Extensions to H_∞ multivariable robust controllers and the relationship to LQG design problems

Abstract

An alternative set of equations for generating H_∞ multivariable controllers is derived which are of quadratic form. These can be solved by Newton-Raphson procedures as in the work by Kwakernaak (1986). It is shown that the H_∞ controller may be put in the form of a Youla parameterization. The particular parameterization employed provides a link with the equivalent LQG robust optimal controller, since when the Youla gain falls to zero the controller becomes identical. It is also shown that for canonical multivariable industrial system models the equations to be solved have a very simple structure. This enables the multivariable problem to be solved using algorithms which are almost as simple as for the scalar case. That the results have a practical application is illustrated in a strip flatness cold rolling problem.