency modes, shows that good stability, robustness, and efficient tracking property can be achieved by moving all the poles of the corresponding closed-loop system further into the left half-plane.