Multivariable tuning regulators: The feedforward and robust control of a general servomechanism problem

A new notion of compensator identification, as opposed to the conventional plant identification problem, is introduced in this paper. It is assumed that it is desired to synthesize a robust feedforward-feedback controller for an unknown plant so that asymptotic tracking, in the presence of disturbances, occurs. The only assumptions made regarding the description of the plant model are that 1) the plant is linear and time-invariant and 2) the uncontrolled plant is stable. Note that it is assumed that the order of the plant model is unknown. It is assumed that the control inputs to the plant can be excited, that the outputs of the plant which are desired to be regulated can be measured, and that the class of disturbance inputs and reference inputs is known. In addition, it is also assumed in the feedforward controller case, that the disturbance inputs can be measured and be excited; this assumption is not required in the robust feedback controller case. Necessary and sufficient conditions which allow the robust feedforward-feedback compensator to be synthesized so that the controlled system is stable and so that asymptotic tracking, in the presence of both measurable and unmeasurable disturbances, occurs are obtained. An algorithm which allows the controllers to be synthesized is given. Some numerical examples are included to illustrate the results.