Non-linear optimal control of articulated-vehicle planar motion based on braking utilizing the state-dependent Riccati equation method

Abstract

In this paper, a new non-linear optimal controller for the planar motion of an articulated vehicle is proposed. The main goal of the control system is to enhance the planar stability through active braking of the wheels. The controller was designed such that the states of the system are forced to follow the reference values using an input-constrained non-linear model including the longitudinal dynamics, the lateral dynamics and the yaw dynamics of both units. Using the state-dependent Riccati equation method a servomechanism was designed which results in reasonable trade-offs between the control efforts and the allowable state errors while representing the non-linearities of the system. Furthermore, the brake torques were derived from the state-dependent Riccati equation control law by imposing constraints on the control inputs. Through proper selection of a weighting matrix, the control system distributes the brake forces optimally among the axles considering the coupling between the longitudinal tyre forces and the lateral tyre forces. In order to evaluate the performance and the effectiveness of the proposed controller, simulations were performed using the non-linear vehicle model. Additionally, the robustness of the controller is evaluated by analysis of its performance in the presence of parameter uncertainties. The simulation results prove the efficacy of the proposed controller in improving the yaw–roll stability, the handling and the manoeuvrability of the tractor–semitrailer.

Keywords

Articulated vehicle input-constrained model lateral performance non-linear system optimal control planar stability state-dependent Riccati equation control tractor–semitrailer

Get full access to this article

View all access options for this article.

References

Åkerman

Jonsson

. European modular system for road freight transport – experiences and possibilities. TFK Report 2007:2E, TransportForsK AB, Stockholm, Sweden, 2007.

Kharrazi

Thomson

. Study of heavy truck accidents with focus on manoeuvres causing loss of control. Int J Veh Safety 2008; 3: 32–44.

Kimbrough

Elwell

Chiu

. Braking controllers and steering controllers for combination vehicles. Int J Heavy Veh Systems 1994; 1: 195–223.

Hac

Fulk

Chen

. Stability and control considerations of vehicle–trailer combination. SAE paper 2008-01-1228, 2008.

Chen

Shieh

. Jackknife prevention for articulated vehicles using model reference adaptive control. Proc IMechE Part D: J Automobile Engineering 2011; 225(1): 28–42.

Palkovics

El-Gindy

. Design of an active unilateral brake control system for five-axle tractor-semi-trailer based on sensitivity analysis. Veh System Dynamics 1995; 24: 725–758.

Fancher

Winkler

Ervin

Zhang

. Using braking to control the lateral motions of full trailers. Veh System Dynamics 1998; 29: 462–478.

MacAdam

Hagan

Fancher

. Rearward amplification suppression (RAMS). Report UMTRI-2000-47, HS-809 320, University of Michigan Transportation Research Institute, Ann Arbor, Michigan, USA, 2000.

Zong

Zhu

Wang

Liu

. Multi-objective stability control algorithm of heavy tractor semi-trailer based on differential braking. Chin J Mech Engng 2012; 25: 88–97.

10.

Yang

. Optimal reconfiguration control of the yaw stability of the tractor–semitrailer vehicle. Mathl Probl Engng 2012; Article ID 602502: 1–23.

11.

Dugoff

Fancher

Segel

. An analysis of tire traction properties and their influence on vehicle dynamic performance. SAE paper 700377, 1970.

12.

Chen

Tomizuka

. Dynamic modeling of articulated vehicles for automated highway systems. In: American control conference, Seattle, Washington, USA, 21–23 June 1995, Vol 1, pp. 653–657. New York: IEEE.

13.

Chung

Kim

. An investigation into differential braking strategies for vehicle stability control. Proc IMechE Part D: J Automobile Engineering 2003; 217(12): 1081–1093.

14.

Ghaffari

Tabatabaei Oreh

Kazemi

Karbalaei

. An intelligent approach to the lateral forces usage in controlling the vehicle yaw rate. Asian J Control 2011; 13: 213–231.

15.

Ervin

. An overview of the dynamic performance properties of long truck combinations. Report UMTRI-84-26, University of Michigan Transportation Research Institute, Ann Arbor, Michigan, USA, 1984.

16.

Mokhiamar

Abe

. Active wheel steering and yaw moment control combination to maximize stability as well as vehicle responsiveness during quick lane change for active vehicle handling safety. Proc IMechE Part D: J Automobile Engineering 2002; 216(2): 115–124.

17.

Oreh

Kazemi

Azadi

. A new desired articulation angle for directional control of articulated vehicles. Proc IMechE Part K: J Multi-body Dynamics 2012; 226: 298–314.

18.

Pape

Arant

Brock

. U32: vehicle stability and dynamics – longer combination vehicles. Report NTRCI-50-2011-025, National Transportation Research Center, Knoxville, Tennessee, USA, 2011.

19.

Çimen

. Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method. A Rev Control 2010; 34: 32–51.

20.

Alirezaie

Ghaffari

Kazemi

. A SVFC approach to design a robust lane keeping assistance system. In: International symposium on advanced vehicle control, Loughborough, Leicestershire, UK, 22–25 August 2010, pp. 1–5. Tokyo: JSAE.

21.

Piyabongkarn

Rajamani

Grogg

Lew

. Development and experimental evaluation of a slip angle estimator for vehicle stability control. IEEE Trans Control Systems Technol 2009; 17: 78–88.

22.

Alirezaei

Kanarachos

Scheepers

Maurice

. Experimental evaluation of optimal vehicle dynamic control based on the state dependent Riccati equation technique. In: American control conference, Washington, DC, USA, 17–19 June 2013, pp. 408–412. New York: IEEE.

23.

Laub

. A Schur method for solving algebraic Riccati equations. IEEE Trans Autom Control 1979; 24: 913–921.

24.

Kiencke

Nielsen

. Automotive control systems: for engine, driveline, and vehicle. Berlin: Springer, 2005.