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2020 | OriginalPaper | Chapter

A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles

Authors: Matteo Veneri, Matteo Massaro

Published in: Advances in Dynamics of Vehicles on Roads and Tracks

Publisher: Springer International Publishing

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Abstract

Minimum-lap-time problems are commonly solved employing quasi-steady-state models on a predetermined trajectory or dynamic models on a free (non-predetermined) trajectory. The current work deals with a third approach, that combines a free-trajectory minimum-lap-time method, together with a quasi-steady-state description of the vehicle. The method is based on the computation of the well known g-g diagrams, which summarise the quasi-steady-state performance of the vehicle. This information is employed for the solution of an optimal-control problem, that allows to determine the optimal trajectory. Numerical models of high complexity can be employed, since all their features (e.g. tyre limits, power limits, aerodynamic drag and downforce, suspensions, etc.) are included in the related g-g diagrams, and do not affect the complexity of the optimal control problem that need be solved. The method allows to employ even experimental g-g diagrams in place of numerical ones, and is suitable for application to both cars and motorcycles.
Literature
2.
go back to reference Gadola, M., Vetturi, D., Cambiaghi, D., Manzo, L.: A tool for lap time simulation. Technical report 1996-12-01, SAE Technical Paper (1996) Gadola, M., Vetturi, D., Cambiaghi, D., Manzo, L.: A tool for lap time simulation. Technical report 1996-12-01, SAE Technical Paper (1996)
3.
go back to reference Siegler, B., Deakin, A., Crolla, D.: Lap time simulation: comparison of steady state, quasi-static and transient racing car cornering stategies. In: Society of Automobile Engineers (ed.) 2000 SAE Motorsports Engineering Conference and Exposition, No. paper 2000-01-3563, p. 9. SAE International (2000) Siegler, B., Deakin, A., Crolla, D.: Lap time simulation: comparison of steady state, quasi-static and transient racing car cornering stategies. In: Society of Automobile Engineers (ed.) 2000 SAE Motorsports Engineering Conference and Exposition, No. paper 2000-01-3563, p. 9. SAE International (2000)
4.
go back to reference Brayshaw, D., Harrison, M.: A quasi steady state approach to race car lap simulation in order to understand the effects of racing line and centre of gravity location. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219(6), 725–739 (2005) CrossRef Brayshaw, D., Harrison, M.: A quasi steady state approach to race car lap simulation in order to understand the effects of racing line and centre of gravity location. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219(6), 725–739 (2005) CrossRef
5.
go back to reference Brayshaw, D., Harrison, M.: Use of numerical optimization to determine the effect of the roll stiffness distribution on race car performance. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219(10), 1141–1151 (2005) CrossRef Brayshaw, D., Harrison, M.: Use of numerical optimization to determine the effect of the roll stiffness distribution on race car performance. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219(10), 1141–1151 (2005) CrossRef
6.
go back to reference Savaresi, S.M., Spelta, C., Ciotti, D., Sofia, M., Rosignoli, E., Bina, E.: Virtual selection of the optimal gear-set in a race car. Int. J. Veh. Syst. Model. Test. 3(1–2), 47–67 (2008) Savaresi, S.M., Spelta, C., Ciotti, D., Sofia, M., Rosignoli, E., Bina, E.: Virtual selection of the optimal gear-set in a race car. Int. J. Veh. Syst. Model. Test. 3(1–2), 47–67 (2008)
7.
