Real Time Implementation of Model Reference Adaptive Controller for a Conical Tank

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ISSN : 2319 – 3182, Volume-2, Issue-1, 2013

57

Real Time Implementation of Model Reference Adaptive Controller for a Conical Tank

Anna Joseph & J Samson Isaac

Department of Electronics & Instrumentation Engineering, Karunya University, Coimbatore, Tamilnadu - 641114 E-mail : [email protected], [email protected]

Abstract – Nonlinear process control is a difficult task in process industries. Conical tank level control is one among them. Real processes often exhibits nonlinear behavior, time variance and delays between inputs and outputs. This paper aims at implementing an adaptive control algorithm for a conical tank system. System identification of the non-linear process is done using black box modelling and found to be first order plus dead time (FOPDT) model. Here Proportional integral (PI) controller based on Ziegler Nichols (ZN) method is designed initially and the results are compared with model reference adaptive controller (MRAC).The real time implementation of process is done in LabVIEW using NI DAQ (BNC 2120). Better controller performance and error can be minimized by using MRAC than that of the ZN tuned PI controller.

Keywords – Conical Tank, Model Reference Adaptive Controller (MRAC), PI Controller, LabVIEW

I. INTRODUCTION

Control of industrial processes is a challenging task for several reasons due to their nonlinear dynamic behavior, uncertain and time varying parameters, constraints on manipulated variable, interaction between manipulated and controlled variables, unmeasured and frequent disturbances, dead time on input and measurements. The control of liquid level in tanks and flow between the tanks is a basic problem in process industries. In many processes such as distillation columns, evaporators, reboliers and mixing tanks, the particular level of liquid in the vessel is of great importance in process operation. A level that is too high may upset reaction equilibria, cause damage to equipment or result in spillage of valuable or hazardous material. If the level is too low it may have bad consequences for the sequential operations. So control of liquid level is an important and common task in process industries.

The majority of the control theory deals with the design of linear controllers with linear systems. PID controllers proved to be a perfect controller for simple and linear processes. When it comes to the control of nonlinear and multivariable processes, the controller parameters have to be continuously adjusted.

Conventional controllers are widely used in industries since they are simple, robust and familiar to the field operator. Practical systems are not precisely linear but may be represented as linearized models around a nominal operating point, the controller parameters tuned at that point may not reflect the real time system characterestics due to variations in process parameters.

So an adaptive control mechanism is designed for controlling the nonlinear tank system.

Here the system used is a conical tank and is highly nonlinear due to the variation in area of cross section of the level system with height. Conical tank finds wide application in petrochemical, papermaking, water treatment industries etc.

Tuning a controller is the adjustment of process parameters. Since conical tank is highly nonlinear we make use of model reference adaptive controller to control the water level. The proposed method can adjust the controller parameters in response to changes and disturbances in plant by referring to the reference model that specifies properties of the desired control system.

In this work the process model is experimentally determined by using system identification technique.

The method adopted here for system identification is step test and is done in real time with LabVIEW using NI DAQ. The conventional controller tuning is accomplished using Zeigler Nichols based PI controller settings and the performances are compared with MRAC based on settling time and Integral Squared Error (ISE).

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58 II. EXPERIMENTAL SETUP

A real time experimental setup for highly nonlinear conical tank is constructed. The process control system is interfaced with LabVIEW using USB-based DAQ module to the Personal Computer (PC). The laboratory set up for this system is shown in Figure 1,it consists of a conical tank ,a water reservoir, pump, rotameter, a differential pressure transmitter, an electro pneumatic converter (I/P converter), a pneumatic control valve, an interfacing USB based DAQ module and a Personal Computer (PC).

Fig. 1: Conical Tank Setup 2.1 Process

The control parameter chosen here is the level.

Capacitance sensor and level transmitter arrangement senses the level from the process and converts into electrical signal. Then electrical signal is fed to the I/V converter which in turn produces propotional voltage signal to the computer.

Fig. 2: Block Diagram of Closed Loop system Figure 2 shows the block diagram of a closed loop system. The control system maintains water level in a

conical tank. The actual storage tank water level sensed by the level transmitter is feedback to the level controller & compared with a desired level to produce the required control action that will position the level control as needed to maintain the desired level. Now the controller decides the control action & it is given to the V/I converter and then to I/P converter. The final control element (pneumatic control valve) is now controlled by the resulting air pressure. This in turn control the inflow to the conical tank & the level is maintained.

The specifications of the tank are as follows :

Height : 80 cm

Volume : 33.5 litres Bottom Diameter : 7.62cm Top Diameter : 36.62 cm

Angle : 10deg

Material : Stainless Steel III. SYSTEM IDENTIFICATION 3.1 Mathematical Modelling

The process considered here is a conical tank system shown in Figure 3 in which the level of the liquid is desired to maintain a constant value. This can be achieved by controlling the input flow rate into the tank. Here q is the inlet flow and q_o is the outlet flow.

= density of the liquid in the system Kg/cm³

= density of the liquid in the inlet stream Kg/cm³

= density of the liquid in the outlet stream Kg/ cm³ V = total volume of the conical tank

= volumetric flow rate of the inlet stream LPH

= volumetric flow rate of the outlet stream LPH.

R = Maximum radius of the conical tank r = Radius of the conical tank at steady state H = Maximum height of the conical tank h = Height of the conical tank at steady state

Fig. 3 : Conical Tank

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59 Using the law of conservation of mass:

Assuming the room temperature as constant, the density of water is same throughout.

