Numerical solution of nonlinear H-2 and H-infinity control problems with application to jet engine compressors

We describe an effective numerical approach. to solving nonlinear H-2 or H- infinity, optimal control problems, Our principal goal will be to use this approach to solve the important problem of jet engine compressor control, T he technique is demonstrated first with the tutorial example of the control of a pendulum. We then apply the numerical approach to the problem of cont rolling jet engine compressor stall and surge instabilities (three-dimensio nal Moore-Greitzer model) while imposing saturation constraints. Standard i n this model is a curve of equilibria along which one may operate the engin e, Here, the instabilities are hardest to control near the highest performa nce equilibria, Our numerical results tell us rather dramatically which equ ilibrium one can optimally control to and which are unmanageable, The magni tude of the rate saturation constraint on the controller turns out to domin ate this phenomenon. We choose a high-performance manageable equilibrium E and compute the H-2 optimal law which will control the system to E, We then describe plots which allow one to find a neighborhood of the equilibrium w ithin which the closed-loop system is guaranteed to remain. The technique s hould work with little modification in dimensions 4 and 5, at which point t he "curse of dimensionality" forces restrictions.