Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part I: A unified approach to the design of linear control system

Due to difficulties in modeling and poor knowledge of parameters, the behavior of flexible structures is subject to significant uncertainty. Hence it is essential that the control system provide an absolutely stable property in the presence of large variations. Over the years, many control laws-proportion and derivative (PD) control, nonlinear, linear-quadratic, adaptive, and linear quadratic Gaussian (LQG)-have been synthesized for flexible structures. The most commonly am plied are the LQG controllers. In spite of its attractive qualities, the LQG controller is sensitive to parameter variations, and therefore its performance will deteriorate when the payload or typical parameters of the system vary with time. At the same time, the LQG controller does not guarantee general stability margins, and this is, perhaps, its main drawback. On the other hand, the PD is one kind of controller that ensures system stability to parameter variations within a certain bound. But a problem with the PD controller is evident; when high-frequency noise is present in the system, this noise will be amplified by the PD controller, which is generally unacceptable. In this paper, instead of using a PD controller, a passive lead compensator is employed, so that (1) no additional power supplies are required and (2) noise due to differentiation is reduced. This lead compensator, together with a composite control strategy designed by the most popularly used sensors, potentiometer and tachometer, for the corresponding closed-loop system, has been shown with very good agreement in terms of system performance requirement. For the design of control system, it is practical to first design the controller based on the linear system model by neglecting the nonlinearities of the system. In Part II the lead compensator, together with complementary control strategy and computer simulation modeling for a rotating flexible structure, with particular application to elastic rod system, is presented for the linear control system. Then the designed controller is applied to the nonlinear system model for evaluation and redesigned by computer simulation. This will be presented in Part II.