Bioreactor temperature control using modified fractional order IMC-PID for ethanol production

Accepted Manuscript Title: Bioreactor Temperature Control using Modified Fractional Order IMC-PID for ethanol production Authors: Nikhil Pachauri, Asha Rani, Vijander Singh PII: DOI: Reference:

S0263-8762(17)30174-0 http://dx.doi.org/doi:10.1016/j.cherd.2017.03.031 CHERD 2629

To appear in: Received date: Revised date: Accepted date:

17-11-2016 24-3-2017 27-3-2017

Please cite this article as: Pachauri, Nikhil, Rani, Asha, Singh, Vijander, Bioreactor Temperature Control using Modified Fractional Order IMCPID for ethanol production.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.03.031 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Bioreactor Temperature Control using Modified Fractional Order IMC-PID for ethanol production Nikhil Pachauri1 [email protected], Asha Rani1 [email protected], Vijander Singh1 [email protected] 1 Instrumentation and Control Engineering Division, Azad Hind Fauz Marg, NSIT, Dwarka Sec-3, New Delhi-110078

Graphical abstract

Highlights    

Modified fractional order IMC-PID (MFOIMC-PID) is proposed for temperature control Water Cycle Algorithm is used to estimate the parameters of MFOIMC-PID Performance of MFOIMC-PID is compared with PID and fractional order PID (FOPID) Production of ethanol is found higher in case of MFOIMC-PID.

Abstract The product quality of a fermentation process depends on a number of factors such as temperature, pH, nutrient balance, dilution rate, dissolved oxygen and CO2 concentration etc. The present work focuses on the precise temperature control of the process and to achieve desired product quality. Therefore a novel control algorithm, which is an amalgamation of fractional mathematics and IMC-PID, having less design parameters is proposed. A fractional order IMC-PID is designed and then modified (MFOIMC-PID) by incorporating an extra control loop with proportional gain to reduce the offset error. A nature inspired optimization technique i.e. water cycle algorithm is utilized for estimation of optimum design parameters of proposed controller which leads to WMFOIMC-PID controller. Fractional order PID (FOPID) and conventional PID are also designed for comparative study. Simulation results show that the proposed controller reduces Integral Absolute Error (IAE) by 57% and 72% in comparison to FOPID and PID respectively for set-point tracking. Similar reduction of IAE is observed for disturbance rejection and noise suppression. Thus WMFOIMC-PID proves to be more robust and efficient in comparison to the other designed controllers.

Keywords: Bioreactor; Fractional order IMC-PID (FOIMC-PID); Modified Fractional order IMC-PID (MFOIMC-PID); Water Cycle Algorithm 1. INTRODUCTION For the last few decades, there have been a multidimensional development in biochemical industries due to its applicability in production of life saving medicines, vaccines for health sector; agro-food products like beer, wine etc. and in the treatment of industrial waste water. It is one of the complex processes in the field of process engineering due to its model uncertainties, nonlinear nature and slow response, hence an accurate and precise control of bioprocess is of substantial concern to many fermentation industries. The automatic optimum control of bioprocess is required so as to minimize the production cost and preserve the quality of final product simultaneously [1]. Table 1 provides an overview of previous works in the field of controller design for bioreactor. Traditional PID controller is still an elementary choice for control engineers due to its simple structure and ease of implementation [11-13]. The performance of PID is improved significantly due to development in the area of fractional calculus. Oustaloup introduced the approximation for fractional differentiator and integrator [14] and later on Podlubny proposed fractional order PID (FOPID) which is an extension of classical PID with two more design parameters [15]. FOPID and its variants are extensively used for control of various systems like automatic generation control, load frequency control, robotic manipulator, 5DOF active magnetic bearing etc. [16-19]. The flexibility of FOPID increases due to increase in design parameters, but the tuning of FOPID is still a critical issue. Further Internal model control (IMC) is used by the researchers for designing of PID and FOPID controller in order to reduce the tuning efforts. Recently few authors have proposed novel tuning techniques for fractional order IMC-PID (FOIMC-PID) [20-21]. In [22] fractional order filter based PID for first order time delay system is proposed. Fractional order model reduction technique based on the retention of dominant dynamic method is proposed in [23] and its application on IMC based tuning of fractional order PI/PID is discussed. Whereas IMC and IMC-PID are also explored recently by researchers for control of CSTR, integrated processes, uncertain heavy duty vehicle, load disturbance rejection, turbocharged gasoline engine , bioreactor etc. [24-27].

It is revealed from the literature that standard IMC and its combinations are comprehensively used in different engineering applications. The benefit of using IMC with PID and FOPID is that it reduces the number of design parameters. IMC has simple construction and easy to implement. However design and implementation of FOIMC-PID is still to be explored for nonlinear processes. In this work a maiden attempt is made to design a modified FOIMC-PID controller for temperature control of nonlinear fermentation process. WCA is used to optimize the controller parameters. The main objectives of this work are 1. FOIMC-PID controller available in literature is designed and implemented for temperature control of bioreactor. 2. The FOIMC-PID provides high offset error for nonlinear bioreactor. This problem is overcome by a modification of FOIMCPID controller. The modification incorporates an extra control loop with proportional gain which leads to MFOIMC-PID. 3. The WCA is used to optimize the proposed MFOIMC-PID controller. 4. The PID and Fractional order PID (FOPID) are also designed for comparison purpose. 5. The performance of proposed controller is tested for set-point tracking, disturbance rejection and noise suppression. The paper is organized as follows: Section 2 and 3 describe the motivation and detailed mathematical modeling of the bioreactor respectively. In section 4 the control strategies are discussed. Water Cycle optimization technique is explained in section 5. Simulation results and conclusion of the article are discussed in Section 6 and section 7 respectively. 2. MOTIVATION OF THE WORK A bioreactor plays an important role to yield vital products and found in numerous applications. It is used in beverage industries for ethanol production which can be used as an alternative source of fuel in place of gasoline and other products. Fermentation is the main process involved in a bioreactor which produces several intermediate as well as final or end products. The microorganisms inside reactor convert the raw material into required products. The quality of products depends on the growth and health of micro-organisms. The growth of these micro-organisms depends on a number of factors such as temperature, dissolved oxygen and CO2 concentration, pH of the solution, osmolarity, nutrient balance, dilution rate etc. Shular and Kargi [36] described the effect of temperature on cell growth rate. The micro-organisms are categorized in three groups according to optimum temperature range: psychrophiles (Topti<20oC), mesophiles (20oC 50oC) [36]. In case of certain microorganisms, classed as thermophiles, temperature can lead to an increase in growth rate until an optimum temperature beyond which growth decreases or altogether stops. Therefore accurate and effective control of temperature is needed for efficient operation of a fermentation process. Thus the motivation of this work is to design a closed loop control mechanism for temperature control of fermentation process, so that it operates effectively in the narrow temperature range. This provides optimum growth of yeast which in turn increases the production of ethanol. 3. MATHEMATICAL MODELING OF BIOREACTOR The bioreactor under consideration is a continuous fermentation process modeled as CSTR, in which supply of influent as well as removal of end product is continuous. Continuous operation is chosen generally for large scale production as it is easy to operate. Fermentation of alcohol is a very important bioprocess because of its product ethanol which can be used as an alternative source of fuel in place of gasoline. Bioreactor under consideration has three main constituents;  Biomass: - The total mass of all microorganisms in bioreactor is termed as biomass, it is a suspension of Saccharomyces cerevisiae (yeast).  Substrate: - refers to the total volume of glucose solution inside the reactor which is consumed by cells (microorganisms) and responsible for conversion of raw material to final product.  Product: - denotes the end product (ethanol). The dilution rate (Fe/V) of bioreactor should be low in comparison to biomass production rate. The cell kinetics of presented model is based on modified Monod equations according to Michaelis-Menten kinetics presented by Aiba et al. (1968) [29].   o

