Pseudo Dynamic Model Reference Nonlinear Control of a Continuous Bioreactor with Input Multiplicities

In the present work, the model reference nonlinear controller (MRNC) based on pseudo dynamic model is designed to a continuous bioreactor which exhibits input multiplicities in dilution rate on productivity. i.e., two values of dilution rate will give the same value of productivity. The performance of MRNC and linear PI controller have been evaluated through simulation studies. The optimal parameters of MRNC have been obtained based on integral square error criterion (ISE) through simulations. As the MRNC provides always the two values of Dilution rate for control action and by selecting value nearer to the operating point, it is found to give stable and better response than linear PI controller. Linear PI controller results in wash out condition or switch over from initial lower input dilution rate to higher input dilution rate or vice versa. Thus, PDMRNC is found to overcome the control problems of PI controller due to the input multiplicities Abbreviations A. List of Symbols D h-1 dilution rate e error K I g/l substrate inhibition constant K m g/l substrate saturation constant K c controller gain P g/l product concentration P m g/l product saturation constant Q g/l/h product cells produced per unit time S g/l substrate concentration S f g/l substrate feed concentration t h time ts h settling time X g/l biomass concentration Y g/lh measured value of productivity Yr reference value for Y B. Greek Letters α g/g product yield parameter β h-1 product yield parameter μ h-1 specific growth rate μ m h-1 maximum specific growth rate τ I h integral time τ D h derivative time ξ damping coefficient ψ g/g cell mass yield II. INTRODUCTION Input multiplicities mean more than one value of an input variable (u) produce the same value of an output variable (y). The condition for the input multiplicities for single input and single output nonlinear systems is that the derivative of output with respect to the input must be zero (i.e., (dy/du)=0). In general input multiplicities occur due to the presence of competing effects in the nonlinear processes [1]-[4]. The nonlinear chemical processes such as the continuous stirred tank reactors (CSTRs) in series with the exothermic reaction(A→B),flash separation unit, the nonlinear processes with recycle structures such as heat exchanger network and the combine unit of reactor and distillation column are shown to exhibit input multiplicities[1],[4]. Also, a single exothermic CSTR with series reversible reaction scheme [1]. Control …