Real-time Infinite Horizon Linear-Quadratic Tracking Controller for Vibration Quenching in Flexible Beams

It is well known that the infinite horizon linear-quadratic tracking problem does not have a solution in the strict sense because in general the performance index is infinite. Additional computational difficulties arise for applications where real-time computations are needed. However, for applications where the reference signal is generated by an asymptotically stable system, then the problem has an optimal solution. In the present paper a methodology that can be used to design real-time infinite horizon linear-quadratic tracking controllers for vibration quenching in flexible beams is presented. A numerical example is included to illustrate the effectiveness of the method.