5. Feedback Control

The aim of this chapter is to illustrate the design of the feedback control system for beam and plate structures. In Sect. 5.1, the linear quadratic regulator (LQR) problem is presented. In Sect. 5.2, the linear quadratic Gaussian (LQG) problem is discussed with vibrating beam and plates. One GUI program is given to compare the control performance between LQR and LQG controllers. In Sect. 5.3, the basic principle of modal control is given. In Sect. 5.4, we review SISO analytical models for a structure and closed-loop analysis techniques. Basic stability criteria tools for feedback control system, such as root locus criterion and Bode plot and Nyquist criterion, and their use in identification of gain and phase margins are discussed. In Sect. 5.5, the internal model control (IMC) is presented. In some special cases, the feedback control system can be seen as a feedforward system by using IMC. In Sect. 5.6, the design of a robust control system is discussed. In this section, the theory of robust control is not presented but the preparation for control design for several practical design cases by using MATLAB is given extensively. Two tutorial examples, i.e., control of vibration of a vibrating beam and control of sound radiation of a plate, are given and discussed in detail. How to generate the generalized plant and how to select the weighting functions are the main topics in this section.