A new LMI solution in the L1 optimal problem for wind turbine-induction generator unit

An application of a new L1-optimal control technique based on linear matrix inequality optimization to a wind turbine-induction generator unit is presented. The new technique, which is proposed as an algorithm, combines the original concept of peak-to-peak gain of designed system with optimal control theory and employs a free design parameter allowing for a flexible management of the tradeoff between robustness to disturbance signals and magnitude of the worst peak-to-peak gain of the design system. For solving this non convex problem,, using several transfer function for linearization and linear matrix inequality optimization approach. For the convergence of this algorithm, a scope is found on the basis of the H∞-norm. If the length of this interval is small, we have a good estimate of the actual optimal peak-to-peak gain that is achievable by control. Application to the wind turbine-induction generator unit provides fast response with a good steady state error, suitable settling time and stability upon severe wind gust.