Running simulations with feedback¶

In the following tutorial we will review the dynamic systems modeling capabilties of SystemLab|Design.

Open the design project “Newton Law Cooling” and run a simulation with feedback

Launch a new application of SystemLab|Design by double left-clicking on the SystemLab-Design.exe executable file.
From the Menu bar, select File/Open project and navigate to the folder “systemlab_design\systemlab_examples\feedback"
Select the design project “Newton Law Cooling” (it will have a suffix “.slb”) and click on the Open button.
On the Tool bar, select the Start button to initiate the simulator.

The simulation will run for a short period of time and results will be displayed as shown in the graph below. The three curves represent the temperature reduction of a stock of pre-heated water that has been left to cool over a period of 100 seconds. The start temperature for each curve is 80, 93.33 and 106.67 C and the ambient temperature is 20 C.

Double left-click on Flow-Cooling to open its functional block properties and select the Ports Manager tab.

To build a feedback loop in a simulation (between functional blocks), one or more ports must be designated as “In-Feedback”. In this example, input port 4 of the “Flow-Cooling” functional block has been set to Direction = “In-Feedback” (see below).

How feedback segments are processed by a functional block script

Select the Edit script icon (next to Script module name) to view the script for “Flow_Cooling”.

On lines 52-56, the following code is used to initiate the feedback mode of operation:
```
if segment == 1 or feedback_mode == 0: #First iteration of feedback mode simulation
    fdk.temp_sig_out = np.zeros(n)
    feed_temp_in = stock_temp_in
else:
    feed_temp_in = input_signal_data[2][4] #Use feedback signal
```
When Feedback mode is enabled for a simulation, each simulation iteration will be repeated multiple times based on the project settings parameter Feedback segments. Each segment represents a shorter-time simulation that is run just like a normal simulation. These subsets are then concatenated together to form a complete picture of system performance over the defined time window of the simulation.

For the first simulation segment, there is no return signal available at the “In-Feedback” port of the Flow-Cooling as this port has a downstream source (in this case the Branch node) and the feedback signal is set to the input stock temperature (the startimg temperature for the simulation). For follow-on segments (else condition), a return signal is available and the signal data from the “In-Feedback” port is used.

On lines 63-74, the following code is used to perform the calculation of the output temperature for a segment:
```
if feedback_mode == 2:
    segment_length = float(n)/float(segments)
    start_index = int(round(segment * segment_length) - segment_length)
    dT_over_dt = -cooling_rate*(feed_temp_in[start_index] - amb_temp_in[0])
    dT = dT_over_dt * segment_length * t_step
    if config.sim_data_activate == True:
        config.sim_data_view.dataEdit.append('dT:')
        config.sim_data_view.dataEdit.append(str(dT))
    for seg in range(start_index, n):
        fdk.temp_sig_out[seg] = feed_temp_in[seg - int(segment_length)] + dT
else:
    fdk.temp_sig_out = stock_temp_in
```
When Feedback mode is enabled for a simulation (feedback_mode == 2), the change in temperature for a defined time span is calculated using the differential equation dT/dt = -k(T-Ta) where k is the cooling rate parameter and Ta is the ambient temp [Ref 1].

The Feedback segments setting is used to define the number segments for the simulation iteration. This regulates the time step delta (dt), which is represented numerically by the number of samples per segment (as shown in the data field Samples/seg under Project settings/Feedback settings)

How to change the feedback settings for a dynamic systems simulation

Select the Settings icon on the Tool bar menu to view the Project settings for the “Newton Law Cooling” design project.
Under the Feedback settings tab, change the Feedback segments from 100 to 25 and select OK to update the settings and close the dialog.

On the Tool bar, select the Start button to initiate the simulator.

The simulation curves, as shown below, now map the temperature change over 25 feedback segments (vs 100). This reduces the resolution of the signal information over time but also reduces the overall simulation time.

Note

The maximum resolution setting for the feedback mode is 1 sample/segment. To increase further the time resolution of a feedback model, simply increase the Sample rate setting.

References¶

[1] Other differential equations, https://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html (accessed April 26, 2019).