Design of model reference control systems using a Lyapunov synthesis technique

The Vfunction synthesis technique for designing adaptive loops, so that a model reference system will be controlled in a stable manner, is extended so that each parameter of a high-order linear plant is adjustable. The plant need not be the same order as the model, and both could incorporate zeros as well as poles. Use of either of the two control forms that are derived leads to a stable adaptive step response; a comparison between these loops and others that may alternatively be used is made. The effect of parameter variation due to environmental changes is considered, and simulator studies verify that the behaviour of a simple system may still be adequately regulated.