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The blending tank shown in figure ( 1 ) below, may be assumed to be perfectly mixed two streams. Figure 1 : stirred - tank

The blending tank shown in figure (1) below, may be assumed to be perfectly mixed two streams.
Figure 1: stirred- tank blending system
Stream 1 is a mixture of two chemical species A and B, its mass flow rate is w1 and its mass fraction of A is x1. Stream 2 is a mixture of the same species A and B, its mass flow rate is w2 and its mass fraction of A is x2. The mass fraction of A in the exit stream is denoted by x and the total mass flow rate is w. It is desired to control the mass fraction of A at the exit "x". The volume of the liquid "V" can change in the tank however, the liquid density "" is constant.
Let w2 be the manipulated variable and w1 be the disturbance, x1 and x2 have constant values x1=0.2 and x2=0.1 the density =1000kgm3, the steady state values for the operating conditions are:
V=10m3
w1=1kgs
w2=3kgs
Study the above system process, then do the following:
Identify state variables, input variables.
Derive the differential equation that describes the dynamics of state variable.
Build the dynamic model of the system.
Linearize the model around the steady state values.
Use Laplace transform to get the transfer function.
Draw the block diagram of the system.
Simulate the uncontrolled system using Simulink.
Design a ratio controller to set the value of x at 0.5.
Describe the advantages and disadvantages of ratio control.
Simulate the controlled system using Simulink.
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