Robust Process Control Based on the Passivity Theorem

A robust process control strategy based on the passivity theorem is proposed in this paper. The uncertainties are characterised in terms of a revised passivity index. The passivity-based robust stability condition is derived and the tradeoffs between the robustness and nominal performance are analysed. Using Semi-Definite Programming, a two-step controller design procedure is developed to meet both the passivity-based stability condition and nominal performance specifications. As both the phase and gain information of the uncertainties are taken into account, the control method proposed may achieve better performance for the same robustness requirement than conventional H∞ control. This is illustrated by an example of the control of a reactor.