﻿ Sample Problems > Usage > Optimization > power_control

# power_control

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# power_control   {  POWER_CONTROL.PDE

This example shows the use of the MINIMIZE optimization feature. It is

We wish to find the required power input to a heater, such that the resulting

average temperature over the domain is a specified value.

}

TITLE "Optimization using MINIMIZE"

VARIABLES

temp     { The temperature field }

DEFINITIONS

setpoint=700     { the desired average temperature }

skintemp=325     { fixed outer boundary temperature }

k=1               { conductivity }

heat=0           { the heat function for the temperature.

it is non-zero only in the heater region }

tcontrol=integral(temp)/integral(1)   { the control function, average temperature }

{ tcontrol=val(temp,0,0)     -- an alternative control method, unused here }

power     ! total power input

INITIAL VALUES

temp = setpoint

EQUATIONS

temp:   div(-k*grad(temp))-heat = 0   { diffusion of temperature field }

{ Here is the optimization request:

Modify "power" until the average temperature is equal to setpoint.

"power" starts at 50, and the initial range of "power" samples is 20.

"power" is constrained to be greater than 0 and less than 1000.

Iteration continues until "abs(tcontrol-setpoint)" is less than OPTERRLIM (default 2e-6)

or "power" is bracketed to less than OPTERRLIM*power. }

MINIMIZE abs(tcontrol-setpoint) vs power(50, 20, 0, 1000)

BOUNDARIES

REGION 'Insulation'

k=0.1

heat=0

start(-4,-4)

value(temp)=skintemp

line to (4,-4) to (4,4) to (-4,4) to close

REGION 'Heater'

k=50

heat=power

start(-1,-1) line to (1,-1) to (1,1) to (-1,1) to close

MONITORS

contour(temp)

report power

report tcontrol

History(abs(tcontrol-setpoint),power)

PLOTS

contour(temp)

report power

report power*integral(1,'heater') as "Total Power"

report tcontrol as "Average Temp"

elevation(temp) from(-4,0) to (4,0)

History(abs(tcontrol-setpoint),power)

Summary

report power*integral(1,'heater') as "Total Power needed to establish an average temperature of 700 "

END