NUMERICAL SIMULATION OF OPTIMAL MULTIPLE-INPUT, MULTIPLE-OUTPUT CONTROL OF JET IMPINGEMENT COOLING OF A GLASS PLATE

Abstract

In the present work, an optimal temperature-tracking control formulation is adopted leading to a comprehensive multiple-input, multiple-output (MIMO) structure for cooling of a glass plate by an impinging air jet. The jet velocity at the exit of the nozzle and the position of the nozzle array over the plate are used as control variables. Following a semidiscrete control-volume formulation of the transient heat conduction, the state-space model of nodal variation of glass temperature with time is derived. Optimal control theory along with the constraint of the state equations is applied for calculating the dynamic gain of the controller offline, following the minimization of a performance index. This minimization portrays control needs such as minimization of the variation of chosen state variables with respect to the input temperature track. The controller gain so obtained is fed to the fully discretized numerical heat transfer model, to evaluate the performance of the control. The numerical study helped us to arrive at an optimal set of weighting parameters for the performance index definition. A novel suboptimal dynamic proportional output control structure is proposed, which requires sensors to be placed only on the surface over which the jets impinge. No noticeable degradation in control performance was observed with respect to the optimal structure. The effect of neglecting radiation inside the glass in the control model is found to be negligible.