Multivariable systems exhibit complex dynamics because of the interactions between input variables and output variables. In this paper an approach to design auto tuned decentralized PI controller using ideal decoupler and adaptive techniques for controlling a class of multivariable process with a transmission zero. By using decoupler, the MIMO system is transformed into two SISO systems. The controller parameters were adjusted using the Model Reference Adaptive reference Control. In recent process industries, PID and MRAC are the two widely accepted control strategies, where PID is used at regulatory level control and MRAC at supervisory level control. In this project, LabVIEW is used to simulate the PID with Decoupler and MRAC separately and analyze their performance based on steady state error tracking and overshoot.

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Analysis and Modeling of PID and MRAC
Controllers
for a Quadruple Tank System Using Lab view
Prof.Krishnamohan.V.S.S Vishal Kumar
Assistant Professor Post Graduate Scholar,MECS
Dept. of EIE,DSCE,Bengaluru-78 DSCE,Bengaluru-78
Krishnamohan60@gmail.com vishiinani@gmail.com
Abstract—Multivariable systems exhibit complex dynamics because of the interactions between input variables and
output variables. In this paper an approach to design auto tuned decentralized PI controller using ideal decoupler and
adaptive techniques for controlling a class of multivariable process with a transmission zero. By using decoupler, the
MIMO system is transformed into two SISO systems. The controller parameters were adjusted using the Model
Reference Adaptive reference Control. In recent process industries, PID and MRAC are the two widely accepted control
strategies, where PID is used at regulatory level control and MRAC at supervisory level control. In this project,
LabVIEW is used to simulate the PID with Decoupler and MRAC separately and analyze their performance based on
steady state error tracking and overshoot.
Keywords—MRAC,PID,MIMO,Quadruple Tank System,Labview.
I. INTRODUCTION
Model reference adaptive control (MRAC) has
become a main research topic during the last few
decades and unlike many other advanced techniques,
it has been successfully applied in industry. It is
accepted that the reason for this success is the ability
of MRAC to optimally control multivariable system
under various constraints. The control of liquid level
in tanks and flow between tanks is a basic problem in
process industries. Industries face a huge number of
interacting control loops. Most of the large and
complex industrial processes are naturally Multi
input Multi Output (MIMO) systems. MIMO systems
are more complex to control due to inherent
nonlinearity and due to existence of interactions
among input and output variables. Control of non-
linear MIMO process is challenging task. Most of the
industry faces control problems that are non-linear
and have manipulated and controlled variables. It is
very common for models of industrial processes to
have significant uncertainties, strong interactions and
non-minimum phase behavior. (i.e., right half plane
transmission zeros).
Model predictive control techniques have been used
in the process industry for nearly 30 years and are
considered as methods that give good performance
and are able to operate during long periods without
almost any intervention. However the main reason
that model predictive control is such a popular
control technique in modern industry is that it is the
only technique that allows system restrictions to be
taken into consideration. The majority of all
industrial processes have nonlinear dynamics,
however most MPC applications are based on linear
models. These linear models require that the original
process is operating in the neighborhood of a
stationary point. However there are processes that
can‘t be represented by a linear model and require the
use of nonlinear models. Working with nonlinear
models give rise to a wide range of difficulties such
as, a non convex optimization problem, different

