Optimal discrete-time structural control using direct output feedback

An optimal direct discrete-time output feedback control algorithm is developed. According to the proposed algorithm, optimal discrete-time output feedback gain is derived through a variational process such that a certain prescribed quadratic performance index is minimized. It is verified that the classical optimal discrete-time state feedback control algorithm is just a particular case of the proposed control algorithm. With the introduction of special matrix operations, optimal output feedback gain is obtained systematically by solving simultaneously linear algebraic equations iteratively. Control forces are then generated directly from output measurements multiplied by the pre-calculated shift-invariant output feedback gain. A small number of sensors and controllers, and simple on-line calculation make the proposed algorithm favorable to real-time control implementation. Numerical verification is illustrated by the control of a single degree-of-freedom (DOF) and a three degree-of-freedom structure subjected to real earthquake excitations. Differences between discrete-time and continuous-time output feedback control are discussed.