Optimal IMC Design via Spectral Factorization

A general analytical solution to the design of optimal integrated mean square error inverses for multivariable Internal Model Controllers (IMC) is presented. The solution to the optimization is arrived at via matrix spectral factorization with the process model representation in pulse transfer function form. The design procedure provides approximate inverses with greatly improved singular values and condition numbers. These inverses yield not only excellent performance, but also allow one to trade-off performance with robustness in a straightforward manner. These inverse designs are evaluated and compared against other IMC designs in a simulated study on a packed bed tubular reactor.