Set Up and Perform a Tradeoff Calibration

A tradeoff calibration is the process of filling lookup tables by balancing different objectives.

Typically there are many different and conflicting objectives. For example, a calibrator might want to maximize torque while restricting nitrogen oxides (NOX) emissions. It is not possible to achieve maximum torque and minimum NOX together, but it is possible to trade off a slight reduction in torque for a reduction of NOX emissions. Thus, a calibrator chooses the values of the input variables that produce this slight loss in torque over the values that produce the maximum value of torque.

This example takes you through the steps required for you to set up this tradeoff, and then to calibrate the lookup table for it.

Set Up a Tradeoff Calibration

Create a Tradeoff

Start CAGE by typing 

cage

at the MATLAB® prompt.

Before you can calibrate the lookup tables, you must set up the calibration.

  1. Select File > Open Project (or the toolbar button) to choose the tradeoffInit.cag file, found in the matlab\toolbox\mbc\mbctraining folder, then click OK.

    The tradeoffInit.cag project contains two models and all the variables necessary for this tutorial.

  2. To create a tradeoff calibration, select File > New > Tradeoff.

    This takes you to the Tradeoff view.

Add Tables to a Tradeoff Calibration

The models of torque and NOX are in the current session. Add the lookup table to calibrate.

Both models have five inputs. The inputs for the torque and NOX models are

  • Exhaust gas recycling (EGR)

  • Air/fuel ratio (AFR)

  • Spark angle

  • Speed

  • Load

For this tutorial, you are interested in the spark angle over the range of speed and load.

To generate a lookup table for the spark angle,

  1. Click  (Add New Table) in the toolbar. This opens the Create Lookup Table dialog box.

    Create Lookup Table dialog with name ‘Spark’, range [-Inf, Inf], rows input L (10 rows) and columns input N (13 columns). Two tables show input values and corresponding outputs for L (0.1 to 1) and N (1000 to 6500).

  2. Enter Spark as the table Name.

  3. Check that N is the X input and L is the Y input.

  4. Enter 10 as the size of the load axis (Rows).

  5. Enter 13 as the size of the speed axis (Columns).

  6. Click OK to open the Table Setup dialog box

    Table Setup dialog showing table name ‘New_2D_Table’ and a field to fill the table with a selected item, with Select, Clear, OK, Cancel, and Help buttons.

  7. Click Select to open the Select Filling Item dialog box.

    “Select Filling Item dialog showing variables N, L, A, SPK (highlighted), and E, with options to display models, variables (selected), or all items, plus a checkbox to hide items filling another table.

    Select the option button Display variables, then select SPK to fill the table and click OK.

  8. Click OK to close the Table Setup dialog box.

Before you can perform the calibration, you must display the models.

Display the Models

For this tutorial, you are comparing values of the torque and NOX models. Thus, you need to display these models.

To display both models:

  • Click Add Model to Display List in the toolbar twice. This moves both available models into the Display list.

  • Alternatively, Shift-click to select both models in the Available Models list and click to include both models in the current display. In this case, you want to include all available models. You can click to select particular models in the list to display.

The Display Models pane following shows both models selected for display.

Additional Display Models dialog with two lists: Available Models (empty) and Display Models showing TQ_Model and NOXFLOW_Model, both labeled as MBC models.

Perform the Tradeoff Calibration

You now fill the lookup table for spark angle by trading off gain in torque for reduction in NOX emissions.

The method that you use to fill the lookup table is

  • Obtain the maximum possible torque.

  • Restrict NOX to below 250 g/hr at any operating point.

Once you have completed the calibration, you can export the calibration for use in the electronic control unit.

Check the Normalizers

A normalizer is the axis of the lookup table (which is the collection of breakpoints). The breakpoints of the normalizers are automatically spaced over the ranges of speed and load. These define the operating points that form the cells of the tradeoff table.

Expand the Tradeoff tree by clicking the plus sign in the display, so you can see the Spark table and its normalizers Speed and Load. Click to highlight either normalizer to see the normalizer view. A tradeoff calibration does not compare the model and the table directly, so you cannot space the breakpoints by reference to the model.

Two normalizer panels for N and L showing input-output tables, normalizer display graphs with points forming straight lines, and breakpoint spacing charts with evenly spaced vertical lines.

Set Values for Other Variables

At each operating point, you must fill the values of the spark table. Both of the models depend on spark, AFR (labeled A, in the session), and EGR (labeled E in the session). You could set the values for AFR and EGR individually for each operating point in the table, but for simplicity you set constant values for these model inputs.

To set constant values of AFR and EGR for all operating points,

  1. Click Variable Dictionary in the Data Objects pane.

  2. Click A and edit the Set Point to 14.3, the stoichiometric constant, and press Enter.

  3. Click E and change the Set Point to 0 and press Enter.

    You have set these values for every operating point in your tradeoff table. You can now fill the spark angle lookup table. The process is described next.

  4. Click Tradeoff in the Processes pane to return to the tradeoff view.

  5. Highlight the Spark table node in the Tradeoff tree display.

  6. In the lower pane, check that the value for A is 14.3, and the value for E is 0, as shown in the following example. You leave these values unchanged for each operating point.

For each operating point, you change the values of spark to trade off the torque and NOX objectives; that is, you search for the best value of spark that gives acceptable torque within the emissions constraint. The following example illustrates the controls you use, and there are step-by-step instructions in the following section.

