A Discrete-Time Pid-Like Consensus Control: Application To The Wind Farm Distributed Control Problem

The problem of discrete-time multi-agent systems governed by general MIMO dynamics is addressed. By employing a PID-like distributed protocol, we aim to solve two relevant consensus problems, namely the leaderless weighted consensus under disturbances and the leader-follower weighted consensus under time-varying reference state. Sufficient conditions for stability as well as a LMI approach to tune the controller gains are provided. The two consensus techniques are then applied to solve two issues concerning the wind farm (WF) power maximization problem under wake effect. Leaderless consensus aims at averaging out zero-mean wind disturbance effects on the optimal WF power sharing, while leader-follower control is employed to restore it in the case of power reference errors. Simulations are carried out on a small WF example, whose wind turbines parameters are the ones of NREL's CART turbine.