G-Field Control of nonlinear systems

Abstract

A typical design approach for controlling dynamic systems is to decompose the system into inner and outer loops while imposing some amount of frequency separation between the inner and outer loop dynamics. Criteria for selection of the inner loop include fast variables an integrator away, and other criteria often based on experience. A systematic approach for identifying inner loop variables, particularly for a complicated or poorly understood nonlinear dynamical system, does not exist. G-Field Control is a design approach for developing inner / outer loop controllers for nonlinear systems. Identification of the inner loop is clearly defined. The goal of the inner loop controller is to tightly control the vector fields g(x) (through which the control input enters the system) to a desired value. The vector fields g(x) are assumed to be at the desired values for development of the outer loop controllers. A G-Field Control design example and simulation results are presented for a hover control problem. Requirements for global stability of two dimensional systems are included.