Coupled Tank System

Abstract- Coupled Tank System is widely popular in industrial applications in chemical industries.  The control of fluid level in the tanks is an important factor in chemical industry and the flow between the tanks also must be regulated. The different processes require the fluid to be pumped into the tank, stored for the required time and direct the fluid to another tank when required. All these processes must happen systematically. This paper presents the designing techniques for development of a controller to control the liquid level in the coupled Tank System

Key words: Pole Placement, Pole placement with integral action, Observer controller, Observer with Integral action, LQR Controller, LQR with integral action

 I. INTRODUCTION:

   The control of liquids in tanks and the flow between the tanks is a major overhead in the chemical industry. The fluid will be pumped into the tank and stored in it. The liquid in the tank will undergo various mixing processes and chemical treatments, yet the liquid level in the tank must e kept under control and the flow rate between the tanks should be regulated. The tanks are often coupled and hence they require additional control [1]. This paper explains the design algorithms of various controllers that can be used to control the liquid level in the tank and the flow rate.

II. MODELLING COUPLED TANK SYSTEM:

   Consider the coupled tank system depicted in the Figure 1. When the two tanks are coupled together the system states are the liquid level H1 in Tank1 and liquid level H2 in Tank2. If the control input is assumed to be qin which is the pump flow rate, then H2 would the variable to be controlled.

   The volumetric flow into tank1 is  qin(cm3/min), the volumetric flow rate from Tank1 to Tank2 is qin(cm3/min), and the volumetric flow rate from tank2 is qo(cm3/min). Both tanks have the same cross sectional area denotes the area of Tank1 is A1 (cm2) and area of Tank2 is A2(cm2).

[pic 1]

                   Fig.1 The block diagram of interacting liquid tanks

For Tank 1

                                                                           (1)[pic 2]

Assuming linear resistance to flow we have

                                                                                               (2)[pic 3]

And

                                                                  (3)[pic 4]

                                           (4)[pic 5]

Taking Laplace Transform

                                      (5)[pic 6]

For Tank 2

                                                                           (6)[pic 7]

Assuming linear resistance to flow we have

                                                                                                     (7)[pic 8]

And

                                                                (8)[pic 9]

                                    (9)[pic 10]

Taking Laplace Transform

                       (10)                             [pic 11]

To obtain     we must cancel      in equation (5) and (10). We get[pic 12][pic 13]

[pic 14]

                   (11)         

We obtain below transfer function by substituting values in the following table:  

                                           (12)   [pic 15]

       Table 1. Parameters values for two tank

III.MATLAB DESIGN RESULTS:

MATLAB has been used to simulate and design the system. During the open loop analysis of the system, the system is found to be unstable and hence there is a need to stabilise the system. We have used the following methods to stabilizes the system and analyse performance. The state space representation obtained is:

A= [-1.2 -0.16;1 0]; B= [1 0];C=[1 0.0016];D=[0]

1. POLE PLACEMENT

A system which is completely controllable and where all the states are observable, feedback of all the states through a gain matrix can be used to place the poles at any desired location in the complex plane.

The control law used for state feedback is:

u = -Kx

Which uses the matrix K to place the poles of the system at desired locations. The initial response of the states has been plotted. 

[pic 16]

            Fig.2Initial Response to Pole placement

1. POLE PLACEMENT WITH INTEGRAL

To eliminate any steady-state offset that may occur, an integrating controller may be added to the controlled system. Integral control is a method of output feedback. The integral control integrates the error between reference signal and output and adds it to the state feedback control effort to eliminate steady-state error. The new state space representation is: