ISSN: 2319-5967 ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 3, Issue 6, November 2014 9 Design and Decoupling of Control System for a Continuous Stirred Tank Reactor (CSTR) Georgeous, N.B *1 and Gasmalseed, G.A, Abdalla, B.K (1-2) University of Science and Technology, Sudan Department of Chemical Engineering. Abstract: To apply the methods of stability analysis and tuning, it is necessary first to develop a control strategy for possible noninteracting and interacting loops. Then the transfer functions were identified by mathematical modeling and the overall gains were cited from the literature. Pairing of the loops were undertaken and the interact in loops were coupled according to the RGA (Relative Gain Array), thus the loops with minimal interaction were selected and put in block diagrams. The characteristic equations were obtained for both closed and open loops. An exothermic reaction in a continuous stirred tank reactor (CSTR) was selected as a case study. The loops were subjected to tuning, stability and offset investigation. Summary of the adjustable parameters, offsets and response behavior were tabulated for comparison between the methods. It is clear that all the methods are in agreement, but the Bode criteria showed a superior consistency over other methods. It is recommended that the method of Bode has to be preferentially selected for tuning and stability analysis. Index Terms: Methods of tuning, Stability, Transfer function identification, Offset investigation. I. INTRODUCTION A control system is composed of interacting loops and that the number of feasible alternative configurations needed to be configured are very large. It must be recognized that for a process with n controlled variables and n manipulated variables there are n different ways to form control the loops [1] . The question is which one to selected? The answer is to consider the interaction between the loops for all n loops and then the RGA is applied to select a loop when the interaction is minimal. The RGA provides such a methodology by pairing the input and output that give minimum interaction when together coupled, RGA was first proposed by Bristol and today it is a very popular tool for selection of control loops giving minimal interaction [1].The methods of pairings and the RGA were applied to an exothermic reaction in a jacketed CSTR, the process is a 2 2 controlled and manipulated variables. The method of stability and tuning were applied using Routh-Hurwitz, direct substitution, root-Locus, and Bode and Nyquist criteria. II. OBJECTIVES 1- To select the loops with minimal interaction in CSTR. 2- To study the dynamics of a CSTR. 3- To investigate the methods of tuning and stability analysis. 4- To compare the accuracy of these methods with respect to stability, adjustable parameters and offset. III. LITERATURE REVIEW Multiple input, multiple output (MIMO) systems describe processes with more than one input and more than one output which require multiple control loops. Examples of MIMO systems include heat exchangers, chemical reactors, and distillation columns. These systems can be complicated through loop interactions that result in variables with unexpected effects. Decoupling the variables of that system will improve the control of that process [2]. An example of a MIMO system is a jacketed CSTR in which the formation of the product is dependent upon the reactor temperature and feed flow rate. The process is controlled by two loops, a composition control loop and a temperature control loop. Changes to the feed rate are used to control the product composition and changes to the reactor temperature are made by increasing or decreasing the temperature of the jacket. However, changes made to the feed would change the reaction mass, and hence the temperature, and changes made to temperature would change the reaction rate, and hence influence the composition. This is an example of loop interactions. Loop interactions need to be avoided because changes in one loop might cause destabilizing changes in another loop [2]. To avoid loop interactions, MIMO systems can be decoupled into separate loops known as single
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ISSN: 2319-5967
ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT)
Volume 3, Issue 6, November 2014
9
Design and Decoupling of Control System for
a Continuous Stirred Tank Reactor (CSTR) Georgeous, N.B
*1 and Gasmalseed, G.A, Abdalla, B.K
(1-2) University of Science and Technology, Sudan Department of Chemical Engineering.
Abstract: To apply the methods of stability analysis and tuning, it is necessary first to develop a control strategy for
possible noninteracting and interacting loops. Then the transfer functions were identified by mathematical modeling and
the overall gains were cited from the literature. Pairing of the loops were undertaken and the interact in loops were
coupled according to the RGA (Relative Gain Array), thus the loops with minimal interaction were selected and put in
block diagrams. The characteristic equations were obtained for both closed and open loops. An exothermic reaction in a
continuous stirred tank reactor (CSTR) was selected as a case study. The loops were subjected to tuning, stability and
offset investigation. Summary of the adjustable parameters, offsets and response behavior were tabulated for comparison
between the methods. It is clear that all the methods are in agreement, but the Bode criteria showed a superior
consistency over other methods. It is recommended that the method of Bode has to be preferentially selected for tuning
and stability analysis.
Index Terms: Methods of tuning, Stability, Transfer function identification, Offset investigation.
