Comparison of pid and mpc controllers for continuous stirred tank reactor (cstr) concentration control

e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
Volume:02/Issue:04/April-2020 www.irjmets.com
www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[133]
COMPARISON OF PID AND MPC CONTROLLERS FOR CONTINUOUS STIRRED
TANK REACTOR (CSTR) CONCENTRATION CONTROL
Mustefa Jibril*1
, Messay Tadese*2
, Eliyas Alemayehu Tadese*3
*1,2
Msc, School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia
*3
Msc, Faculty of Electrical & Computer Engineering, Jimma Institute of Technology, Jimma, Ethiopia
ABSTRACT
Continuous Stirred Tank Reactor (CSTR) is amajorarea in process, chemical and control engineering. In this paper, PID
and MPC controllers are designed for CSTR in order to analyze the output concentration of the system by comparing
the two proposed systems using Matlab/Simulink. Comparison have been made using two desired concentration input
(Random reference and step) signals with and without input side disturbance (Flow rate error). The simulation result
shows that the continuous stirred tank reactor with MPC controller have better response in minimizing the overshoot
and tracking the desired concentration for the system without input disturbance and with the effect of the disturbance
makes the continuous stirred tank reactor with MPC controller output with small fluctuations and still better than the
continuous stirred tank reactor with PID controller. Finally the comparative analysis and simulation results prove the
effectiveness of the continuous stirred tank reactor with MPC controller.
Keywords: Continuous Stirred Tank Reactor (CSTR), PID controller, MPC controller
I. INTRODUCTION
A Continuous Stirred Tank Reactor (CSTR) a highly nonlinear system and is an essential system in many industrial
processes that require continuous addition and removing of reactants and products. In order to maximize the industrial
productivity in process plants, these reactors are maintained at very high precision rates. A CSTR sometimes be an
opposite of an idealized well-stirred batch reactor. The series of operating points should exhibit a stable steady estate
dealing under the demeanor of disturbance as well. Linear controllers designed for such tendency fail to deliver optimal
achievement outside the linear operating range.
1. Continuous Stirred Tank Reactor Description Model
In this paper, we've adopted a nonlinear model of a CSTR under the idea that contents are properly mixed and for this
reason, concentration is equal anywhere inside the reaction vessel. A diagram of the system is shown in Figure 1 below.
Figure 1: Continuous stirred tank reactor system

e-ISSN: 2582-5208
[134]
The dynamic model of the system is
 
       1 2 0.2 1
dh t
w t w t h t
dt
         
 
  
 
 
  
 
 
 
  
 1 2 1
1 2 2
2
2
1
b b
b b b b
b
dC t w t w t k C t
C C t C C t
dt h t h t k C t
           

Where
h (t) Liquid level,
 bC t Product concentration at the output of the process,
 1w t Flow rate of the concentrated feed 1bC , and
 2w t Flow rate of the diluted feed 2bC .
2. The Proposed Controllers
2.1 PID Control
A proportional–integral–derivative control is a control closed-loop feedback system which is widely used in control
systems. A PID controller achieves to maintain the error between a measured variable and a desired set point by
adjusting and outputting an exact action that can maintain the process fatly and accurately, to keep the error minimal.
The PID controller involves three separate parameters; the proportional, the integral and derivative values. The
proportional value determines the response to the contemporary error, the integral value determines the response
primarily based at the sum of latest error, and the derivative value determines the response primarily based at the rate at
which the error has been changing.
Figure 2: Block Diagram of PID Controller
A PID controller may be referred to as a PI, PD, P or I controller inside the absence of the respective manage
movements. PI controllers are specifically common, considering that derivative action may be very touchy to size noise,
and the absence of an integral value can also save you the device from accomplishing its target value because of the
manage action. In this paper, we have use automatic tuning of PID controller. Table 1 shows the PID parameter values.
Table 1: PID parameters
No Parameters Value
1
PK 2.88847879306232
2
IK 0.9787824154907306
3
DK -0.0884151983707181

e-ISSN: 2582-5208
[135]
2.2 Model Predictive Control
The overall objectives of an MPC controller are
1. Prevent violations of input and output constraints.
2. Drive some output variables to their most desirable set points, even as retaining different outputs inside exact tiers
3. Prevent immoderate movement of the input variables.
4. Control as many process variables as feasible when a sensor or actuator isn't always available.
Figure 3: Block diagram for model predictive control.
A block diagram of a model predictive manipulate system is shown in Figure 3. A system model is used to expect the
modern values of the output variables. The residuals, the differences among the actual and anticipated outputs, serve as
the feedback sign to a Prediction block. The predictions are used in two forms of MPC calculations that are done at each
sampling immediately: set-factor calculations and manage calculations. Inequality constraints on the input and output
variables, inclusive of higher and decrease limits, can be protected in both kind of calculation.
II. RESULT AND DISCUSSION
In this section the simulation of a continuous stirred tank reactor with PID and MPC controller’s output concentration
using desired output concentration signals (Random reference input and step input) for with and without input
disturbance is done. In this paper, the input concentrations are set to Cb1 = 24.9 and Cb2 = 0.1. The constants associated
with the rate of consumption are K1 = 1 and K2 = 1. The objective of the controller is to maintain the product
concentration by adjusting the flow W1(t). To simplify the Simulink model, we choose to set W2(t)= 0.1. The level of
the tank h(t) is not controlled for this paper.
Comparison of continuous stirred tank reactor with PID and MPC controller without Input Disturbance
The Simulink model for a continuous stirred tank reactor with PID and MPC controllers for a Random reference input
and step input signals without input disturbance is shown in Figure 4 and Figure 5 respectively.
Figure 4: Simulink model for a continuous stirred tank reactor with PID and MPC controllers for a Random reference
input without input disturbance