go back to reference Kelly, D.P., Sharp, R.S.: Time-optimal control of the race car: influence of a thermodynamic tyre model. Veh. Syst. Dyn. 50(4), 641–662 (2012) CrossRef Kelly, D.P., Sharp, R.S.: Time-optimal control of the race car: influence of a thermodynamic tyre model. Veh. Syst. Dyn. 50(4), 641–662 (2012) CrossRef
8.
go back to reference Völkl, T., Muehlmeier, M., Winner, H.: Extended steady state lap time simulation for analyzing transient vehicle behavior. SAE Int. J. Passeng. Cars Mech. Syst. 6, 283–292 (2013) CrossRef Völkl, T., Muehlmeier, M., Winner, H.: Extended steady state lap time simulation for analyzing transient vehicle behavior. SAE Int. J. Passeng. Cars Mech. Syst. 6, 283–292 (2013) CrossRef
9.
go back to reference Tremlett, A., Assadian, F., Purdy, D., Vaughan, N., Moore, A., Halley, M.: Quasi-steady-state linearisation of the racing vehicle acceleration envelope: a limited slip differential example. Veh. Syst. Dyn. 52(11), 1416–1442 (2014) CrossRef Tremlett, A., Assadian, F., Purdy, D., Vaughan, N., Moore, A., Halley, M.: Quasi-steady-state linearisation of the racing vehicle acceleration envelope: a limited slip differential example. Veh. Syst. Dyn. 52(11), 1416–1442 (2014) CrossRef
10.
go back to reference Hendrikx, J., Meijlink, T., Kriens, R.: Application of optimal control theory to inverse simulation of car handling. Veh. Syst. Dyn. 26(6), 449–461 (1996) CrossRef Hendrikx, J., Meijlink, T., Kriens, R.: Application of optimal control theory to inverse simulation of car handling. Veh. Syst. Dyn. 26(6), 449–461 (1996) CrossRef
11.
go back to reference Cossalter, V., Da Lio, M., Lot, R., Fabbri, L.: A general method for the evaluation of vehicle manoeuvrability with special emphasis on motorcycles. Veh. Syst. Dyn. 31(2), 113–135 (1999) CrossRef Cossalter, V., Da Lio, M., Lot, R., Fabbri, L.: A general method for the evaluation of vehicle manoeuvrability with special emphasis on motorcycles. Veh. Syst. Dyn. 31(2), 113–135 (1999) CrossRef
12.
go back to reference Casanova, D., Sharp, R.S., Symonds, P.: Minimum time manoeuvring: the significance of yaw inertia. Veh. Syst. Dyn. 34(2), 77–115 (2000) CrossRef Casanova, D., Sharp, R.S., Symonds, P.: Minimum time manoeuvring: the significance of yaw inertia. Veh. Syst. Dyn. 34(2), 77–115 (2000) CrossRef
13.
go back to reference Casanova, D.: On minimum time vehicle manoeuvring: the theoretical optimal lap. Ph.D. thesis, School of Engineering, Cranfield University (2000) Casanova, D.: On minimum time vehicle manoeuvring: the theoretical optimal lap. Ph.D. thesis, School of Engineering, Cranfield University (2000)
14.
go back to reference Bertolazzi, E., Biral, F., Da Lio, M.: Symbolic-numeric efficient solution of optimal control problems for multibody systems. J. Comput. Appl. Math. 185(2), 404–421 (2006) MathSciNetMATHCrossRef Bertolazzi, E., Biral, F., Da Lio, M.: Symbolic-numeric efficient solution of optimal control problems for multibody systems. J. Comput. Appl. Math. 185(2), 404–421 (2006) MathSciNetMATHCrossRef
15.
go back to reference Kelly, D.P.: Lap time simulation with transient vehicle and tyre dynamics. Ph.D. thesis, Cranfield University (2008) Kelly, D.P.: Lap time simulation with transient vehicle and tyre dynamics. Ph.D. thesis, Cranfield University (2008)
16.
go back to reference Bobbo, S., Cossalter, V., Massaro, M., Peretto, M.: Application of the optimal maneuver method for enhancing racing motorcycle performance. Int. J. Passeng. Cars Mech. Syst. 1(1), 1311–1318 (2009) Bobbo, S., Cossalter, V., Massaro, M., Peretto, M.: Application of the optimal maneuver method for enhancing racing motorcycle performance. Int. J. Passeng. Cars Mech. Syst. 1(1), 1311–1318 (2009)
17.
go back to reference Tavernini, D., Massaro, M., Velenis, E., Katzourakis, D., Lot, R.: Minimum time cornering: the effect of road surface and car transmission layout. Veh. Syst. Dyn. 51(10), 1533–1547 (2013) CrossRef Tavernini, D., Massaro, M., Velenis, E., Katzourakis, D., Lot, R.: Minimum time cornering: the effect of road surface and car transmission layout. Veh. Syst. Dyn. 51(10), 1533–1547 (2013) CrossRef
