A mixing process consists of a single stirred-tank instrumented as shown in figure. The concentration of a single species A in the feed stream varies. The controller attempts to compensate for this by varying the flow rate of pure A through the control valve. The transmitter dynamics are negligible.

(a) Draw a block diagram for the controlled process.

(b) Derive a transfer function for each block in your block diagram.

Process

(1) The volume is constant (5 m3).

(ii) The Iced flow rate is constant (qF = 7 m3/min).

(iii) The flow rate of the A stream vanes but is small compared to qF (qA = 0.5 m3/min).

(iv) cp = 50 kg/m3 and cA = 800 kg/m3.

(v) All densities are constant and equal.

Transfer Line

(i) The transfer line is 20 m long and has 0.5 m inside diameter.

(ii) Pump volume can be neglected.

Transmitter dynamics are neglible.

PID Controller

(1) Derivative on measurement only (cf. Eq. 8-17)

(ii) Direct or reverse acting, as required

(iii) Current (mA) input and output signals

An equal percentage valve is used, which has the following relation:

For a step change in input pressure, the valve requires approximately 1 min to move to its new position.

Transcribed Image Text:

Composition Trausmitter Data Cm (mA) c (kg/m?) 4 200 20