Modeling, System Identification and Linearization of Underwater Turbine Power Plant Dynamics

A suite of nonlinear dynamical simulations of in-stream hydrokinetic devices has been developed and this paper discussed the linearization of these models for control system development. One of these numerical simulations represents a small 3 meter rotor diameter, 35 kW turbine with fixed pitch blades, and the other a 20 meter, 700 kW turbine with variable pitch blades. Each turbine simulation can be operated to represent a bottom mounted tidal turbine or a moored ocean current turbine. These nonlinear dynamical models can serve as stepping stones toward control system design using linear or nonlinear, time or frequency-domain methodologies. A common step further toward controller synthesis is to obtain linearized models of the system dynamics. Towards this end, two linearization techniques are presented. The first is based straightforward analytical and numerical linearization of the full nonlinear state-space equations of the plant; this method has been applied for the underwater flight dynamics of the 700 kW plant. The second is a phenomenological system identification approach consisting of data analysis performed on time series obtained through simulations; it has been used to model the system of systems in the case of the 35 kW plant. In the first approach, the linearized model is valid for specific operating conditions around equilibrium values of the state variables. In the second approach, the plant dynamical model is used as a black-box in order to obtain the simulated response of the system to a variety of test input signals, like e.g. sinusoids of relatively small amplitudes and various frequencies superimposed to steady-state offsets; in effect, a phenomenological model is derived describing the plant dynamics. The outcomes of both approaches are assessed and several conclusions are drawn from the analysis.