CS K C e 1 P K s C S

(1)

Fermentation processes have slow dynamics and large delay time due to which inorganic salts are added with yeast. These salts are responsible for the formation of co-enzymes and affect the equilibrium concentration of oxygen and reactor temperature. Figure 1 shows the block diagram of bioethanol production. Few assumptions have been taken while modelling the bioreactor i.e. stirring speed, pH of the bioreactor and substrate feed flow are taken to be constant , perfect mixing, outlet flow from the reactor and input concentration of substrate and biomass are also constant. Volume is also considered to be constant [4, 6]. The schematic diagram of continuous bioreactor is shown in Figure 2. 3.1. Mass balance equation for biomass rate of change of    production of biomass   biomass  yeast        -  biomass  yeast concentration   in fermentation reaction   leaving the reactor 

(2)

d (C X * V )   X CX dt

CS * V KS

 CS

e KPCP  Fe C X

(3)

3.2. Mass balance equation for substrate

 substrate consumed by  rate of change  substrate consumed    glu cos e   biomass      -  -     of substrate  by biomass for growth  supplied by feed   for ethanol production

(4)

 glu cos e leaving  -    the reactor 

d (C S * V )  dt

1 RSX

X CX

CS * V KS

 CS

e  K P CP 

1 RSP

P CX

CS * V K S 1  CS

e K P 1 CP 

Fi CS , in



(5)

Fe CS

3.3. Mass balance equation for product    product  ethanol    production of product  rate of change of       -  in fermentation reaction  leaving the reactor   product  ethanol concentration   

(6)

d (CP *V ) CS *V  K P1CP  P CX e  Fe C P dt K S 1 CS

(7)

3.4. Mass balance equation for dissolved oxygen concentration    concentration of oxygen dissolved in   consumption of oxygen in  concentration of dissolved      -   oxygen in substrate during reaction inlet feed sup plied to the reactor      fermentation reactions 

dCO

(8)

*

2  (k a)(CO  CO )  rO (9) l dt 2 2 2 Dissolved oxygen plays a vital role in the growth rate of yeast. It permits the cells to grow at a faster rate and cell density is increased. Its primary role is to accept electron from the respiratory chain and simultaneously helps in the synthesis of eolic and ergosterol in order to increase the yeast growth in an anaerobic condition. Nagodawithana et al. [33] suggested that the cell mass production of yeast is unswervingly related to oxygen supply. The cells have the ability to retain the oxygen and use it anaerobically. It is also discussed that an increase in aeration from threshold value will increase the biomass and ethanol production is decreased. Maximum ethanol production is obtained if the dissolved oxygen is maintained at an optimum level. The models available in the literature [34-35] are simple and do not simulate the real time process efficiently. The dissolved oxygen, temperature and pH are some of the important variables which affect the operation of bioprocess. Therefore the dynamics of dissolved oxygen, reactor and jacket temperature are also incorporated in the mathematical model to obtain a better replication of real time system. The equilibrium concentration of oxygen in the liquid phase is *

2

3

CO  (14.6  0.3943 Tr  0.00714 Tr  0.0000646 Tr ) *10

  H i Ii

(10)

2

The global effect of ionic strengths are given as follows  Hi Ii  0.5 H Na

mCaCO M mMgCl M Mg mNaCl M Na 3 Ca 2 + 2H Ca  2 H Mg M CaCO V M MgCl V M NaCl V 3

mMgCl m 2  0.5 H Cl ( NaCl  2 M NaCl M MgCl

2

)

M Cl V

2

 2 H CO

3

mCaCO

3

M CaCO

3

M CO

3

V

(11)  0.5H H 10

 pH

The mass transfer coefficient for oxygen and rate of oxygen consumption are given by

+ 0.5H OH 10

 (14  pH )

Tr  20

( kl a)  (kl a)0 (1.024) rO  O 2

2

(12)

CO 1 2 * * CX * YO KO CO 2

2

(13)

2

3.5. Energy balance equation for reactor  Heat Accumulated   Heat at   Heat at   Heat generated   Heat transfered       -      -   in Reactor  inlet   outlet   from reaction  to the jacket 

(14)

ro H rV KT AT (Tr Tag ) d (Tr *V ) 2  F (Tin  273)  F (Tr  273)  i e dt 32  r C heat , r  r C heat , r

(15)

3.6. Energy balance equation for jacket  Heat Accumulated   Heat at   Heat at    =   +   in jacket   coolent inlet  coolent outlet 

dTag dt



Fag Vj

(16)

K A (T T ) (T

in ,ag

 Tag ) 

T

T

Vj C ag

r

ag

(17)

heat , ag

The mathematical model of bioreactor described above is simulated on Intel® CoreTM i5 CPU with 2.4 GHZ frequency and 4 GB RAM in MATLAB version 8.0.1.604. The fundamental model parameters, nominal operating values and nomenclature are given in appendix A, B, and C [6] and its open loop response is shown in Figure 3. 4. CONTROL STRATEGIES 4.1. Fractional operators Fractional calculus came into existence since the development in the field of regular calculus. The primary reference to this is linked with Leibniz and L. Hopital in 1695 where half derivative was discussed. Fractional mathematics is an induction of integer order integration and differentiation to fractional order differ-integral, given as follows  d b dt b   1  b  Dt =  t   ( dt )  b   