I. INTRODUCTION
A control system is composed of interacting loops and that the number of feasible alternative configurations
needed to be configured are very large. It must be recognized that for a process with n controlled variables and n
manipulated variables there are n different ways to form control the loops [1]
. The question is which one to
selected? The answer is to consider the interaction between the loops for all n loops and then the RGA is
applied to select a loop when the interaction is minimal. The RGA provides such a methodology by pairing the
input and output that give minimum interaction when together coupled, RGA was first proposed by Bristol and
today it is a very popular tool for selection of control loops giving minimal interaction [1].The methods of
pairings and the RGA were applied to an exothermic reaction in a jacketed CSTR, the process is a 2 2
controlled and manipulated variables. The method of stability and tuning were applied using Routh-Hurwitz,
direct substitution, root-Locus, and Bode and Nyquist criteria.
II. OBJECTIVES
1- To select the loops with minimal interaction in CSTR.
2- To study the dynamics of a CSTR.
3- To investigate the methods of tuning and stability analysis.
4- To compare the accuracy of these methods with respect to stability, adjustable parameters and offset.
III. LITERATURE REVIEW
Multiple input, multiple output (MIMO) systems describe processes with more than one input and more than
one output which require multiple control loops. Examples of MIMO systems include heat exchangers, chemical
reactors, and distillation columns. These systems can be complicated through loop interactions that result in
variables with unexpected effects. Decoupling the variables of that system will improve the control of that
process [2].
An example of a MIMO system is a jacketed CSTR in which the formation of the product is dependent upon the
reactor temperature and feed flow rate. The process is controlled by two loops, a composition control loop and a
temperature control loop. Changes to the feed rate are used to control the product composition and changes to
the reactor temperature are made by increasing or decreasing the temperature of the jacket. However, changes
made to the feed would change the reaction mass, and hence the temperature, and changes made to temperature
would change the reaction rate, and hence influence the composition. This is an example of loop interactions.
Loop interactions need to be avoided because changes in one loop might cause destabilizing changes in another
loop [2]. To avoid loop interactions, MIMO systems can be decoupled into separate loops known as single
ISSN: 2319-5967
ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT)
Volume 3, Issue 6, November 2014
10
input, single output (SISO) systems. Decoupling may be done using several different techniques, including
restructuring the pairing of variables, minimizing interactions by detuning conflicting control loops, opening
loops and putting them in manual control, and using linear combinations of manipulated and/or controlled
variables. If the system can’t be decoupled, then other methods such as neural networks or model predictive
control should be used to characterize the system [2,3,4].
There are two ways to see if a system can be decoupled. One way is with mathematical models and the other
way is a more intuitive educated guessing method. Mathematical methods for simplifying MIMO control
schemes include the relative gain array (RGA)[2]
. The RGA provides a quantitative approach to the analysis of
the interactions between the controls and the output, and thus provides a method of pairing manipulated and
controlled variables to generate a control scheme. The RGA is a normalized form of the gain matrix that
describes the impact of each control variable on the output, relative to each control variable's impact on other
variables. The process interaction of open-loop and closed-loop control systems are measured for all possible
input-output variable pairings [5]. A ratio of this open-loop gain to this closed-loop gain is determined and the
results are displayed in a matrix. The array will be a matrix with one column for each input variable and one row
for each output variable in the MIMO system[5]
. The best pairing is discovered by taking the maximum value of
RGA Matrix for each row.
A digital computer can be used to control simultaneously several outputs, the control program is composed of
several subprograms, each one used to control a different loop. Furthermore, the control program should be able
to coordinate the execution of the various subprograms so that each loop and all together function properly [6].
Although a controller may be stable when implemented as an analog controller, it could be unstable when
implemented as a digital controller due to a large sampling interval. During sampling the aliasing modifies the
cutoff parameters. Thus the sample rate characterizes the transient response and stability of the compensated
system, and must update the values at the controller input often enough so as to not cause instability. When
substituting the frequency into the z operator, regular stability criteria still apply to discrete control systems.
Nyquist criteria apply to z-domain transfer functions as well as being general for complex valued functions.
Bode stability criteria apply similarly. Jury criterion determines the discrete system stability about its
characteristic polynomial [6].
The system stability can be tested by considering its response to a finite input signal. This means the analysis of
system dynamics in the actual time domain which is usually cumbersome and time consuming. Several methods
have been developed to deduce the system stability from its characteristic equation. They are short-cut methods
for providing information without finding out the actual response of the system. They give information from the
s-domain without going back to the actual time-domain. All these methods are based on the criterion that a
sufficient condition for stability of a control loop is to have a characteristic equation with only negative real
roots and or complex roots with negative real parts. The short-cut methods for assessment of the stability of a
system include the direct method, the Routh–Hurwitz stability criterion and graphical methods of investigating
the behavior of the roots of the characteristic equation, i.e. Root Locus method and Nyquist stability criterion.
Bode plots are common graphical method. It depends only upon the open loop transfer function (OLTF). The
OLTF relates the feedback or measured variable to the set point, when the feedback loop is disconnected from
the comparator when the loop is broken or opened.
IV. RESULTS AND DISCUSSION
Interaction, coupling and control of CSTR
Consider a process with two controlled outputs and two manipulated inputs (Figure 1.). The transfer functions