As control system complexity has increased, design of reduced order controllers (controllers with lower order than the design plant) has become an area of great interest. A new method of reduced order controller design based on the Youla parameterization of all stabilizing controllers is presented. In this method, a reduced order controller can be designed if a set of matrices which solves a Sylvester equation coupled with a standard linear equation can be found. A numerically stable and computationally efficient algorithm is developed which generates the solution and yields controllers with order equal to the minimum of v0-1 and vc-1, where v0 and vc represent the observability and controllability indices, respectively, of the design plant. Because v0 and vc are lower than the plant order for many multi-input, multi-output systems, reduced order controller designs are possible. Design examples are presented based on a control systems test fixture at NASA Marshall Space Flight Center.
The algorithm can also be applied to H∞ controller design problems to yield reduced order H∞ controllers for some systems. Examples of successful reduced order controller designs are presented for a normalized H∞ control problem and a mixed sensitivity H∞ problem.
Additional work shows that the Youla parameterization method has a direct interpretation in linear geometric control theory. This connection allows the designer to approach the reduced order controller design problem through the Youla Parameterization method or through geometric techniques.