(b ) > 0  (b ) = 0

(18)  (b ) < 0

where α and t are limits of the operation and b is the order. There are generally two definitions used for describing the fractional order differ-integral proposed by Grunwald-Letnikov (GL) and Riemann-Liouville (RL). The GL definition is given as [19] t  r  b b i  b (19)  ( 1)   f (t ir )  Dt f (t ) = lim r r 0

i 0

i 

A common method for approximation of fractional derivative or integral given by Oustaloup’s is used in this article. It is based on the recursive disposition of poles and zeros within specified frequency range [νl, νh]. The final estimated transfer function obtained corresponds to fractional operator sb where b is fractional power of s [14]. s

b

N 1 ( s  z , m ) G  m 1 1 ( s  p , m )

(20)

where G is the gain, νz,m and νp,m are frequencies of zeros and poles of the filter respectively and are represented as follows [14]:(21)  z ,1  l m  p ,m   z ,m 

m=1……….N

(22)

 z,m1 p,m 



 = h l

m=1……….N

(23)

/ N





 = m l



(24)

(1 )/ N

(25)

4.2. Standard fractional order internal model control PID (FOIMC-PID) The basic block diagram for standard fractional order internal model control PID (FOIMC-PID) based control system is shown in Figure 4. CFOIMC (s) denotes fractional order IMC, CFOIMC-PID(s) signifies FOIMC-PID controller, G(s) is the actual plant, Gm(s) is the corresponding plant model and D(s) is the external disturbance. [21] The output of the above block diagram is written as Y (s) =

G ( s )CFOIMC ( s ) [1CFOIMC ( s )Gm ( s )] R ( s)  D(s ) 1 CFOIMC ( s )[G ( s ) Gm ( s )] 1CFOIMC ( s )[G ( s ) Gm ( s )]

(26)

The relationship between CFOIMC(s) and CFOIMC-PID(s) can be easily deduced and is given by CFOIMC  PID ( s ) =

CFOIMC ( s ) 1 CFOIMC ( s )Gm ( s )

(27)

From equation (26) and (27) the output can be written as G ( s )C Y (s) =

FOIMC  PID

(s)

1 C FOIMC  PID ( s )G ( s )

R(s) 

1 1C

FOIMC  PID

( s )G ( s )

(28)

D(s)

The design process for FOIMC-PID controller is analogous to the IMC which can be summarized in the following steps: [21] Step 1. Evaluate the approximated two non-integer plus time delay (NIOPTD-2) plant model. K1 t s Gm ( s )   e d s 2n s n2

(29)

Step 2. Factorize the plant model in inverted and non-inverted part 



(30)

Gm ( s )  Gm ( s ) * Gm ( s ) 

Gm ( s )  e

 td s



contains time delays and zeros on the right half of s plane, and Gm ( s) 

K1 s 2n s n2

contains poles and gain of

the plant model. Step 3. The controller CFOIMC (s) is calculated as 1 CFOIMC  s  =  F ( s) Gm ( s ) F (s) 

1

(31) (32)

(1 s )n

where F(s) is the low pass filter, which can be chosen in such a way that controller CFOIMC (s) is realizable. Substituting F(s) in equation (31) and taking the value of n= 2 to make the proper ratio, then we get: C FOIMC  s  =

s   2n s   n2 K1

1 (1 s ) 2

(33)

Step 4. Calculate CFOIMC-PID (s) by substituting the value of CFOIMC (s) in equation (27). Arrange the RHS in such a way that it transforms into conventional fractional order PID (FOPID) cascaded with filter [21]. The time delay term is approximated using Pade’s approximation. e

 td s



1 0.5td s 1 0.5td s

(34)

C

FOIMC  PID

(s) =

2n  n   (1 0.5td s ) 1     s 1 s   1   2 2 2 K 2  2   1  n  s (0.5 td s ( td  ) s(2 td ))           PI D filter

(35)

The nonlinear bioreactor is approximated to NIOPTD-2 plant model using the impulse response invariant discretization method in time domain [31]. The controller is designed according to the steps described above. The value of filter coefficient, α=0.231 is chosen after rigorous experimentation. Gm ( s ) 

C

5.8 50.3 s1.12  7.8 s 0.95 1

FOIMC  PID

( s) =

e 1.23 s

(36)





(1 0.625s ) 1 1.344 1 s 0.95  6.44 s 0.17 0.05 2 7.8 s (0.03335 s  (0.3401) s 1.087)       PI 0.95 D 0.17 filter

(37)

It is observed from Figure 5 that reactor temperature for standard FOIMC-PID does not reach the desired set point and saturates to 30.5530C. Different values of filter coefficient α are used but it fails to track the set point. Similar problem [27] is observed with standard IMC applied to speed control of heavy duty vehicles (HDV). To overcome this problem a modification is suggested in FOIMC-PID as discussed in the subsequent section. 4.3. Modified fractional order internal model control PID (MFOIMC-PID)

The standard FOIMC-PID provides good performance for linearized model of the plant. However it is not able to track the desired temperature profile for bioreactor. The bioreactor has nonlinear, interacting and dynamic characteristics (section 2) and it needs to be linearized to implement FOIMC-PID. As the behavior of system depends on many interacting parameters which are considered to be constant and linear but in reality they are not. Therefore FOIMC-PID does not cope-up with its inherent nonlinearity and shows a high offset error. A modification is therefore proposed in the control structure, which leads to modified FOIMC-PID. This modification introduces an additional feedback control loop with a proportional controller i.e. C1(s). The proposed control scheme is the amalgamation of fractional order IMC-PID and conventional proportional controller as shown in Figure 6. The proportional controller C1(s) increases overall gain of the system. The modified output equation (Figure 6) can be written as Y (s) =

(CFOIMC  PID ( s ) C1 ( s )) G ( s ) 1 R(s)  D( s ) 1  (CFOIMC  PID ( s ) C1 ( s )) G ( s ) 1  (CFOIMC  PID ( s ) C1 ( s )) G ( s )

(38)

The previous output (equation (28)) may be compared with equation (38). It is observed that the feedback control term C1(s) may be adjusted properly to make (CFOIMC-PID (s) + C1(s))*G(s) >>1 which rejects the disturbance occurred due to environmental conditions. Thus additional gain Kp1 enhances not only the overall system gain but also the tracking performance. However, large system gain may lead the plant towards oscillatory and unstable behavior. This effect of high gain may easily be overcome by damping provided by FOIMC-PID controller. Thus both the control loops complement each other and may improve the overall performance of bioreactor. The detailed performance investigation of MFOIMC-PID is discussed in section 6. 5. WATER CYCLE OPTIMIZATION ALGORITHM (WCA) The fundamental and most important requirement for efficient execution of any control strategy is the optimization of design parameters. There have been significant advances in the field of optimization which provide solution to the controller tuning problem. In this work a newly suggested metaheuristic optimization algorithm by H. Eskandar et al. i.e. Water Cycle Algorithm, is used to tune the parameters of designed controller. It is stated that WCA is better than Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm optimization (PSO), Artificial Bee Colony (ABC) etc. The WCA is inspired from nature and based on the observation of water cycle and how rivers and streams flow downhill towards the sea in real world. Water cycle comprises of four elementary phases i.e. evaporation, condensation, precipitation and collection. The algorithm is represented mathematically as given below. The detailed description of equations and variables are given in [30]. k 1

k

k

k

X stream  X stream  R  D  ( X River  X stream ) k 1

k

k

k

(39)

