Introduction

The objective of a control system is to influence the dynamic system to make it behave in a desirable manner (Ref. [1–9]). Typical objectives of a control system are regulation and tracking. In a regulation problem, the system is controlled so that its output is maintained at a certain set point. In a tracking problem, the system is controlled so that its output follows a particular desired trajectory. A special case of the regulation problem is the stabilization problem, in which a control system is designed to bring the system to rest from any nonzero initial conditions (i.e., the desirable set point is zero). For a flexible structure that may be subjected to unwanted vibration, this is usually the most important goal of a controlled system. Stabilization is the focus of this chapter. In particular, we consider a special but very important class of control systems, namely state-feedback control, in which the control input is some function of the system states. For the moment we assume that there are enough sensors to measure the state of the system at any point in time to be used in computing the control input. If the state of the system cannot be measured directly, then a state observer is needed to estimate the system state from the measurements. The estimated state is then used in a state-feedback-control law. This subject of state estimation will be dealt with in the next chapter.