Abstract: This paper studies the discrete-time optimal control of a flexible cantilever beam with time delay in control. The mode-controlled equation with time delay is presented and then discretized and transformed into the standard discrete form which contains no time delay. The continuous performance index is also discretized into the standard discrete form. Thus the discrete optimal controller can be designed based on the discrete optimal control theory.Since no approximation is made in the derivation of the time-delay optimal controller from the mode-controlled equation, the system stability is easy to guarantee. In addition, the extraction of modal coordinates from actual measurement and the transformation of actual control force from the modal control force are presented in this paper too. Feasibility and effectiveness of the proposed control algorithm are illustrated by numerical simulations at the end of thispaper.

Key words: flexible cantilever beam, independent mode space method, time delay, discrete optimal control, continuous performance index