X River  X River  R  D  ( X sea  X stream )

(40)

k k X sea  X River  d max k  1, 2, 3..............N SR  1

(41)

k 1

k

d max  d max 

k d max

max iterartions

(42)

where X= R= D= d= NSR =

Position for stream, river or sea A random number whose value lies between 0 and 1 Constant having value between 1 and 2 A small value near to zero Summation of number of rivers and sea

The water cycle algorithm may be described in the following steps: a) Initialize the parameters of WCA like maximum iteration, population size etc. b) Randomly generate initial population and form the preliminary streams, rivers, and sea. c) Estimate the value of objective function for each stream. d) Arbitrate the strength of flow for rivers and sea. e) Calculate the new position of streams flowing to rivers and rivers flowing to sea which is the most downhill place. f) Swap the location of river with a stream according to the finest solution. g) Similar to step (f), if a river discovers an improved solution than the sea, the location of river is switched with the sea. h) Investigate the evaporation situation. i) If the evaporation situation is satisfied, raining process will occur. j) Reduce the value of dmax which is user defined parameter. k) Examine the stopping criteria, if it is met then stop, otherwise return to step (e). Governing parameters of WCA are given in Table 2.

6.

RESULTS AND DISCUSSION

As discussed previously the reactor temperature is one of the responsible parameters for change in microbial growth. The fermentation process operates in a narrow temperature range, therefore tight control of temperature is needed for optimum microbial growth. Thus in the present work modified fractional order internal model control PID (MFOIMC-PID) is proposed for the purpose. The mathematical model of bioreactor is simulated in MATLAB 8.0.1.604. The conventional PID controller and fractional order PID (FOPID) controllers are also designed for comparison purpose. 5th order Oustaloup’s filter approximation is used to design fractional order operator and Nou= 2, and frequency range, = [10-3,103] rad/s are considered. A control technique works effectively if the optimal values of design parameters for a particular application are used. Therefore parameters of the proposed controller are tuned using newly suggested metaheuristic water cycle algorithm which leads to WMFOIMC-PID controller. Figure 7 demonstrates the schematic diagram of WCA tuned MFOIMC-PID based temperature control of continuous bioreactor. Any optimization problem requires the selection of a suitable cost function that is to be minimized or maximized. The most commonly used objective functions for single objective problems are given as follows: Integral absolute error (IAE) S1   e(t ) dt

(43)

Integral square error (ISE) S 2   e2 (t ) dt

(44)

Integral time absolute error (ITAE) S   t e(t ) dt 3

(45)

From Figure 5 it is observed that the response of the system is not able to reach to the desired set-point using standard FOIMCPID controller. There is a permanent large error between desired and actual response. For this purpose weighted sum of ISE and IAE is preferred and given by equation (46). ISE is chosen to suppress the large error present in the system so that system reaches desired set-point, whereas IAE is selected to reduce the small errors near the desired set-point so that settling time is reduced. S 4  w1 * ISE  w2 * IAE (46) where w1 and w2 are weights allotted in an optimum manner according to the system requirement. The combination of these weights should satisfy following constraint [32]. l

 wj  1

(47)

j 1

where l denotes the number of design specifications. The values selected for w1 and w2 are 0.60 and 0.40 respectively after rigorous experimentation.

According to a popular “no free-lunch” theorem [37] there is no metaheuristic algorithm which can optimally solve all optimization problems. Hence it is always advisable to test different algorithms for a particular optimization problem and choose the best one. Due to this reason, various metaheuristics have been attempted for optimum tuning of MFOIMC-PID. However for fair comparison, parameters like, lower bound and upper bound of tuning parameters, population size, stopping criteria and objective function are considered same for all the optimization algorithms. The commonly used parametric settings are considered to get best performance of each algorithm. Figure 8 shows the convergence comparison of different optimization algorithms. It is observed from the results, that GA converges prematurely whereas SA could not explore the optimal region in the specified stopping criterion. The possible reason for such poor execution is that the performance of GA and SA heavily depends on parametric settings and for this purpose there is no generalized rule available in literature. As an illustration, in literature there exists several types of selection operator for GA and each affects its performance. In case of SA, to find appropriate cooling schedule is a cumbersome task. On the other hand, WCA, CSA as well as DA succeed in finding the optimal region, but WCA is found most accurate and computationally least expensive as it takes only 40 number of function evaluations to get the optimal solution. Apart from this WCA offers very high convergence rate with appreciable accuracy. As the controller tuning is a combinatorial problem so accuracy is an important attribute which may lead to better combination of controller parameters and hence optimal performance of the plant under study. The high convergence rate makes WCA the most suitable choice for online tuning of the proposed controller in case of real industrial application. Hence it is deduced that WCA is most suitable optimization technique in comparison to other algorithms for the proposed application. Table 3 demonstrates analytical comparison of all the employed algorithms on the basis of the fitness value. The performance comparison of WMFOIMC-PID with FOIMC-PID for temperature control of bioreactor is shown in Figure 9. It is observed from the Figure that WMFOIMC-PID tracks the desired set-point in minimum time with less overshoot and less settling time. This overcomes the problem of large offset error encountered in standard FOIMC-PID for temperature control of nonlinear bioreactor. The performance of WMFOIMC-PID controller is further compared with WCA tuned conventional PID (KP=4, KI = 0.85, and KD = 1.5) and FOPID (KP=10, KI = 0.98, KD = 4.4, λ = 1.103, and μ = 0.92) (Figure 10). The comparison of results reveals the effectiveness of proposed WMFOIMC-PID controller. It is obvious from the results that introduction of extra control loop to FOIMC-PID controller reduces the overshoot, settling time and rise time significantly as compared to WPID and WFOPID controllers. Thus the proposed controller handles the situation of tight temperature control of bioreactor most effectively as compared to other designed controllers. The quantitative analysis shown in Table 4 verifies the good performance of WMFOIMC-PID. The designed controllers are analyzed for set point tracking, disturbance rejection and noise suppression in subsequent sections. 6.1. Robustness Analysis A controller must be robust enough to provide satisfactory control performance in the facets of disturbance, noise and changes in set point. The designed controllers are tested for set point tracking, disturbance rejection and noise suppression in order to analyse the robustness. (a). Set-point tracking The performance of a nonlinear process may entirely change for variations in the set-point. The controller once tuned at some static operating point should not require retuning for such changes in set point. The robustness of a controller may be analyzed at different set points for which it is not tuned. Analyzing the controller for different set-points, establishes the capability of controller to handle uncertainties in the process. Therefore the designed controllers are tested for positive and negative changes in the set point. Initially for 100hrs the temperature is maintained at 31oC then temperature is changed from 31oC to 32oC, 32oC to 33oC, 33oC to 34oC, 34oC to 30oC and 30oC to 31oC at intervals of 100hrs. It is observed from the results shown in Figure 11(a) that WMFOIMC-PID considerably reduces the overshoot and settling time in contrast to the other implemented controllers. Thus the proposed controller excels the other controllers in set point tracking. The corresponding variations in ethanol concentration are shown in Figure 11(b) and the amount of ethanol production is found to be 17052.9 g/l for WMFOIMC-PID which is higher in comparison to WFOPID (15474 g/l) and WPID (12591.9 g/l). The comparison of IAE for various designed controllers is shown in Figure 12. It is obvious from the results that the proposed WMFOIMC-PID control scheme adapts the set-point changes quite efficiently. Further the performance of controllers is also investigated for combined step and sinusoidal input. Figure 13 shows the tracking performance of designed controllers for combined step and sinusoidal profile tracking. It is observed from the Figure that

