Optimizing Torque Delivery for an Energy-Limited Electric Race Car Using Model Predictive Control
Round 1
Reviewer 1 Report
The manuscript describes an MPC method to improve lap times for a 150m manoeuvre in a FS context. The manuscript is well written, the results are clearly presented and show a positive benefit, but it contains some limitations as described below.
The literature review is extremely limited – what are other researchers doing in this area and how does your work add to this body of knowledge? Following p2, line70 what has been done in other related scientific literature, not specific to electric motorsport?
Provide evidence for why MPC was used, and other methods were investigated and discarded.
P5 line 154 E should be in kWh
P5 line 166 ? should be 2
Figure 5 – to avoid confusion with the second “continuous torque request” scenario, change the caption to refer to the acceleration event
For scenario 2 clarify “continuous positive torque request” – Fig 6 shows it is varying significantly.
The conclusions should include a ‘contributions to knowledge’ section, where the contributions to filling the gaps identified in the literature review are discussed.
Author Response
The manuscript describes an MPC method to improve lap times for a 150m manoeuvre in a FS context. The manuscript is well written, the results are clearly presented and show a positive benefit, but it contains some limitations as described below:
- The literature review is extremely limited – what are other researchers doing in this area and how does your work add to this body of knowledge? Following p2, line70 what has been done in other related scientific literature, not specific to electric motorsport?
R. The introduction was extended and restructured, 13 papers were added.
- Provide evidence for why MPC was used, and other methods were investigated and discarded.
R. A brief discussion about PID and LQR was added to the introduction.
- P5 line 154 E should be in kWh
R. Corrected
- P5 line 166 ? should be 2
R. Corrected
- Figure 5 – to avoid confusion with the second “continuous torque request” scenario, change the caption to refer to the acceleration event
R. The caption was changed
- For scenario 2 clarify “continuous positive torque request” – Fig 6 shows it is varying significantly.
R. The ‘continuous positive request’ was rephrased to better express the meaning we wanted. It was also added a brief explanation was also added on line 195.
- The conclusions should include a ‘contributions to knowledge’ section, where the contributions to filling the gaps identified in the literature review are discussed.
R. The contributions were added at the end of the conclusion
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Objective: This paper presents an energy optimized torque controller for the powertrain of an energy-limited electric Formula Student car, that, due to a limited battery capacity, requires specific energy management solutions to minimize race time while simultaneously controlling and managing overall energy consumption to finish the race.
Solution: An energy-managing torque control algorithm was developed in order to use the finite onboard energy in a manner that optimized lap time performance and decreased energy consumption when energy deficits occurred.
Modeling: The longitudinal dynamics of the vehicle was represented by a linearized first-principles model. The plant was validated against a parameterized electric Formula Student race car model in a commercial lap time simulation software.
Simulation: A Simulink-based Model Predictive Controller (MPC) controller architecture was created to balance energy use requirements with optimum lap time. This controller was then tested against a hardware-limited system as well as a torque-limited system in a constant torque request and varying torque request scenario.
Results: The controller decreased the elapsed time to complete a 150m straight line acceleration by 11.4% over the torque-limited solution, and 13.5% in a 150m representative Formula Student maneuver.
Recommendations:
The A, B, C and D matrices are function of the plant dynamics and were determined through the process of system identification.
Mention the obtained matrices in the appendix.
Energy consumption is optimized based on the feedback of the battery energy capacity, torque output and vehicle velocity.
The MPC controller calculates an optimal solution to a quadratic control problem
Details the optimization function or procedure.
Details the MPC design.
In this work, a prediction horizon of ten time steps and a control horizon of two time steps were used.
In order to investigate instabilities caused by reducing the predictive and control horizons, these values were reduced to five and one respectively, further discussed in the results section.
Details the selection decision. Has trial and error method been used also for other values of the prediction and control horizon?
Include references from the last 3 years (minimum 50%) to highlight the timeliness of this research study
Line 70: Compared to a torque-limited approach [include a reference] ...
Minor editing errors; see for example:
Line 88: In this paper, a motorsport specific, model based predictive energy managing torque control system is described.
Cd in (1), but CD in Table 1
The CL value is missing in Table 1
Line 166: Table ??.
Author Response
“The A, B, C and D matrices are function of the plant dynamics and were determined through the process of system identification”.
- Mention the obtained matrices in the appendix.
R. Matrices added
“Energy consumption is optimized based on the feedback of the battery energy capacity, torque output and vehicle velocity. The MPC controller calculates an optimal solution to a quadratic control problem”
- Details the optimization function or procedure. Details the MPC design.
R. The MPC Design section was restructured
“In this work, a prediction horizon of ten time steps and a control horizon of two time steps were used. In order to investigate instabilities caused by reducing the predictive and control horizons, these values were reduced to five and one respectively, further discussed in the results section.”
- Details the selection decision. Has trial and error method been used also for other values of the prediction and control horizon?
R. Yes, this was added on line 181
- Include references from the last 3 years (minimum 50%) to highlight the timeliness of this research study
R. Recent papers were added and the introduction was restructured.
- Line 70: Compared to a torque-limited approach [include a reference].
R. The comparison was with the other scenario of torque request. This sentence was rewritten for better clarity.
- Minor editing errors; see for example:
Line 88: In this paper, a motorsport specific, model based predictive energy managing torque control system is described.
Cd in (1), but CD in Table 1
The CL value is missing in Table 1 Line 166: Table ??.
R. The paper was proofread once again
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have addressed the reviewer comments adequately.
Reviewer 2 Report
The authors revised.