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approach to guarantee stability and in general a slow
process.
II.LITERATURE SURVEY
Deepa[1] proposed a Multivariable process for a four
tank system with dead time and without dead time
process is demonstrated in this paper. The model can
capture the essential dynamics of a unit. Design of a
Discrete time Model Predictive Contorl is discussed
based on this model. The control vector is optimized
in the design of predictive control using MATLAB.
These results are compared with de-centralized PI
controller. The simulation results shows that the
method is easy to apply and can achieve acceptable
performance.
In Karl Henrik Johansson[2] a novel multivariable
laboratory process that consists of four
interconnected water tanks is presented. The
linearized dynamics of the system have a
multivariable zero that is possible to move along the
real axis by changing a valve. The zero can be placed
in both the left and the right half-plane. In this way
the quadruple-tank process is ideal for illustrating
many concepts in multivariable control, particularly
performance limitations due to multivariable right
half-plane zeros. The location and the direction of the
zero have an appealing physical interpretation.
Accurate models are derived from both physical and
experimental data and decentralized control is
demonstrated on the process.
Most of the large and complex industrial processes
are naturally Multi Input Multi Output systems.
MIMO systems in comparison with SISO systems are
difficult to control due to inherent nonlinearity and
due to the existence of interactions among input and
output variables. Control of nonlinear MIMO process
is cumbersome because nonlinear process does not
obey superposition and homogeneity property.[3] in
this paper Nagammai presents an implementation of
decentralized PID controller and pole placement
controller to quadruple tank process with two input
and two output model. The process is firstly
decoupled through a stable simplified decoupler to
attain the benefits of decentralized control
techniques. Then, a single input single output PID
controller tuning method is used to determine optimal
PID controllers for each loop. Finally, performance
of the designed controller is measured by the
simulation.
A quadruple tank apparatus has been developed in
many universities for use in undergraduate chemical
engineering laboratories. The control experiment
presented by Tomi Roinila[4] illustrates the
performance limitations for multivariable systems
posed by ill-conditioning, right half plane
transmission zeros, and model uncertainties. The
experiment is suitable for teaching how to select
among multiloop, decoupling, and fully multivariable
control structures. A number of these reports are,
however, based on erroneous mathematical modeling
and thus resulting incorrect results. Obviously all
these reports refer originally to the one and same
paper which includes this incorrect part of modeling.
The error is significant if the pumps used in the
experiment are not identical. If they are identical the
error is, however, negligible. Mathematical
derivation and simulation results are provided to
give a corrected model and illustrate the effect of the
widespread incorrect modeling.
The quadruple-tank process has been widely used in
control literature to illustrate many concepts in
multivariable control, particularly, performance
limitations due to multivariable right half-plane
zeros. The main feature of the quadruple-tank process
is the flexibility in positioning one of its
multivariable zeros on either half of the‗s‘
plane.Modeling is one of the most important stages in
the design of a control system. Although, nonlinear
tank problems have been widely addressed in
classical system dynamics, when designing
intelligent control systems, the corresponding model
for simulation should reflect the whole characteristics
of the real system to be controlled. If assumptions are
made during the development of the model, it may
lead to the degraded performance.In [5] this paper a
quadruple tank system is modeled using soft
computing techniques such as neural, fuzzy and
neuro-fuzzy. The simulation results are presented to
analyze the performance of soft computing
techniques. The ANFIS model is shown to achieve an
improved accuracy compared to other soft computing
models, based on Root Mean Square Error values.

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III.METHODOLOGY
3.1 Block Diagram
Figure 1. Block Diagram.
The basic block diagram of MRAC system is shown
in the Figure.1. As shown in the figure,ym(t) is the
output of the reference model and yet) is the output
of the actual plant and difference between them is
denoted by e(t).
e(t) = yet) - ym(t) -----------------
-- (1)
MIT rule was first developed in 1960 by the
researchers of Massachusetts Institute of Technology
(MIT) and used to design the autopilot system for
aircrafts. MIT rule can be used to design a controller
with MRAC scheme for any system. In this rule, a
cost function is defined as,
----------------
--- (2)
where e is the error between the outputs of plant and
model, θ is the adjustable parameter. Parameter θ is
adjusted such that the cost function can be minimized
to zero. For this reason, the change in the parameter θ
is kept in the direction of the negative gradient of J,
ie
------------------
- (3)
From Eq (2),
-----------------
-- (3)
Where, the partial derivative term is called as the
sensitivity derivative of the system. This term
indicates how the error is changing with respect to
the parameter θ. eq.(2) describes the change in the
parameter θ with respect to time so that the cost
function J(θ) can be reduced to zero. Here y
represents the positive quantity which indicates the
adaptation gain of the controller. Thefirst order
process the adaptation laws are framed based on the
MIT rule as follows:
For process,
------------
-------------- (4)
For the model,

