Real-time ASCEND/Solver

←back to Real-time ASCEND.

Contributed by: Dipak Chirmade

Real-time solver

Runge Kutta based single step solver

Work in progress!

Real-time solver using Runge Kutta method is currently implemented as an extern method for initial testing purpose. Building a stand alone real-time solver is already in progress.

Using real-time data reader, one can calculate dCoffee/dt for cooling of coffee example. From initial test, I have collected following logs Source:dipak:models/dipak/Workspace_Broken/sensorreadings.logs

If we calculate dCoffee/dt we can get a graph as shown in following diagram

File:DTCoffee.png

<img src="/skins/common/images/magnify-clip.png" width="15" height="11" alt="" />

Rate of change of coffee temperature with reference to environment temperature.

Todo: Application: Once we have dCoffee/dt, we can solve model like following

Qdot = h A (T_coffee - T_amb)

Qdot = - m_coffee * cp_coffee * dT_coffee / dt

where Qdot is the heat transfer rate
  h is the convection coefficient
  A is the heat transfer surface area
  T_coffee and T_amb are the coffee (+ cup) and ambient air temperatures, respectively.

  m_coffee is the mass of the coffee + cup
  cp_coffee is the average specific heat capacity of the cup + coffee etc

Following graph shows simulated results from real-time solver Vs real-reading over 10 mins of time slot.

Source can be found at: Source:dipak:models/dipak/RealtimeSolver

File:RK Solver.png

<img src="/skins/common/images/magnify-clip.png" width="15" height="11" alt="" />

Simulated results after 1*10 steps vs real reading

As you can see, prediction after 1st step starts differing than actual measured reading meaning we needed to tune the step to get accurate simulated results.