Table 1 The parameters of the CSTH process.

From: Quadratic interpolation optimization-based 2DoF-PID controller design for highly nonlinear continuous stirred-tank heater process

Parameter

Value

Description

\(\rho\)

1200 kg/m3

Tank fluid density

\(A\)

0.0707 m2

Tank inside cross-sectional area

\({C}_{p}\)

4190 J/(kg·°C)

Tank fluid heat capacity

\(g\)

9.8 m/s2

Gravity acceleration

\({K}_{T}\)

2%/°C

Temperature transmitter gain

\({K}_{vL}\)

1.25 × 10⁻5

Level control valve constant

\({K}_{vT}\)

32 × 10⁻⁶

Temperature control valve constant

\({K}_{xL}\)

0.01/%

Level control valve stem constant

\({Q}_{i}\)

7 × 10⁻4 m3/s

Normal tank inlet fluid flow rate

\({T}_{i}\)

24 °C

Fluid inlet temperature

\({T}_{L}\)

2 s

Level transmitter time constant

\({T}_{T}\)

15 s

Temperature transmitter time constant

\({T}_{vL}\)

3 s

Level control valve time constant

\({T}_{vT}\)

5 s

Temperature control valve time constant

\({\rho }_{c}\)

800 kg/m3

Heating fluid density

\({A}_{c}\)

0.6362 m2

Heat exchanger transfer area

\({C}_{pc}\)

2400 J/(kg·°C)

Heating fluid heat capacity

\({K}_{L}\)

125%/m

Level transmitter gain

\({K}_{xT}\)

0.01/%

Temperature control valve stem constant

\({P}_{cp}\)

4.14 × 105 Pa

Heating fluid pump discharge pressure

\({P}_{cr}\)

1.38 × 105 Pa

Heating fluid system return pressure

\({R}_{c}\)

5.5 × 105 Pa/(m3/s) 2

Heating system pipe nominal flow resistance

\({R}_{vT}\)

50

Temperature control valve rangeability

\({T}_{ci}\)

320 °C

Heating fluid inlet temperature

\(U\)

440 J/(s·m2·°C)

Overall heat-transfer coefficient

\({V}_{c}\)

0.0139 m3

Heat exchanger volume