Optimizing the Aero-Suspension Interactions in a Formula One Car

The interactions between the multilink suspension system of an open-wheeled race car and the vehicle's aerodynamic performance are modeled and optimized. The closed-kinematic loops associated with the suspension mechanisms are modeled as a set of nonlinear equations that are derived using a first principle kinematic analysis. For the purpose of optimal control calculations, the solutions to these equations are approximated by multivariate polynomials in the normal tire forces. It is shown that the car's suspension motion can have a significant impact on the aerodynamic performance of the vehicle. Optimal control calculations are used to illustrate the impact of aero-suspension interactions and adjustments on the lap-time performance of the car.

[1]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[2]  Ramon Sancibrian,et al.  Kinematic design of double-wishbone suspension systems using a multiobjective optimisation approach , 2010 .

[3]  Roberto Lot,et al.  A General Method for the Evaluation of Vehicle Manoeuvrability with Special Emphasis on Motorcycles , 1999 .

[4]  Donald L. Cronin.  MacPherson strut kinematics , 1981 .

[5]  Jean-François Richard,et al.  Methods of Numerical Integration , 2000 .

[6]  M. Raghavan,et al.  Number and dimensional synthesis of independent suspension mechanisms , 1996 .

[7]  B. Goh.  Necessary Conditions for Singular Extremals Involving Multiple Control Variables , 1966 .

[8]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[9]  Anil V. Rao,et al.  GPOPS-II , 2014, ACM Trans. Math. Softw..

[10]  George Trapp,et al.  Using Complex Variables to Estimate Derivatives of Real Functions , 1998, SIAM Rev..

[11]  Badih Jawad,et al.  Numerical Design of Racecar Suspension Parameters , 1999 .

[12]  Alessandro Rucco,et al.  Development and numerical validation of a reduced-order two-track car model , 2014, Eur. J. Control.

[13]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007, DAC 2006.

[14]  David J. N. Limebeer,et al.  Optimal control for a Formula One car with variable parameters , 2014 .

[15]  Daniel Patrick Kelly.  Lap time simulation with transient vehicle and tyre dynamics , 2008 .

[16]  Jörnsen Reimpell,et al.  The automotive chassis : engineering principles : chassis and vehicle overall, wheel suspensions and types of drive, axle kinematics and elastokinematics, steering - springing - tyres, construction and calculations advice , 2001 .

[17]  Anil V. Rao,et al.  Optimal control of Formula One car energy recovery systems , 2014, Int. J. Control.

[18]  P. A. Simionescu,et al.  Synthesis and analysis of the five-link rear suspension system used in automobiles , 2002 .

[19]  G. Bliss.  The problem of Mayer with variable end points , 1918 .

[20]  Dr.-Ing. habil Manfred Hiller,et al.  ROAD VEHICLE BENCHMARK 2: FIVE-LINK SUSPENSION , 1993 .

[21]  David G. Beale,et al.  Base Dynamic Parameter Estimation of a MacPherson Suspension Mechanism , 2003 .

[22]  David J. N. Limebeer,et al.  Optimal Control of a Formula One Car on a Three-Dimensional Track—Part 2: Optimal Control , 2015 .

[23]  H. Robbins.  A generalized legendre-clebsch condition for the singular cases of optimal control , 1967 .

[24]  David J. N. Limebeer,et al.  Optimal Control of a Formula One Car on a Three-Dimensional Track—Part 1: Track Modeling and Identification , 2015 .

[25]  Thierry Dargent,et al.  Using Multicomplex Variables for Automatic Computation of High-Order Derivatives , 2010, TOMS.

[26]  W. Hager,et al.  An hp‐adaptive pseudospectral method for solving optimal control problems , 2011 .

[27]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[28]  J. Merlet,et al.  Exact kinematics analysis of Car's suspension mechanisms using symbolic computation and interval analysis , 2005 .

[29]  H. Kelley.  A second variation test for singular extremals , 1964 .

[30]  J. Knapczyk,et al.  Displacement and Force Analysis of Five-Rod Suspension With Flexible Joints , 1995 .

[31]  Ion Stiharu,et al.  Development of kineto-dynamic quarter-car model for synthesis of a double wishbone suspension , 2011 .

[32]  A. Krener.  The High Order Maximal Principle and Its Application to Singular Extremals , 1977 .