IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017
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International e-Journal For Technology And Research-2017
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 Dept. of EIE,DSCE,Bengaluru-78 Krishnamohan60@gmail.com
Post Graduate Scholar,MECS DSCE,Bengaluru-78 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 nonlinear 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
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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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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017
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International e-Journal For Technology And Research-2017 approach to guarantee stability and in general a slow process.
PID controllers for each loop. Finally, performance of the designed controller is measured by the simulation.
II.LITERATURE SURVEY
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.
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 IDL - International Digital Library
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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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017
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International e-Journal For Technology And Research-2017 III.METHODOLOGY 3.1 Block Diagram ------------------ (3) From Eq (2), 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,
------------------ (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,
------------------ (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
-------------- (4)
For the model,
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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017
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International e-Journal For Technology And Research-2017
------------------(5) For controller,
----------------------------(6) Fig 2.Minimum Phase Circuit - MRAC
Output:
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 continuoustime 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.
Fig 3.Output Response of Minimum Phase Circuit MRAC
4.2 MRAC for Non minimum phase circuit design in Labview
4.1 MRAC with minimum phase circuit design in Labview
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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017
Available at: www.dbpublications.org
International e-Journal For Technology And Research-2017 Fig 4.Non Minimum Phase Circuit - MRAC
Output:
Fig 7.Output Response of Minimum Phase Circuit - PID
4.4 PID for Non minimum phase circuit design in Labview Fig 5.Output Response of Non Minimum Phase Circuit - MRAC
4.3 PID with minimum phase circuit design in Labview
Fig 8. Non Minimum Phase Circuit - PID
Output: Fig 6. Minimum Phase Circuit - PID
Output:
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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017
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International e-Journal For Technology And Research-2017 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).
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.
[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]. https://www.projectsatbangalore.com/Download/MR AC.pdf
Future work of this project can be extended by using MRAC with kalman filter. The real-time
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