whenever sinusoidal change occurs, the tracking ability of WPID and WFOPID are degraded, but WMFOIMC-PID is able to track the profile effectively. Figure 14 shows the IAE variation for combined profile tracking performance of all controllers. The ethanol production in this case is 20732 g/l, 17226 g/l, and 12591 g/l for WMFOIMC-PID, WFOPID and WPID respectively. (b). Disturbance The vital concern for all chemical processes is the rapid change in input variable which affects the output adversely. These ecological turbulences greatly affect the product quality of bioreactor. So controller must be robust enough to reject the input disturbances and maintain the product quality simultaneously. Thus a ±5% change in input temperature, input substrate concentration and pH are taken as disturbance for the chemical processes. Figure 15 demonstrates the disturbance rejection capability of all the implemented controllers for positive and negative changes in input temperature. Table 5 shows the quantitative examination of all the designed controllers for disturbance rejection with ±5% change in Tin, Cs,in , pH individually and simultaneously. It is observed from Table 5 that value of IAE is less for WMFOIMC-PID controller as compared to other designed controllers, which proves the effectiveness of proposed controller. The volume of the process is assumed to be constant in the mathematical model. However there may be the chances of external disturbance which makes this assumption void and the quality of ethanol gets affected. In order to simulate the disturbance due to control valve failure, the input (Fi) and output (Fe) flow of the bioreactor are varied one at a time. A small change of ±0.5% is considered in Fi and Fe in the interval 150-155hrs. Comparative analysis of designed controllers for the disturbance is shown in figure 16 (a) and (b). It is clearly observed from the results that the proposed controller effectively maintains the desired temperature in the events of positive and negative changes of flow rates in comparison to PID and FOPID controllers. The quantitative analysis given in Table 6 verifies the observations. Further a 1% change is observed in the volume for ±0.5% change of flow rate which lies in the acceptable limits. If the disturbance is of larger magnitude, i.e. ±5% change in Fi or Fe, the volume increases by 12%. In case of complete valve failure volume may change to such a large extent that it leads to overflow or empty tank condition and system will shut down automatically (c). Noise Suppression Robustness of the controller is also demonstrated in terms of noise suppresssion. A random noise of amplitude -0.1 to +0.1 is added to feedback path of the system for various set points. The effect of designed controllers for noise supression on temperature control of bioreactor is shown in Figure 17 (a). It is observed that the control performance of WMFOIMC-PID is better in comparison to other designed controllers in the presence of noise. Figure 17 (b) shows the variation of ethanol concentration for all the designed controllers. The comparative study of IAE for noise suppression by the designed controllers is given in Figure 18. It is revealed that IAE value is less for WMFOIMC-PID as compared to WPID and WFOPID controllers. Hence, the ability of WMFOIMC-PID to suppress the noise is better than the other designed controllers. The above analysis proves that WCA tuned modified fractional order IMC-PID controller is a robust, efficient and precise controller for tight temperature control of nonlinear systems. 7. CONCLUSION In this article WCA tuned modified fractional order internal model control PID (WMFOIMC-PID) controller is designed and employed for proficient and precise temperature control of continuous bioreactor. The tuning performance of WCA is found to be better than GA, SA, CSA and DA optimization algorithms. It is observed from the results that in case of nonlinear system WMFOIMC-PID is able to achieve desired temperature profile effectively, whereas FOIMC-PID fails. Further the performance of proposed controller is compared with WCA tuned PID and FOPID controllers for set point tracking, disturbance rejection and noise suppression. The quantitative analysis reveals that IAE value is significantly reduced for WMFOIMC-PID controller in comparison to WPID and WFOPID controllers. Hence it is concluded from the simulation results that proposed controller not only provides robust, proficient and accurate temperature control of bioreactor but also increases the production of ethanol.

APPENDICIES

A. Fundamental model parameters A1=9.5×108 A2 = 2.55 ×1033 AT= 1m2 Cheat,ag=4.18 Jg-1K-1 Cheat,r= 4.18 Jg-1K-1 Ea1 = 55,000 J/mol Ea2 = 220,000 J/mol HCa = -0.303 HCl = 0.844 HCO3 = 0.485 HH = -0.774 HMg = -0.314 HNa = -0.550 HOH = 0.941

(kla)0 = 38 h-1 KO2 = 8.86 mg/l KP = 0.139 g/l KP1 =0.07 g/l KS = 1.03 g/l KS1 = 1.68 g/l KT = 3.6×105 J h-1m-2K-1 mCaCO3 = 100 gm mMgCl2 = 100 gm mNaCl = 500 gm MCa = 40 g/mol MCaCO3 = 90 g/mol MCl = 35.5 g/mol MCO3 = 60 g/mol

MMg = 24 g/mol MMgCl2 = 95 g/mol MNa = 25 g/mol MNaCl = 58.5 g/mol R = 8.31 J mol-1 K-1 RSP = 0.435 RSX = 0.607 YO2 = 0.97 mg/mg ΔHr = 518 kJ/molO2 μO2 = 0.5 h-1 μP = 1.79 h-1 ⍴ag = 1000 g/l ⍴r = 1080 g/l

B. Operating conditions of the process Parameter Fi Fe

Description Input Flow Output Flow

Values 51 l/h 51 l/h

Tin Te Tin,ag Cs,in kla V Vj pH Fag

Input flow temperature Output flow temperature Temperature of input cooling agent Concentration of glucose input flow Mass transfer coefficient for oxygen Total volume of reaction medium Volume of the jacket Potential of Hydrogen Flow rate of cooling agent

