Numerical Solution of Nonlinear 2 and Control Problems with Application to Jet Engine Compressors

We describe an effective numerical approach to solving nonlinear 2 or optimal control problems. Our principal goal will be to use this approach to solve the important problem of jet engine compressor control. The technique is demonstrated first with the tutorial example of the control of a pendulum. We then apply the numerical approach to the problem of controlling jet engine compressor stall and surge instabilities (three-dimensional Moore–Greitzer model) while imposing saturation constraints. Standard in this model is a curve of equilibria along which one may operate the engine. Here, the instabilities are hardest to control near the highest performance equilibria. Our numerical results tell us rather dramatically which equilibrium one can optimally control to and which are unmanageable. The magnitude of the rate saturation constraint on the controller turns out to dominate this phenomenon. We choose a high-performance manageable equilibrium E and compute the 2 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. The technique should work with little modification in dimensions 4 and 5, at which point the “curse of dimensionality” forces restrictions.