Multivariable Temperature Control of a Heated Rod by Using a Reduced-Order Internal MIDR-Model

In this contribution, a tracking control design based on a reduced-order internal model control (IMC) approach 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, where the first and the third ones are employed as distributed control inputs. The method of integro-differential relations in combination with a projection approach yields a state-space model of order nine. After a balanced model-order reduction, which results in a model order of four, an observer-based IMC is designed with an approximate inverse system model. The time lag behaviour of the IMC structure can be addressed by a dynamical feedforward control that improves the tracking behaviour further. An implementation at a test rig at the Chair of Mechatronics, University of Rostock, points out that an acceptable decoupling of both outputs and an accurate tracking of desired trajectories can be achieved with the proposed control structure.