Feedback Control Design for Three-Time-Scale System using Two-Time-Scale Approach

In this paper, three-stage feedback control design for a three-time-scale system is proposed by the two-time-scale approach. Using two-time-scale similarity transformations, the original three-time-scale system is converted into lower triangular form with slow, fast and fastest subsystems. Then, feedback controls are designed separately for the subsystems, once again utilizing two-time-scale methodology. Finally, feedback control for the full order system is obtained from subsystem controls using state variable transformation matrices. The presented method is found to be simple and easy to implement. In this method, simply four linear transformations are needed, i.e. only four linear algebraic equations are required to be solved. Due to the use of two-time-scale structure, matrix calculations are also minimized compared to three-time-scale one. As a result, the overall time required for computation is reduced considerably. Performance of the suggested design technique is evaluated by comparing it with the recently published method.