In this paper we present estimation and control results for wind plants, based on FLORIDyn, a novel control-oriented dynamic model for wake interaction effects between wind turbines in a wind plant. The model predicts wake locations, effective flow velocities, and electrical energy production at each turbine as a function of the control degrees of freedom of the turbines. The model includes the dynamic wake propagation effects that cause time delays between control-setting changes and the response of downstream turbines. These delays are a function of the state of the flow field in the wind plant. The model has a state-space structure combined with a nonlinear feedback term. A Kalman filter is developed for the model that corrects the flow field predictions using wind turbine power production measurements. The computational complexity of the model is small enough that it has the potential to be used for optimizing the control reference signals for improved wind plant control, as demonstrated in a case study.