Closed loop identification of transfer function model for unstable bioreactors for tuning PID controllers

Abstract

Closed loop identi®cation of transfer function model for an unstable bioreactor is proposed based on an optimization method using either a step or a pulse response of PI/PID controlled bioreactor. A simple method is proposed for the initial guesses of the parameters of the ®rst order plus time delay (FOPTD) transfer function model. A PID controller is designed for the identi®ed model. Simulation study on the nonlinear model equations of an unstable bioreactor exhibiting multiple steady-states shows that the PID controller designed on the identi®ed FOPTD model gives a good closed loop response similar to the one designed based on the linearized model from the nonlinear model equations. List of symbolsD dilution rate (1/h) k c controller gain k p open loop process gain K I substrate inhibition rate constant (g/l) K m substrate saturation constant (g/l) L time delay of the open loop system s Laplace variable S substrate concentration in the bioreactor (g/l) S f feed substrate concentration (g/l) t time (h) t s settling time of the closed loop system (h) X cell mass concentration g/l y p,cl output of the closed loop system y m,cl output of the closed loop model y p output of the open loop system Greek symbols s time constant of the open loop system s I integral time of the controller s D derivative time of the controller f damping coef®cient of the open loop system f cl damping coef®cient of the closed loop system l speci®c growth rate constant l m maximum speci®c growth rate constant c yield coef®cient D deviation variable from the steady-state condition 1 Introduction Identi®cation of transfer function model of a bioreactor is required for the design of PID controllers. Identi®cation of transfer function model can be carried out by open loop or by closed loop method. Closed loop identi®cation is preferable since the method is insensitive to disturbances and measurement noise. Further, identi®cation of transfer function model for unstable bioreactors can be carried out only by closed loop method. In this method, closed loop response for a step change in the set point is obtained by using a proportional controller. The controller gain is adjusted such that the closed loop response resembles that of an underdamped second order plus time delay model. From this response, the closed loop transfer function model is ®rst identi®ed. Then the open loop transfer function model is assumed whose parameters are extracted from the closed loop transfer function model. Kavdia and Chidambaram [1] have applied this method to identify an unstable FOPTD model of an unstable bioreactor. The method is an extension of the method proposed by Yuwana and Seborg [2] for stable system. Since the proportional controller introduces offset, the method may not be permitted in industries. For unstable systems with a ratio of time delay to time constant >0.67, the proportional controller cannot stabilize the reactor [3]. Recently Ananth and Chidambaram [4]have proposed a method to identify a FOPTD model for an unstable bioreactor by using a PID cont...

Fuzzy servo controller for CSTB with substrate inhibition kinetics

“…Pramod and Chidambaram [4] designed a PID stabilizer for an unstable bioreactor. However, classical linear control algorithms have shown unsatisfactory performance in bioprocesses under uncertain parameters and disturbances [5].…”

Subspace Identification of Transfer Function Models for an Unstable Bioreactor

“…Kavdia and Chidambaram (1996) proposed a method for tuning controllers online for an unstable bioreactor. Pramod and Chidambaram (2000) proposed a closed loop method of identifying a transfer function model for an unstable bioreactor based on an optimization method. Identification of bioreactors by a non-linear auto-regressive moving average with exogenous input is discussed by Rishi and Prabirkumar (2007).…”

Optimal PID Controller Designing for Uncertain Bioreactor Using BFO Algorithm

“…Figure.1 depicts the diagram of abioreactor [1,2]. [5,6,18]. In this work, a small scale bioreactor widely analysed by the researchers is considered and the corresponding mathematical equations are represented below [3,5];…”

“…Zhao and Skogestad discussed various possible control configuration of the bioreactor system [4]. Pramod and Chidambaram discussed the identification and model based PID controller design for bioreactor operating at unstable steady state [6]. Rajinikanth and Latha proposed heuristic algorithms such as Particle Swarm Optimization (PSO) and BFO to tune the PID and modified structured PID controller for a class of unstable systems [8 -17].…”

“…In the process control literature, a variety of methods have been discussed to employ a robust control scheme for the bioreactor operating at single or multiple steady states [3,5].PID controllers are still extensively employed in industrial process control systems because of their structural simplicity, reputation, robust behavior, and easy implementation [5,6]. The traditional PID tuning procedure existing for stable and unstable processes are model dependent and require numericalcomputations.…”