Robust Fixed Order Dynamic Compensation: a Differential Game Approach

H-infinity control theory has gained wide acceptance over the past 10 years as a valuable method of controller design. However, for most applications the solution results in a controller of higher dimension than that of the plant. As an alternative to controller order reduction, low order controllers can be designed by fixing the order of the controller apriori. Probably the most well-known approach to fixed order robust control is the optimal projection theory of Bernstein and Haddad. Unfortunately, the computational aspects of this approach are formidable. In this paper, a method is presented which allows the use of more standard numerical techniques. The robust control problem is formulated in the time domain as a differential game. Three coupled, first order necessary conditions are derived and a conjugate gradient algorithm is used to search for solutions. Two examples are used to test the approach: a simple, second order example and a 7th order problem describing the longitudinal dynamics of a fighter aircraft.