Therefore

Applying the steady state values, and solving the equations (1) and ( 2) , for linearzing the non - linearity in the conical tank,

Where is the process gain, is the time

constant, , R α h_t ^s²

3.2 Black Box Modelling

System identification is a methodology for building mathematical models of dynamic systems using measurements of the system’s input and output signals, ie, system identification utilizes input-output experimental data to determine a system's model. In real time implementation, system identification of nonlinear process is done using step test fig 4.

Steps to find transfer function are:

1. Note down initial steady state value of process variable (ISS).

2. Give noticeable change in input at time (t1).

3. Note the time delay.

4. Observe the change in the process variable and note down new sready state (NSS).

5. Find total change in process variable.

6. Compute

7. Note down t2 8. Then time constant

9. Process gain Kp is PV/V where v is change in the input in volts.

Fig. 4: Process Reaction Curve

At a fixed inlet flow rate, outlet flow rate, the system is allowed to reach the steady state. After that a step increment in the input flow rate is given, and various readings are noted till the process becomes stable in the conical tank. The experimental data are approximated to be a FOPDT model. The model parameters chosen here at 25-35cm operating range is:

IV. PI CONTROLLER

The PI control scheme consists of propotional term

& integral term. The PI controller equation is given as:

( ) _P _p _i ( )

u t K e K



e t dt

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60 ( )

g

in t g

p

i

u t co n tro llero u tp u t K p ro p o tio n a l a in

K eg ra l a in



The propotional term makes a change in the controller output propotional to the current error value.

If the propotional gain value is high it results in a large change in the controller output for given error. Very large values for propotional term make the system unstable. The contribution of integral term will be propotional to the error and also the time. Since the integral term takes into account the past values of the error to give the current controller output. So the error accumulated over time will be multiplied by the integral gain and added to the controller output.

There are different methods for tuning a PI controller of which the simplest method is the Zeigler Nichols method. But the Zeigler Nichols method can be used to tune a controller for a process if the ratio of dead time (t_d) to time constant (τ) must be within the range .1< τ <.6 .So here ZN method cannot be employed, thus we use trial and error method. The criteria for selecting the PI gains was integral squared error (ISE) ie; the controller setting which gives less ISE was selected as the gains of the controller. The real time implementation results are shown in fig 5 and 6.

Fig. 5: Block diagram of PI controller

Fig. 6: Response of process with PI controllerfor setpoint 30cm

V. MODEL REFERENCE ADAPTIVE CONTROLLER The MRAC scheme is presented in fig 7.It consists of four blocks such as process, controller, reference model and adaptor. The reference model is an ideal model and its output ym(t) directly denotes the required dynamic response. The adaptive regulation process of the controller parameters is described as follows: when the input value r(t) is set to the controller, it is also simultaneously added to the reference model input; at the initial stage, since the origin parameters of controlled object are unknown, the controlled parameters are not determined causing the output response y(t) not in accordance with ym(t) and e(t) is produced. When e(t) is introduced into the adaptive regulation loop, through the calculation by adaptive laws and then proper dynamic signal of changing the controller parameters is derived to make the y(t) get approaching to ym(t), i.e.e(t) → 0 with adaptive process ceased.

Fig. 7: Block diagram of MRAC

The adjustment mechanism of MRAC system constructed by adaptive control rule called MIT rule which performs the algorithms as following:

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Tracking error: –

Cost function:

MIT Rule says that the time rate of change of θ is proportional to negative gradient of J.

That is

Controller law:

Update rule:

Tuning parameter is Adjustable parameter is

Control signal is u and command signal is

uc,

Where e denotes the model error and θ is the controller parameter vector. The components of ^𝜕𝑒

𝜕𝜃 are the sensitivity derivatives of the error with respect to θ .The parameter γ is known as adaptation gain. The MIT rule is a gradient scheme that aims to minimize the squared model cost function .The real time implementation of a processs is shown in fig 7 and 8.

Fig. 7: Block Diagram of the plant with MRAC in LabVIEW

Fig. 8: Response of Plant with MRAC for setpoint 30cm.

VI. COMPARATIVE RESULTS

The comparative results of the controller for setpoint 30 cm are shown in the below table.

TABLE 6.1 Comparative results of process performance parameters

PROCESS PERFORMANCE PARAMETERS

PI MRAC

Rise time(sec) 189 111

Settling time(sec) 115 128

Steady state error (cm) .95 .41 Table 6.1 Comparative results of performance indices

CONTROLLER ISE IAE

PI 11397.2 7967.8

MRAC 2463.7 1729.8

VII. CONCLUSION &FUTURE WORK

The nonlinearity of the conical tank is analyzed.

Conventional PI controller and MRAC is implemented in LabVIEW and is tested in real time for the nonlinear tank. The result shows that better controller performance and error is minimized in model reference adaptive controller. In future we can optimize MRAC using soft computing techniques such as Genetic Algorithm.

VIII. REFERENCES

[1] Anandarajan.R, M.Chidambaram, T.Jayasingh,

”Limitations Of A PI controller for a first order nonlinear process with dead time”,ISA Trancastions,Vol.45.No.2,pp 185-199,2006

[2] Pankaj Swarnkar, Shailendra Jain,R.K.Nema, ”Effect of Adaptation Gain on System Performance for Model Reference Adaptive Control Scheme Using MIT

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Rule”, WorldAcademy Of Science, Engineering And Technology,pp 621-626,2010

[3] Rathikarani.D and D.Sivakumar,” Adaptive PI Controller for a nonlinear system”, Dept.Of InstrumentationEngineering, Annamalai University,Sensors & Transducers Journal,Vol.109,Issue 10,pp 43-58,2009.

[4] J Satheesh Kumar , P Poongodi and K.Rajasekaran:Modelling and Implementation of Labview Based Non-linear PI Controller for a Conical Tank. Journal of Control & Instrumentation Volume 1, Issue 1, November, 2010, Page 1-9.

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