Application of μ-interaction measures for decentralized temperature control of packed-bed chemical reactor

The objectives of this study are two-fold; to apply robust control tools hitherto used mostly for lumped parameter systems (LPS) to distributed parameter systems (DPS); and to investigate robustness of decentralized distributed controllers when operated under a full MIMO plant in the presence of unmeasured disturbance. The energy balance model of the packed-bed reactor is discretized using orthogonal collocation with the heat of reaction regarded as unmeasured disturbance. The resulting MIMO state space model is used for designing a decentralized temperature controller. Employing the IMC tuning rules as baseline, a decentralized PI controller is designed using only the diagonal elements of MIMO model treating off-diagonal terms as uncertainty. The off-diagonal interactions are used to design bounds called μ-interaction measures which are imposed on nominal closed-loop transfer functions. Satisfaction of these bounds guarantees that the designed decentralized controller will yield robustness over the full MIMO plant.