Multivariable trajectory tracking control for a heated rod based on an integro-differential approach to control-oriented modelling

In this contribution, a model-based tracking control design is proposed for the temperatures at two selected points of a spatially one-dimensional iron rod. The rod is equipped with four Peltier elements on the lower surface, of which the first and the third ones serve as distributed control inputs. For a semi-discretisation of the partial differential equation, the method of integro-differential relations is combined with a projection approach. Introducing four finite elements, a statespace representation of order nine is obtained and used for the subsequent design of a tracking control structure that involves a decoupling dynamic feedforward control as well as proportionalintegral state feedback control. Furthermore, an optimal observer is designed that provides estimates for the complete state vector as well as four additional disturbance variables. Simulations and experimental results at a test rig at the Chair of Mechatronics, University of Rostock, show that a decoupling of both outputs and an accurate tracking of desired trajectories is achievable.