ABSTRACT
We propose a novel model control with dynamic adaptation to improve the control accuracy and speed of heat exchangers. The proposed method first applies an accurate mathematical model of heat exchanger as a motion model to create the inverse problem algorithm of manipulated variable. Subsequently, it improves the transient performance using a dynamic adaption of manipulated variable. Compared the control performance to feedback control method, the dynamic adaptation of manipulated variable fed in an exponential function resulted in both approximately a 100% reduction in overshoot and settling time elimination in response to inlet temperature and flow rate disturbances of objective fluid.
Nomenclature
A | = | heat exchange area (m2) |
cp | = | specific heat at constant pressure of the fluid (J/kg/K) |
G | = | mass flow rate (kg/s) |
h | = | convective heat transfer coefficient for fluids (W/m2/K) |
H(s) | = | transfer function of outlet parameter |
K | = | coefficient |
KD | = | the differential coefficient |
KI | = | the integral coefficient |
KP | = | the proportional coefficient |
m(s) | = | variations of mass flow rate in the complex domain |
Mp | = | maximum overshoot |
qv | = | volume flow rate (m3/s) |
Q | = | heat transfer rate (W) |
t | = | temperature (°C) |
tp | = | qualitative temperature of fluids (°C) |
= | average settling time (s) | |
T | = | time constant (s) |
Ts | = | the sample period (s) |
U | = | the total heat transfer coefficient (W/m2/K) |
= | output temperature response in the complex domain | |
λ | = | thermal conductivity (W/m/K) |
ν | = | kinematic viscosity (m2/s) |
ξ | = | damp ratio |
ρ | = | density of fluid (kg/m3) |
τ | = | time, time constant, or delay time (s) |
Superscripts | = | |
= | the assumed value | |
Subscripts | = | |
c | = | cold fluid |
h | = | hot fluid |
lm | = | log-mean |
out | = | outlet |
0 | = | the initial condition |
1 | = | the objective fluid |
2 | = | the assistance fluid |
Nomenclature
A | = | heat exchange area (m2) |
cp | = | specific heat at constant pressure of the fluid (J/kg/K) |
G | = | mass flow rate (kg/s) |
h | = | convective heat transfer coefficient for fluids (W/m2/K) |
H(s) | = | transfer function of outlet parameter |
K | = | coefficient |
KD | = | the differential coefficient |
KI | = | the integral coefficient |
KP | = | the proportional coefficient |
m(s) | = | variations of mass flow rate in the complex domain |
Mp | = | maximum overshoot |
qv | = | volume flow rate (m3/s) |
Q | = | heat transfer rate (W) |
t | = | temperature (°C) |
tp | = | qualitative temperature of fluids (°C) |
= | average settling time (s) | |
T | = | time constant (s) |
Ts | = | the sample period (s) |
U | = | the total heat transfer coefficient (W/m2/K) |
= | output temperature response in the complex domain | |
λ | = | thermal conductivity (W/m/K) |
ν | = | kinematic viscosity (m2/s) |
ξ | = | damp ratio |
ρ | = | density of fluid (kg/m3) |
τ | = | time, time constant, or delay time (s) |
Superscripts | = | |
= | the assumed value | |
Subscripts | = | |
c | = | cold fluid |
h | = | hot fluid |
lm | = | log-mean |
out | = | outlet |
0 | = | the initial condition |
1 | = | the objective fluid |
2 | = | the assistance fluid |