18.
go back to reference Tavernini, D., Velenis, E., Lot, R., Massaro, M.: The optimality of the handbrake cornering technique. J. Dyn. Syst. Meas. Control 136(4), 041019 (2014) CrossRef Tavernini, D., Velenis, E., Lot, R., Massaro, M.: The optimality of the handbrake cornering technique. J. Dyn. Syst. Meas. Control 136(4), 041019 (2014) CrossRef
19.
go back to reference Perantoni, G., Limebeer, D.J.N.: Optimal control for a formula one car with variable parameters. Veh. Syst. Dyn. 52(5), 653–678 (2014) CrossRef Perantoni, G., Limebeer, D.J.N.: Optimal control for a formula one car with variable parameters. Veh. Syst. Dyn. 52(5), 653–678 (2014) CrossRef
20.
go back to reference Limebeer, D.J.N., Perantoni, G., Rao, A.V.: Optimal control of formula one car energy recovery systems. Int. J. Control 87(10), 2065–2080 (2014) MathSciNetMATH Limebeer, D.J.N., Perantoni, G., Rao, A.V.: Optimal control of formula one car energy recovery systems. Int. J. Control 87(10), 2065–2080 (2014) MathSciNetMATH
21.
go back to reference Masouleh, M.I., Limebeer, D.J.N.: Optimizing the aero-suspension interactions in a formula one car. IEEE Trans. Control Syst. Technol. 24(3), 912–927 (2016) CrossRef Masouleh, M.I., Limebeer, D.J.N.: Optimizing the aero-suspension interactions in a formula one car. IEEE Trans. Control Syst. Technol. 24(3), 912–927 (2016) CrossRef
22.
go back to reference Tremlett, A., Massaro, M., Purdy, D., Velenis, E., Assadian, F., Moore, A., Halley, M.: Optimal control of motorsport differentials. Veh. Syst. Dyn. 53(12), 1772–1794 (2015) CrossRef Tremlett, A., Massaro, M., Purdy, D., Velenis, E., Assadian, F., Moore, A., Halley, M.: Optimal control of motorsport differentials. Veh. Syst. Dyn. 53(12), 1772–1794 (2015) CrossRef
23.
go back to reference Tremlett, A., Limebeer, D.J.N.: Optimal tyre usage for a formula one car. Veh. Syst. Dyn. 54(10), 1448–1473 (2016) CrossRef Tremlett, A., Limebeer, D.J.N.: Optimal tyre usage for a formula one car. Veh. Syst. Dyn. 54(10), 1448–1473 (2016) CrossRef
24.
go back to reference Dal Bianco, N., Lot, R., Gadola, M.: Minimum time optimal control simulation of a GP2 race car. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 232(9), 1180–1195 (2017) CrossRef Dal Bianco, N., Lot, R., Gadola, M.: Minimum time optimal control simulation of a GP2 race car. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 232(9), 1180–1195 (2017) CrossRef
25.
go back to reference Dal Bianco, N., Bertolazzi, E., Biral, F., Massaro, M.: Comparison of direct and indirect methods for minimum lap time optimal control problems. Veh. Syst. Dyn. 57(5), 1–32 (2019) Dal Bianco, N., Bertolazzi, E., Biral, F., Massaro, M.: Comparison of direct and indirect methods for minimum lap time optimal control problems. Veh. Syst. Dyn. 57(5), 1–32 (2019)
26.
go back to reference Limebeer, D.J.N., Massaro, M.: Dynamics and Optimal Control of Road Vehicles. Oxford University Press, Oxford (2018) MATHCrossRef Limebeer, D.J.N., Massaro, M.: Dynamics and Optimal Control of Road Vehicles. Oxford University Press, Oxford (2018) MATHCrossRef
27.
go back to reference Veneri, M., Massaro, M.: A free-trajectory quasi-steady-state optimal-control method for minimum lap-time of race vehicles. Veh. Syst. Dyn. 1–22 (2019) Veneri, M., Massaro, M.: A free-trajectory quasi-steady-state optimal-control method for minimum lap-time of race vehicles. Veh. Syst. Dyn. 1–22 (2019)
Metadata
Title
A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles
Authors
Matteo Veneri
Matteo Massaro
Copyright Year
2020
DOI
https://doi.org/10.1007/978-3-030-38077-9_146

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