25 oC 25 oC 15 oC 60 g/l 38.(1024)Tr-20 1000 l 50 l 6 18 l/h

C. Nomenclature Cs

Glucose concentration (g/l)

CP

Ethanol concentration (g/l) -1

V

Volume of mass of reaction (l)

Mi

RSX

Ratio of cell produced per glucose consumed for growth Ratio of ethanol produced per glucose consumed for fermentation Maximum specific fermentation rate (h-1)

Hi

Substrate term constant for ethanol production (g/l) Fermentation inhibition constant by ethanol (g/l) Product of mass transfer coefficient for oxygen and gas specific area (h-1) Product of mass transfer coefficient at 20oC for oxygen and gas specific area (h1 ) Equilibrium concentration of oxygen in liquid phase (mg/l) Rate of oxygen consumption (mg l1 -1 h ) Maximum specific oxygen consumption rate (h-1) Yield factor of biomass on oxygen Oxygen consumption constant (g/l)

KT

Molecular mass of salt/ion i (Nacl,CaCO3, MgCl2) Specific ionic of ion i (i= Na, Ca, Mg, Cl, CO3) Ionic strength of ion i (i= Na, Ca, Mg, Cl, CO3) Quantity of inorganic salt i (Nacl,CaCO3, MgCl2) (g) Heat transfer coefficient (Jh-1m -2K-1)

AT

Heat transfer area (m -2)

Vj

Volume of jacket (l)

⍴ag

Density of cooling agent (g/l)

Tin,ag Cheat,ag

Temperature of cooling agent entering to the jacket(oC) Heat capacity of cooling agent (Jg-1K-1)

Cheat,r

Heat capacity of mass of reaction (Jg-1K-1)

Fag

Flow rate of cooling agent (lh )

RSP

Tin

Temperature of input flow (oC)

μP

Tr

Temperature of bio-reactor (oC)

KS1

Te

Temperature of outflow ( oC)

KP1

Fi

Input flow (lh-1)

k la

Fe

Exceeding flow (lh-1)

(kla)0

Tag

Jacket Temperature (oC)

Co2*

Co2

Dissolved concentration of oxygen (mg/l) Maximum specific growth rate (h-1)

ro2

Substrate growth constant (g/l) growth inhibition constant by ethanol (g/l)

Yo2 Ko2

μX KS KP

μo2

Ii mi

and and and and

References [1] Bastin G. , Dochain D.1990 , On-line Estimation and Adaptive Control of Bioreactors, Elsevier, Amsterdam. [2] Nagy Z. K.2007, “Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks”, Chemical Engineering Journal 127 (1) 95–109. [3] Condorena E. G. B., Atala D.I. P. , da Costa A. C.2011, “Non-linear Predictive Control of a Fermentor in a Continuous Reaction-separation Process”, Proceedings of the World Congress on Engineering and Computer Science WCECS 2011, October 19-21, 2011, San Francisco, USA. [4] Schaum A. , Alvarez J. , Lopez-Arenas T.2012, “Saturated PI control of continuous bioreactors with Haldane kinetics”, Chemical Engineering Science 68 (1) 520–529. [5] Hu D. , Zhang H., Zhou R., Li M., Sun Y.,“Controller development of photo bioreactor for closed-loop regulation of O2production based on ANN model reference control and computer simulation”, Acta Astronautica 83 (2013) 232–238. [6] Imtiaz U., Jamuar S. S., Sahu J.N., Ganesan P.B.2014, “Bioreactor profile control by a nonlinear auto regressive moving average neuro and two degree of freedom PID controllers”, Journal of Process Control 24 (11) 1761–1777. [7] Savran A, Kahraman G,“A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes”, ISA Transactions 53 (2014) 280–288. [8] Liu B., Ding Y., Gao N., Zhang X.2015, “A bio-system inspired nonlinear intelligent controller with application to bio-reactor system”, Neurocomputing 168 (30) 1065–1075. [9] Pimentel G. Araujo, Benavides M, Dewasme L, Coutinho D., Vande Wouwer A,“An Observer-based Robust Control Strategy for Overflow Metabolism Cultures in Fed-Batch Bioreactors”, IFAC-Papers On Line 48-8 (2015) 1081–1086. [10] Perez PA, Gonzalez MIN, Lopez RA,“Increasing the bio-hydrogen production in a continuous bioreactor via nonlinear feedback controller”, international journal of hydrogen energy 40 (2015) 17224-17230. [11] Aström K.J., Hagglund T. ,“PID Controllers: Theory, Design, and Tuning, Instrument Society of America”, Research Triangle Park, NC, 1995. [12] Aström K.J., Hagglund T.,“The future of PID control”, Control Eng. Pract. 9 (2001) 1163–1175. [13] Aström K.J., Hagglund T.,“Revisiting the Ziegler–Nichols step response method for PID control”, J. Process Control 14 (2004) 635–650. [14] A. Oustaloup,La commande CRONE: commande robuste d’ordre non entire, Hermes, 1991. [15] Podlubny,“Fractional-order systems and PI λDμ controllers”, IEEE Trans. Autom. Control 44 (1999) 208–214. [16] Chen S. Yi, Lin F.J.,“Decentralized PID neural network control for five degree-of-freedom active magnetic bearing”, Engineering Applications of Artificial Intelligence 26 (2013) 962–973. [17] Sondhi S., Hote Y V,“Fractional order PID controller for load frequency control”, Energy Conversion and Management 85 (2014) 343–353. [18] Debbarma S., Saikia L. C., Sinha N.2014, “Automatic generation control using two degree of freedom fractional order PID controller”, Electrical Power and Energy Systems 58 120–129. [19] Sharma R., Gaur P., Mittal A.P.,“Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload”, ISA Transactions 58 (2015) 279–291. [20] Maamar B, Rachid M.,“IMC-PID-fractional-order-filter controllers design for integer order systems”, ISA Transactions 53 (2014) 1620–1628.

