Optimal IMC inverses: Design and robustness considerations

A general method for obtaining least-squares optimal inverses for multivariable internal model controllers (IMCs) is presented. An analytical solution is arrived at using a well-known method for optimally factorizing discrete transfer function matrices. The procedure automatically handles unbalanced, noninvertible and nonsquare systems, and provides controllers with excellent performance and robustness properties. These IMC designs are compared with some of the more traditional IMC designs where tunable diagonal filters are used with fixed but usually suboptimal inverses. Robustness properties are investigated using four approahces: singular values and condition numbers of the approximate inverse models, singular-value analysis assuming unstructured norm-bounded uncertainty, a single-parameter structured singular value analysis based on disk uncertainties in each element of the transfer function matrix.