| The control of plasma position, shape, and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coil and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting magnets, instability arising from the plasma vertical motion, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Physical models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including generating a nominal trajectory, dealing with the ill-conditioning of the system, complex equilibrium control, choice of the cost functional weights, discrete control, and order reduction. Results indicate that linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained. |