[21] Li D, Liu L, Jin Q, Hirasawa K,“Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay”, Journal of Process Control 31 (2015) 17–29. [22] Amoura K, Mansouri R, Bettayeb M., Saggaf UM,“Closed-loop step response for tuning PID-fractional-order-filter controllers”, ISA Transactions In press. [23] Kakhki MT, Haeri M,“Fractional order model reduction approach based on retention of the dominant dynamics: Application in IMC based tuning of FOPI and FOPID controllers”, ISA Transactions 50 (2011) 432–442. [24] Q.B. Jin, Q. Liu,“Analytical IMC-PID design in terms of performance/robustness trade off for integrating processes: From 2Dof to 1-Dof”, Journal of Process Control 24 (2014) 22–32. [25] D.B. Santosh Kumar, R. Padma Sree,“Tuning of IMC based PID controllers for integrating systems with time delay”, ISA Transactions in press. [26] T. Liu, F. Gao,“Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics”, ISA Transactions 50 (2011) 239–248. [27] A. K. Yadav, P. Gaur,“Intelligent modified internal model control for speed control of nonlinear uncertain heavy duty vehicles”, ISA Transactions 56 (2015) 288–298. [28] G. Stephanopoulos, H.P. Huang,“the 2-port control system”, chemical engineering science, 41(1986) 1611-1630. [29] Aiba S., M., Shoda M. N.1968, “Kinetics of product inhibition in alcoholic fermentation”, Biotechnology. Bioeng. 10 (6) 846-864. [30] Eskandar H., Sadollah A., Bahreininejad A., Hamdi M.,“Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems”, Computers and Structures 111 (2012) 151–166. [31] Chen YQ.Impulse response invariant discretization of fractional order integrators/differentiators is to compute a discrete-time finite dimensional (z) transfer function to approximate sr with r a real number URL . [32] H. Ishibuchi, Y. Nojima,“Optimization of scalarizing functions through evolutionary multiobjective optimization, in: Lecture Notes in Computer Science 4403: Evolutionary Multi-Criterion Optimization - EMO 2007, Springer, Berlin, 2007, pp. 51–65. [33] T. W. Nagodawithana, C. Castellano, K.H. Steinkraus,“Effect of Dissolved Oxygen, Temperature, Initial Cell Count, and Sugar Concentration on the Viability of Saccharomyces cerevisiae in Rapid Fermentations”, Applied Microbiology, 28 (1974) 383-391. [34] S. Ramaswamy, T.J. Cutright, H.K. Qammar,“Control of a continuous bioreactor using model predictive control”, Process Biochemistry 40 (2005) 2763–2770. [35] A. V. Vinod, K.A. Kumar, G.V. Reddy,“Simulation of biodegradation process in a fluidized bed bioreactor using genetic algorithm trained feedforward neural network”, Biochemical Engineering Journal 46 (2009) 12–20. [36] M.L. Shuller, F. Kragi,Bioprocess Engineering : Basic concepts, prentice hall, New Jersey 2nd edition, 2002.

[37] D. H. Wolpert and W. G. Macready,

“No Free Lunch Theorems for Optimization”, IEEE Tran. On Evoluti. Compu., 1 (1997) 67-82.

Ethanol Biomass handling

Enzyme production

Biomass Pretreatment

Cellulose Hydrolysis

Simultaneous saccharification and fermentation (SSF)

Glucose Fermentation

Ethanol Recovery

Pentose fermentation

Lignin utilization

Fig. 1 Block diagram of bioethanol production CS = Glucose Concentration CP = Ethanol Concentration CX = Cell Concentration Tr = Reactor Temperature Tag= Jacket temperature Fag = Flow of cooling agent CO2 = Dissolved Oxygen Concentration

Tin, Cso, Fin

Tr

Tag

Fag

CS , CX , CP , Tr , Fe , CO2

Fig.2. Schematic diagram of continuous bioreactor

14

1.15

13.6

Yeast Concentration Cx (g/l)

Ethanol Concentration Cp (g/l)

13.8

13.4 13.2 13 12.8

1.1

1.05

1

0.95

12.6 12.4 0

50

100

150

200

250

300

350

400

0.9

Time (hr)

0

50

100

(a) Ethanol Concentration

250

300

350

400

Jacket Temperature Tag (degree centi.)

30.5

31.5

31

30.5

30

0

50

100

150

200

250

300

350

30 29.5 29 28.5 28 27.5

27 0

400

50

100

150

200

250

Time (hr)

Time (hr)

(c) Reactor Temperature

(d) Jacket Temperature

3.2

Dissolved Oxygen Concentration Co2 (mg/l)

Reactor temperture Tr (degree centi.)

200 Time (hr)

(b) Yeast Concentration

32

29.5

150

3.15 3.1 3.05 3 2.95 2.9 2.85 2.8 0

50

100

150

200

250

300

350

400

Time (hr)

(e) Dissolved oxygen concentration

Fig.3. Open loop response of simulated continuous bioreactor

300

350

400

D(s) U(s)

R(s) CFOIMC

Y(s)

G(s)

CFOIMC-PID Ym(s) Gm(s)

Fig.4. Basic Block diagram of FOIMC-PID controller

Reactor Temperature Tr (degree centi.)

30.8

30.6

30.4

30.2 alpha=2.20 alpha=1.28 alpha=0.998 alpha=0.908 alpha=0.810 alpha=0.416 alpha=0.231

30

29.8

29.6

29.4

0

50

100

150

200

250

300

350

400

Time (hr)

Fig.5. Temperature control using FOIMC-PID controller for different filter coefficients

C1(s) = Kp1 U(s) D(s)

R(s) CFOIMC

G(s)

Y(s)

Ym(s) CFOIMC-PID (s)

Gm(s)

Fig.6. Block Diagram of MFOIMC-PID controller

Tin, Cso, Fin

Tr,set

Error e(s) Tr

WCA optimized Kp1 and filter constant α

Fag

MFOIMC-PID CS , CX , CP , Tr , Fe , CO2

Manipulated variable m(s)

Fig. 7. Schematic diagram of WCA tuned MFOIMC-PID based temperature control of continuous bioreactor

9.065

GA DA SA CSA WCA

9.06

Fitness value

9.055

9.05

9.045

9.04

9.035

0

10

20

30

40

50

60

70

80

90

100

Ge ne ration 9.035

9.0324

9.0345

9.0324

9.034

9.0324

9.0335

9.0324 70

72

74

76

78

9.033

9.0325 2

3

4

5

6

7

8

9

10

Fig. 8. Convergence rate comparison of various optimization techniques 31.5

Reactor Temeprature Tr (degree centi.)

1

Setpoint FOIMC-PID WMFOIMC-PID 31

30.5

30

29.5

0

50

100

150

200 Time (hr)

250

300

350

400

Fig.9. Performance comparison of WMFOIMC-PID and FOIMC-PID for temperature control of bioreactor

80

31.4

13.5 WPID WFOPID WMFOIMC-PID

13.4

31 30.8 30.6 30.4 30.2 30 Set point WPID WFOPID WMFOIMC-PID

29.8 29.6

13.3

Ethanol concentration Cp (g/l)

Reactor Temperature Tr (degree centi.)

