Additional control strategies are often incorporated into inverter-based renewable energy sources to enhance the stability of power systems, which introduce frequency response and damping controls that affect the small-signal stability of the system. To address the issues of diminished frequency support capability and damping levels in power systems following the integration of multiple wind farms (WFs), this study investigates the interaction between integrated inertia control and power oscillation damping control. We then propose a grid-friendly coordinated robust control of multiple WFs to simultaneously provide system frequency support and damping enhancement. First, the coupling characteristics of the additional control loops in the WFs are analyzed using a multi-machine damping torque analysis. Then, based on the principles of optimal frequency response ability and optimal damping support ability of WFs, a coordinated robust control model of multiple WFs is established to maximize frequency offset improvements and maximize the minimum damping ratio of dominant oscillation modes. Finally, a multi-objective model-solving algorithm based on eigenvalue sensitivity analysis is proposed to determine the optimal control coefficients. Simulation results demonstrate the effectiveness of the proposed control for WFs in system frequency support and damping enhancement.