Robust controller design for linear dynamic systems using approximate models

Controller design for scalar or multivariable systems whose models are unknown or highly complex are frequently based in practice on the use of a highly simplified approximate plant model. In such circumstances it is vital to be able to quantify the degree of uncertainty to be expected from the use of such a model for prediction of closed-loop characteristics. It is shown how frequency-domain design techniques can be simply extended to incorporate information deduced from the observed differences between open-loop plant and the approximate model step response to quantify this uncertainty and, in particular, to guarantee closed-loop stability and tracking of step demands. A modification of this analysis also yields the possibility of bounding the error in prediction of closed-loop transient performance. The approaches are all graphical in nature and are easily implemented in an interactive computer-aided-design mode.