31.2

13.2 13.1 13 12.9 12.8 12.7 12.6

29.4

0

50

100

150

200

250

300

350

400

12.5

Time (hr)

0

50

100

150

200

250

300

350

400

Time (hr)

(a) Reactor Temperature

(b) Ethanol Concentration

Fig.10. Temperature control of bioreactor by WPID, WFOPID and WMFOIMC-PID 35

15

32.5

31.5 31 100

33

14.5

32 31 150

30 29 400

32

450

500

31 Setpoint WPID WFOPID WMFOIMC-PID

30

29

0

100

200

Ethanol concentartion Cp (g/l)

Reactor temperature Tr (degree centi)

32 34

14

13.5

13

WPID WFOPID

12.5

WMFOIMC-PID 300

400

500

600

12

0

100

200

Time (hr)

300

(a) Reactor Temperature

(b) Ethanol Concentration

Fig.11. Set-point tracking performance of all the designed controllers 158.23

200 102.34

150 100

400

Time (hr)

43.68

50 0 WMFOIMC-PID

WFOPID

WPID

Fig.12. IAE variations of different controllers for set-point tracking

500

600

15

35 32

34

14.5

30 33

28 400

450

500

32 34 31

33 32

30

Setpoint 200 WPID WFOPID WMFOIMC-PID

29

28

0

100

200

250

300

Ethanol concentration Cp (g/l)

Reactor temperature Tr (degree centi.)

34

14

13.5

13

WPID

12.5

WFOPID WMFOIMC-PID 300 Time (hr)

400

500

12

600

0

100

200

300

400

500

600

Time (hr)

(a) Reactor Temperature

(b) Ethanol Concentration

Fig.13. Set-point tracking performance of all the designed controllers for combined step and sinusoidal profile 351.54 219.84

400 56.13

200 0

WMFOIMC-PID

WFOPID

WPID

Fig.14. IAE of different controllers for set-point tracking of combined step and sinusoidal profile 15

Setpoint WPID WFOPID WMFOIMC-PID

34 34 33.5 33 300

33

320

340

32 33.5 31

33 32.5

30

29

0

100

14.5

Ethanol Concentration Cp (g/l)

Reactor Temperature Tr (degree centi)

35 34.5

14

13.5

13 WPID WFOPID WMFOIMC-PID

12.5

32 200 210 220 230 240 250 200 300 400

Time (hr)

(a) Reactor Temperature

12

500

600

0

100

200

300

400

Time (hr)

(b) Ethanol Concentration

Fig. 17 Noise suppression by WPID, WFOPID, and WMFOIMC-PID controllers

500

600

IAE 200 156.989

150 100

75.2161 45.326

50 0

WMFOIMC-PID

WFOPID

WPID

Fig.18 IAE comparison of designed controllers for noise suppression

Tables Table.1. Literature survey of various controllers designed for bioreactor. Control strategies

Performance characteristics

Nagy (2007) [2]

Authors

Model predictive controller based on artificial neural network (NNMPC)

The NNMPC controller takes less overshoot and settling time in comparison to LMPC and PID controllers.

Condo Rena et.al (2011) [3]

Two control structures of nonlinear neural network model predictive controller (NNNMPC) using DMC algorithm

The control structure 2 is superior in terms of IAE and settling time (13.55, and 30 min) in comparison to control structure 1 (104, and 50 min).

Schaum et.al (2012) [4]

Saturated output feedback PI controller with Halden kinetics.

The suggested control scheme is closed loop stable and simple in terms of construction and tuning procedure.

Hu et.al (2013) [5]

Artificial neural network based model reference controller (ANN-MRC) for growth of microalgae in closed loop.

ANN-MRC effectively controls the light intensity of photo bioreactor for maximum O2 generation.

Imtiaz et.al (2014) [6]

(NARMA) neuro-controller for temperature control and a 2-DOF-PID controller for pH and dissolved oxygen control of the biochemical reactor

The designed controllers are effective and competent in comparison to industry standard Anti-wind up PID (AWU-PID) for servo and regulatory problem in terms of MSE.

Savran and Kahraman (2014) [7]

Fuzzy model based adaptive PID controller.

MSE for Fuzzy-PID are 1.95 * 10-3 and 4.38* 10-3 for set-point tracking and noise suppression respectively, which is less as compared to classical PID.

Liu et.al (2015) [8]

Bio-system inspired nonlinear intelligent controller (NGIC) for a nonlinear bioreactor system

NGIC controller takes 41hrs to settle with 0.11% overshoot which is significantly less in comparison to IMC, PID and ANN controllers.

Pimentel et.al (2015) [9]

Observer based robust control strategy for control of an overflow metabolism culture operated in fed batch mode.

The concentration of bi-products and substrate is regulated at critical level in order to increase the biomass concentration. The biomass concentration is increased by 15% in comparison to other schemes.

Perz et.al (2015) [10]

Nonlinear feedback controller to maximize the production of biogenic hydrogen.

The value of ITSE for proposed controller (7989) is less in contrast to PI controller (8100).

Table.2. Governing parameters of WCA WCA parameter

Value

Number of design variable

2 (MFOIMC-PID)

Population size

20

Number of rivers and sea in a population

4

Evaporation criteria

1˟10-6

Maximum iteration

100

Parameter bounds for MFOIMC-PID

KP1 ∈ [1700, 2100], α ∈ [0.2, 0.4]

Table 3. Optimized parameter vales of MFOIMC-PID and fitness values for all the optimization techniques Tuning Techniques GA DA SA CSA WCA

Kp1 2092 2096 2083 2094 2098

Fitness value 9.032610 9.032442 9.038451 9.032445 9.032422

α 0.2940 0.2132 0.3981 0.2842 0.2034

Table 4. Quantitative analysis of WPID, WFOPID and WMFOIMC-PID controllers Controllers

%Os

Settling time (hr)

Rise Time (hr)

WPID WFOPID WMFOIMC-PID

1.7671 0.5320 0.0371

96.0582 59.4686 9.4590

14.595 12.614 7.371

Table 5 Quantitative analysis of designed controllers for disturbance rejection Controllers

WPID

WFOPID

WMFOIMC-PID

(a) +5 % change in Tin

24.2930

15.1402

5.5156

25.6412 25.6284 24.3264

14.9980 15.0021 15.1430

7.7876 7.7820 5.5222

29.5314 25.6031 25.6279 29.5250

16.7502 15.0021 15.0128 16.7634

11.2134 7.7750 7.7280 11.2093

Cs,in pH Tin, Cs,in and pH simultaneously (b) -5% change in Tin Cs,in pH Tin, Cs,in and pH simultaneously

Table 6. IAE variations of designed controllers for various changes in input and output flow Controllers WPID WFOPID WMFOIMC-PID

Fi +0.5% 30.18 17.80 7.604

Fe -0.5% 30.08 17.75 7.609

+0.5% 30.21 17.79 7.621

-0.5% 30.31 17.89 7.594