Optimal non‐linear control with application to level control system

Abstract

The methodology of the optimal control strategy of the non‐linear control system, x = f (x) + g (x) u, with the quadratic performance index based on the original non‐linear system variables, x and u, is developed and the optimal non‐linear control law which is the function of the non‐linear system properties, f(x) and g(x), and the weighting factor ρ, is obtained. For the limiting case of the linear system, x = Ax + Bu, the non‐linear control can be reduced to the linear state feedback control which is exactly the same as that obtained by solving the well‐known Riccati equation. The simulations of an illustrative example of a level control system and the previous work of Ogunnaike are given to demonstrate this work.

Key words:

• non‐linear system
• level control
• optimal control
• nonlinear control law

Notes

Correspondence addressee