Tradeoff interface showing Spark table with selected cell L=0.1, N=500, a 3D plot of Spark values, and six graphs displaying TQ_Model and NOXFLOW_Model responses versus variables A, SPK, and E. Left panel lists project hierarchy with Spark and normalizers.

Fill Key Operating Points

You now fill the key operating points in the lookup table for spark angle.

The upper pane displays the lookup table, and the lower pane displays the behavior of the torque and NOX emissions models with each variable.

The object is to maximize the torque and restrict NOX emissions to below 250 g/hr.

At each operating point, the behavior of the model alters. The following display shows the behavior of the models over the range of the input variables at the operating point selected in the table, where speed (N) is 4500 and load (L) is 0.5. You can show confidence intervals by selecting View > Display Confidence Intervals.

Six graphs showing TQ_Model and NOXFLOW_Model outputs versus variables A, SPK, and E. Vertical orange lines mark current values, with A set to 14.3, SPK to 0, and E to 0. Top row represents TQ_Model, bottom row NOXFLOW_Model.

The top three graphs show how the torque model varies with the AFR (labeled A), the spark angle (SPK), and the EGR (E), respectively. The lower panes show how the NOX emissions model varies with these variables.

You are calibrating the Spark table, so the two spark (SPK) graphs are green, indicating that these graphs are directly linked to the currently selected lookup table.

  1. Select the operating point N = 4500 and L = 0.5 in the lookup table.

  2. Now try to find the spark angle that gives the maximum torque and restricts NOX emissions to below 250 g/hr. You can change the value of spark by clicking and dragging the orange line on the SPK graphs, or by typing values into the SPK edit box. You can change the values of any of the other tradeoff variables in the same way, but as you have already set constant values for A and E you should not change these. Try different values of spark and look at the resulting values of the torque and NOX models.

  3. Click to select the top SPK - TQ_Model graph (TQ_Model row, SPK column). When selected the graph is outlined as shown in the following example.

  4. Now click 'Find maximum of output' () in the toolbar. This calculates the value of spark that gives the maximum value of torque. The following display shows the behavior of the two models when the spark angle is 26.4458, which gives maximum torque output.

    Two graphs showing Torque model and NOX model behavior versus SPK, with vertical orange line marking current spark value (26.4458). Torque model graph includes 99% confidence interval lines.

    At this operating point, the maximum torque that is generated is 48.136 when the spark angle is 26.4989. However, the value of NOX is 348.968, which is greater than the restriction of 250 g/hr. Clearly you have to look at another value of spark angle.

  5. Click and drag the orange bar to change to a lower value of spark. Notice the change in the resulting values of the torque and NOX models.

  6. Enter 21.5 as the value of SPK in the edit box at the bottom of the SPK column.

    The value of the NOX emissions model is now 249.154. This is within the restriction, and the value of torque is 47.2478.

    At this operating point, this value of 21.5 degrees is acceptable for the spark angle lookup table, so you want to apply this point to your table.

  7. Press Ctrl+T or click (Fill lookup tables with current tradeoff values and save) in the toolbar to apply that value to the spark table.

    This automatically adds the selected value of spark to the table and turns this cell yellow. It is blue when selected, yellow if you click elsewhere. Look at the table legend to see what this means: yellow cells have been added to the extrapolation mask, and the tick mark indicates that you saved this input value by applying it from the tradeoff. You can use the View menu to choose whether to display the legend.

  8. Now repeat this process of finding acceptable values of spark at four more operating points listed in the table following. In each case,

    • Select the cell in the spark table at the specified values of speed and load.

    • Enter the value of spark given in the table (the spark angles listed all satisfy the requirements).

    • Press Ctrl+T or click (Fill lookup tables with current tradeoff values and save) in the toolbar to apply that value to the spark table.

      Speed, NLoad, LSpark Angle, SPK

      2500

      0.3

      25.75

      3000

      0.8

      10.7

      5000

      0.7

      8.2

      6000

      0.2

      41.3

Fill the Table by Extrapolation

When you have calibrated several key operating points, you can produce a smooth extrapolation of these values across the whole table.

When you apply the value of the spark angle to the lookup table, the selected cell is automatically added to the extrapolation mask. This is why the cell is colored yellow. The extrapolation mask is the set of cells that are used as the basis for filling the table by extrapolation.

Click in the toolbar to fill the table by extrapolation.

The lookup table is filled with values of spark angle.

The following figure displays the view after extrapolation over the table.

Tradeoff interface showing Spark table with selected cell L=0.7, N=5000, a 3D plot of Spark values, and six graphs displaying TQ_Model and NOXFLOW_Model outputs versus variables A, SPK, and E. Current values: A=14.3, SPK=8.3, E=2.22044604.

Note

Not all the points in the lookup table will necessarily fulfill the requirements of maximizing torque and restricting the NOX emissions.

Export Calibrations

To export your table and its normalizers:

  1. Select the Spark node in the branch display.

  2. Select File > Export > Calibration.

  3. Choose the file type you want for your calibration. For the purposes of this tutorial, select Comma Separated Value (.csv).

  4. Enter tradeoff.csv as the file name and click Save.

This exports the spark angle table and the normalizers, Speed, and Load.

See Also

Topics