Optimal control of a batch fermentation process with nonlinear time-delay and free terminal time and cost sensitivity constraint

Abstract

In this paper, we consider a nonlinear time-delay dynamic system with uncertain system parameters to characterize the process of batch fermentation. Our goal is to design an optimal control scheme to maximize the productivity of 1,3-propanediol (1,3-PD). Accordingly, we introduce an optimal control problem governed by the nonlinear time-delay dynamic system, in which the control variables are the free terminal time of the batch fermentation process and the initial concentrations of biomass and glycerol. The optimal control problem is subject to a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved and continuous state inequality constraints for ensuring that the concentrations of biomass, glycerol, 1,3-PD, acetate, ethanol lie within specified limits. Then, the optimal control problem with free terminal time is transformed, via a hybrid time-scaling strategy, into an equivalent problem with fixed terminal time, which is much preferred for numerical computation. Using the constraint transcription and local smoothing approximation techniques, we approximate these continuous state inequality constraints by conventional inequality constraints to yield an approximate optimal control problem. Because of the highly complex nature of this approximate problem, a parallel algorithm based on the filled function method is constructed to solve this approximate problem. Finally, it is observed that the optimal control obtained is satisfactory through numerical simulations.

A Two-Stage Method for Parameter Identification of a Nonlinear System in a Microbial Batch Process

“…By introducing Equations (8)- (12) into Equations (1)-(5), Equations (1)-(7) have the following formulations:…”

“…Liu et al [11] presented the bi-objective dynamic optimization of a nonlinear time-delay system to optimize 1,3-PD production in a microbial batch process. Yuan et al [12] gave an optimal control strategy of a nonlinear batch system with a time delay to maximize 1,3-PD production. Hirokawa et al [13] used the engineered cyanobacterium Synechococcus elongatus to improve the production of 1,3-PD by optimizing the gene expression level of a metabolic pathway and operation conditions.…”

A Graphical User Interface for dynamics and feedback control studies focus on chemical reactors

“…The issue of their automatic process control, although widely investigated in research and teaching literature, still remains a live one. Chemical reactor design and control was covered by Luyben [3] [4]; more recently, a continuity diagram analysis at open as well as closed loop was developed by Cosenza et al [5] to improve the operability of a reactor; a nonlinear model predictive control of a batch fluidized bed dryer for pharmaceutical particles was proposed by Gagnon et al [6]; Holmqvist and Magnusson developed an open-loop optimal control of batch chromatographic separation processes using direct collocation methods [7]; an optimal control of batch cooling crystallizers by using genetic algorithm was proposed by Amini et al [8]; Wu et al improved design of constrained model predictive tracking control for batch processes against unknown uncertainties [9], Yuan et al [10] realized an optimal control of a batch fermentation process with nonlinear timedelay and free terminal time and cost sensitivity constraint. Dieulot proposed a productivity signal feedback controller for continuous bioreactors [11]; Imtiaz et al [12] proposed a bioreactor profile control by a nonlinear autoregressive moving average neuro and two degree of freedom PID controllers; Gerardo et al [13] suggested an extremum seeking approach via variable-structure control for fed-batch bioreactors with uncertain grow rate; an estimation problem of a class of continuous bioreactors with unknown input was advanced by Moreno and Alvarez [14]; advanced control strategies for bioreactors were proposed by Pörtner et al [15]; a bioreactor temperature control using modified fractional order IMC-PID was used by Pachauri et al, for ethanol production [16].…”

A control parametrization based path planning method for the quad-rotor uavs

“…Continuous state inequality constraints [16,12,20], which are also referred to as path constraints, are difficult to handle. This is because there are infinite number of constraints on the time horizon.…”

“…Further, by applying the control parametrization technique [16,12,20,19], the original time optimal control problem is transformed into an optimal parameters selection problem subject to canonical constraints [12,20,19]. The transformed problem can be treated as a nonlinear program, and there are many existing computational method for solving such problems.…”