e-ISSN: 2582-5208
[136]
Figure 5: Simulink model for a continuous stirred tank reactor with PID and MPC controllers for a Step input without
input disturbance
The simulation result of a continuous stirred tank reactor with PID and MPC controllers for a Random reference input
and step input signals without input disturbance is shown in Figure 6 and Figure 7 respectively.
Figure 6: Random reference response of output concentration without input disturbance

e-ISSN: 2582-5208
[137]
Figure 7: Step input response of output concentration without input disturbance
As the result shown from Figure 6 and Figure 7, the continuous stirred tank reactor with MPC controller have better
response in minimizing the overshoot and tracking the desired concentration better than the continuous stirred tank
reactor with PID controller.
Comparison of continuous stirred tank reactor with PID and MPC controller with Input Disturbance
The Simulink model for a continuous stirred tank reactor with PID and MPC controllers for a Random reference input
and step input signals with input disturbance is shown in Figure 8 and Figure 9 respectively.
Figure 8: Simulink model for a continuous stirred tank reactor with PID and MPC controllers for a Random reference
input with input disturbance

e-ISSN: 2582-5208
[138]
Figure 9: Simulink model for a continuous stirred tank reactor with PID and MPC controllers for a Step input with
input disturbance
The simulation result of a continuous stirred tank reactor with PID and MPC controllers for a Random reference input
and step input signals with input disturbance is shown in Figure 10 and Figure 11 respectively.
Figure 10: Random reference response of output concentration with input disturbance

e-ISSN: 2582-5208
[139]
Figure 11: Step input response of output concentration with input disturbance
As the result shown from Figure 10 and Figure 11, the continuous stirred tank reactor with MPC controller have better
response in minimizing the overshoot and tracking the desired concentration with the effect of the disturbance makes
the output with small fluctuations and it is better than the continuous stirred tank reactor with PID controller.
III. CONCLUSION
The modeling description and design of continuous stirred tank reactor with the proposed controllers have been done
successfully. The performance investigation of the systems including comparisons of the proposed controllers for the
output concentration control purpose analysis is done using Matlab/Simulink. The simulation results of continuous
stirred tank reactor without input disturbance shows that the continuous stirred tank reactor with MPC controller almost
exactly follow the desired concentration efficiently in both the random reference and step input signals. The simulation
results of continuous stirred tank reactor with input disturbance shows that the continuous stirred tank reactor with MPC
controller shows a small effect of the disturbance vibration and follows the desired concentration in both the random
reference and step inputs. Finally the comparative simulation results proved the effectiveness of the continuous stirred
tank reactor with MPC controller.
IV. REFERENCE
[1] KC Cheng et al. “Model of Hyper branched Polymers Prepared via Polymerization of AB2 and Core C3 Monomers
in a Continuous Stirred Tank Reactor” Journal of chemical Engineering Research and Design (Elsevier), 2020.
[2] Neha K. et al. “Control System Design and Performance Analysis of PID and IMC Controllers for Continuous
Stirred Tank Reactor (CSTR)” Journal of Control and Instrumentation, Vol. 10, No. 1, 2019.
[3] DD Mohite et al. “Performance Optimization of Anaerobic Continuous Stirred Tank Reactor Operating on
Distillery Spent Wash” Journal of Environmental Engineering, 2019.
[4] Z Ye et al. “Disturbance Observer Based Adaptive Sliding Mode Control for Continuous Stirred Tank Reactor”
Chinese Control Conference (CCC), 2019.
[5] GB S. et al. “Fuzzy Based Nonlinear PID Controller and its Application to CSTR” Korean Journal of Chemical
Engineering, 2018.

e-ISSN: 2582-5208
[140]
[6] A Sinha et al.”Control of a Nonlinear Continuous Stirred Tank Reactor via Event Triggered Sliding Modes”
Journal of Chemical Engineering Science (Elsevier), 2018.
[7] Matusu et al. ”Robust Stabilization of a Continuous Stirred Tank Reactor Model” Annals of DAAAM and
Proceedings, Vol.27, pp. 147-150, 2016.
[8] Lee J. et al.” Temperature Control of a CSTR using a Nonlinear PID Controller” Journal of Institute of Control,
Robotics and Systems, Vol. 21, Issue. 5, pp. 482-489, 2015.

Comparison of pid and mpc controllers for continuous stirred tank reactor (cstr) concentration control

More Related Content

What's hot (19)

Similar to Comparison of pid and mpc controllers for continuous stirred tank reactor (cstr) concentration control (20)

More from Mustefa Jibril (20)

Recently uploaded (20)

Comparison of pid and mpc controllers for continuous stirred tank reactor (cstr) concentration control