This paper deals with the power capture control of variable-speed wind energy conversion systems. The control objective is to optimize the capture of wind energy by tracking the desired power output. Arbitrary steady-state performance is achieved in the sense that the tracking error is guaranteed to converge to any predefined small set. In addition, to maximize the wind energy capture, transient performance is enhanced such that the convergence rate can be larger than an arbitrary value, which further limits the maximum overshoot. First, an adaptive controller is designed for the case where known aerodynamic torque is assumed. Then, by utilizing an online approximator to estimate the uncertain aerodynamics, the need for the exact knowledge of the aerodynamic torque is waived to imitate the practical experience. With the aid of a novel output error transformation technique, both of the proposed controllers are capable of shaping the system performance arbitrarily on transient and steady-state stages. Meanwhile, it is also proved that all the signals in the closed-loop system are bounded via Lyapunov synthesis. Finally, the feasibility of the proposed controllers is demonstrated on an 1.5-MW three-blade wind turbine using the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code developed by the National Renewable Energy Laboratory.