Design of LQG and H∞ multivariable robust controllers for process control applications

The computation of H∞ and LQG optimal controllers is considered for process control applications. There are many process control problems where significant uncertanties exist in the system models which therefore require robust control designs. A simple solution for the optimal H∞ robust design problem is considered and the relationship to super-optimal solutions is discussed. For special types of weighted plant model the main H∞ equations to be solved are shown to be decoupled so that the calculations are similar to the scalar case. This situation is shown to arise when a mixed-sensitivity cost-function is selected and the plant has an interaction structure typical of many hot or cold rolling mill gauge control applications. A simplified design procedure is also introduced which further simplifies the calculations of the optimal controller and enables standard eigenvector/eigenvalue algorithms to be employed in solving the equations. The procedures are illustrated using a multivariable metal processing control design example.