Nonlinear adaptive inverse control

Adaptive control is seen as a two part problem, (a) control of plant dynamics, and (b) control of plant disturbance. Conventionally, one uses feedback control to treat both problems simultaneously. Tradeoffs and compromises are necessary to achieve good solutions, however. The method proposed here, based on inverse control, treats the two problems separately without compromise. The method applies to SISO and MIMO linear plants, and to nonlinear plants. An unknown linear plant will track an input command signal if the plant is driven by a controller whose transfer function approximates the inverse of the plant transfer function. An adaptive inverse identification process can be used to obtain a stable controller, even if the plant is nonminimum phase. A model-reference version of this idea allows system dynamics to closely approximate desired reference-model dynamics. No direct feedback is used, except that the plant output is monitored and utilized by an adaptive algorithm to adjust the parameters of the controller. Although nonlinear plants do not have transfer functions, the same idea works well for nonlinear plants. Control of internal plant disturbance is accomplished with an adaptive disturbance canceler. The canceler does not affect plant dynamics, but feeds back plant disturbance in a way that minimizes plant output disturbance power. This approach is optimal for linear plants, and works surprisingly well with nonlinear plants.