## Saturday, April 04, 2015

### Optimal control theory and Ferrari's turbo-electric hybrid

The Department of Engineering Science at the University of Oxford, published an interesting paper in 2014 which appears to shed some light on the deployment of energy-recovery systems in contemporary Formula One.

Entitled Optimal control of Formula One car energy recovery systems, (a free version can be downloaded here), the paper considers the most efficient use of the kinetic motor-generator unit (ERS-K), and the thermal motor-generator unit (ERS-H), to minimise lap-time, given the various regulatory constraints. (Recall that the primary constraints are: 100kg fuel capacity, 100kg/hr maximum fuel flow, 4MJ Energy Store capacity, 2MJ per lap maximum energy flow from ERS-K to the Energy Store, and 4MJ per lap maximum energy flow from the Energy Store to the ERS-K). The paper outlines a mathematical approach to this Optimal Control problem, and concludes with results obtained for the Barcelona track.

In the course of the paper, a number of specific figures are quoted for engine power. For example, the power of the internal combustion (IC) engine under the maximum fuel-flow rate, with the turbo wastegate closed, is quoted as 440kW (590bhp); it is claimed that by having the turbo wastegate open, the power of the IC engine can be boosted by 20kW (~27bhp), but in the process the ERS-H has to use 60kW of power from the Energy Store to power the compressor; and with the wastegate closed, the 20kW reduction in IC power is compensated by the 40kW generated by the ERS-H. (Opening the wastegate boosts IC power because the back-pressure in the exhaust system is reduced).

Running with the wastegate closed is therefore considered to be the most efficient solution for racing conditions. However, the paper also considers qualifying conditions, where the Energy Store can be depleted over the course of a lap without any detrimental consequences:

"In its qualifying configuration the engine is run with the waste gate open for sustained periods of time when maximum engine power is needed. During these periods of time the energy store will be supplying both the MGU-K and the MGU-H, with the latter used to drive the engine boost compressor...In contrast to the racing lap, the waste gate is typically open when the engine is being fully fuelled. On the entry to turns 1, 4, 7 and 10 the waste gate is being closed a little before simultaneously cutting the fuel and the MGU-K."

Professor of Control Engineering David Limebeer delivered a presentation of the work at a Matlab conference the same year (video here). Another version of the work, Faster, Higher and Greener, featuring Spa rather than Barcelona, was published in the April 2015 edition of the IEEE Control Systems Magazine. In his Matlab presentation, Professor Limebeer also credits Peter Fussey, Mehdi Masouleh, Matteo Massaro, Giacomo Perantoni, Mark Pullin, and Ingrid Salisbury.

After reading their work, I e-mailed Professor Limebeer, and asked if he'd considered collaborating with a Formula One team. I received a slightly odd response. After a further internet search, I found out why. In the November 2014 issue of Vehicle Electronics, David reports "We have done this work with one of the Formula One teams, but we can’t tell you which one."

Which is totally understandable. University departments have to protect the confidentiality of their work with Formula One teams. Unfortunately, however, the University of Oxford, Department of Engineering Science Newsletter 2013-2014, proudly reveals:

The Ferrari F1 Connection.
Mr Stefano Domenicali, Scuderia Ferrari Team Principal, visited the Department in May 2013 to deliver the annual Maurice Lubbock Memorial Lecture. During this lecture he announced the evolving research partnership between the University and Ferrari.

DPhil Engineering Science students Chris Lim, Giacomo Perantoni and Ingrid Salisbury are working with Ferrari on novel ways to improve Formula One performance. Chris Lim said: “I’m very excited that I’ll be the first student working with Ferrari in the Department’s Southwell Laboratory, under the supervision of Professor Peter Ireland, the Department’s Professor of Turbomachinery. It’s a privilege to work with a prestigious manufacturer such as Ferrari in an industry like Formula One where the application of thermo-fluids has such a large impact”.

Pictured from left to right are: Chris Lim (postgraduate), Ingrid Salisbury (postgraduate), Mr Stefano Domenicali, Giacomo Perantoni (postgraduate) and Professor David Limebeer (supervisor to Giacomo Perantoni and Ingrid Salisbury).

In light of this, then, the figures quoted in these papers can be interpreted as pertaining to Ferrari's turbo-electric hybrid. The first paper was submitted for publication in late 2013, and the assumptions used there are the same as those used in the 2015 paper, so it appears that Ferrari development data from no later than 2013 was used throughout.