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-------------------
(5)
For controller,
-----------------------------
(6)
IV. SIMULATION RESULTS AND
IMPLEMENTATION
In order to analyze the performance of the proposed
controllers, the system is simulated using
LABVIEW.The LabVIEW Control and Simulation
Module contains a block diagram based environment
for simulation of linear and nonlinear continuous-
time and discrete-time dynamic systems. Many
simulation algorithms (i.e. numerical methods for
solving the underlying differential equations) are
available, e.g. various Runge-Kutta methods. The
mathematical model to be simulated must be
represented in a simulation loop, which in many ways
is similar to the ordinary while loop in LabVIEW.
We can make the simulation run as fast as the
computer allows, or we can make it run with a real or
scaled time axis, thus simulating real-time behaviour,
with the possibility of the user to interact with the
simulated process. The simulation loop can run in
parallel with while loops within the same VI.
4.1 MRAC with minimum phase circuit design in
Labview
Fig 2.Minimum Phase Circuit - MRAC
Output:
Fig 3.Output Response of Minimum Phase Circuit -
MRAC
4.2 MRAC for Non minimum phase circuit design
in Labview

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Fig 4.Non Minimum Phase Circuit - MRAC
Output:
Fig 5.Output Response of Non Minimum Phase
Circuit - MRAC
4.3 PID with minimum phase circuit design in
Labview
Fig 6. Minimum Phase Circuit - PID
Output:
Fig 7.Output Response of Minimum Phase Circuit - PID
4.4 PID for Non minimum phase circuit design in
Labview
Fig 8. Non Minimum Phase Circuit - PID
Output:

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Fig 9.Output Response of Non Minimum Phase Circuit
- PID
VI. CONCLUSION AND FUTURE SCOPE
The Quadruple Tank Process is modeled and
simulation is done with conventional PID controller
and MRAC controller. The transfer function matrix is
obtained for the minimum phase and non-minimum
phase using the corresponding operating conditions.
PID controller was simulated for minimum phase and
non-minimum phase with step input. Model
Reference Adaptive Control is designed based on the
state space implementation in LabVIEW and tested
for minimum phase and non-minimum phase
condition. MRAC performs better than PID in terms
of steady state error and overshoot. The PID
controller failed to control the system in achieving
the desired set point in the case of Non-minimum
phase behavior. MRAC was able to control both
minimum phase and non-minimum phase modes of
behavior.
Future work of this project can be extended by using
MRAC with kalman filter. The real-time
implementation of Model Reference Adaptive
Control in Quadruple Tank Setup can be done.
REFERENCES
[1]. ―Level Control of Quadruple tank process using
Discrete time Model Predictive Control‖,By
T.Deepa, P.Lakshmi, S.Vidya – in 2011 3rd
International Conference on Electronics Computer
Technology (ICECT).
[2]. ―The Quadruple-Tank Process: A Multivariable
Laboratory Process with an Adjustable Zero‖,By Karl
Henrik Johansson – in 456 IEEE TRANSACTIONS
ON CONTROL SYSTEMS TECHNOLOGY, VOL.
8, NO. 3, MAY 2000
[3]. "Design of State Feedback Controller for a
Quadruple Tank Process",By S. Nagammai,S.Latha,
N.Gowtham Kannan, R.S.Somasundaram,B.Prasanna
- in International Journal of Research in Advent
Technology, Vol.3, No.8, August 2015,E-ISSN:
2321-9637
[4]. ―Corrected Mathematical Model of Quadruple
Tank Process ―, By Tomi Roinila, Matti Vilkko, Antti
Jaatinen – in Proceedings of the 17th World Congress
The International Federation of Automatic Control
Seoul, Korea, July 6-11, 2008.
[5]. ―Modeling of Quadruple Tank System Using
Soft Computing Techniques‖,By R.Suja Mani Malar,
T.Thyagarajan - in European Journal of Scientific
Research ISSN 1450-216X Vol.29 No.2 (2009),
pp.249-264.
[6].
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