  A lumped parameter model for tokamak plasma current and inductance time
evolution as function of plasma resistance, non-inductive current drive sources
and boundary voltage or poloidal field (PF) coil current drive is presented.
The model includes a novel formulation leading to exact equations for internal
inductance and plasma current dynamics. Having in mind its application in a
tokamak inductive control system, the model is expressed in state space form,
the preferred choice for the design of control systems using modern control
systems theory. The choice of system states allow many interesting physical
quantities such as plasma current, inductance, magnetic energy, resistive and
inductive fluxes etc be made available as output equations. The model is
derived from energy conservation theorem, and flux balance theorems, together
with a first order approximation for flux diffusion dynamics. The validity of
this approximation has been checked using experimental data from JET showing an
excellent agreement.
