Numerical solution of nonlinear H2 and H∞ control problems with application to jet engine control

We describe an effective numerical approach to solving nonlinear H₂ or H_∞ optimal control problems. We apply it to the problem of controlling jet engine compressor stall and surge instabilities (3D Moore-Greitzer model) while imposing saturation constraints. There is a curve of equilibria along which one may operate the engine, where the instabilities are hardest to control near the highest performance equilibria. Our numerical results show which equilibrium one can optimally control and which are unmanageable. Rate saturation constraints turn out to dominate this phenomenon. We choose a high performance manageable equilibrium E and compute the H₂ optimal law which will control the system to E. We then describe plots which allow one to find a neighborhood of the equilibrium within which the closed-loop system is guaranteed to remain.