An Application of the Βalanced Τruncation Αlgorithm Using Linear Mapping to the Robust Control Problem for the Ward-Leonard System in Wind Turbines

The Balanced Truncation Algorithm (BTA) is one of the most used model order reduction algorithms, while multiple new algorithms have been developed based on the former. This paper presents in detail a solution that applies linear mapping to the subdivision process to reduce the order of a stable linear system. To demonstrate the correctness and applicability of the improved algorithm, the latter was applied to reduce the order of a 6th-order controller in a Wind Turbine (WT) system. After evaluating several reduced-order controllers, the 2nd-order controller was identified as the most suitable replacement for the original 6th-order controller. The results show that the system’s output response using the 2nd-order controller closely matches that of the original system using the 6th-order controller.