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Semitrailer Steering Control for Improved Articulated Vehicle Manoeuvrability and Stability

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Semitrailer Steering Control for Improved Articulated Vehicle Manoeuvrability and Stability Nonlinear Engineering 2019; 8: 568–581 Sina Milani, Y. Samim Ünlüsoy*, Hormoz Marzbani, and Reza N. Jazar Semitrailer Steering Control for Improved Articulated Vehicle Manoeuvrability and Stability https://doi.org/10.1515/nleng-2018-0124 Vehicles (AHVs) are among the most widely used means Received August 21, 2018; revised November 16, 2018; accepted of road transport [1, 2]. On the other hand, AHVs impose November 16, 2018. higher highway safety concerns which are dierent from Abstract: Articulated heavy vehicles have some specic single unit vehicles; heavy weights, large dimensions, ge- performance limitations and safety risks due to their spe- ometrical conguration, high centres of gravity, and in- cial dynamic characteristics. They show poor manoeuvra- ner forces acting on their articulation points are the main bility at low speeds and may lose their stability in dier- sources for these dierences [3]. ent manners at high speeds. In this study, the potential of The presence of the articulation joint helps to reduce active steering control of the semitrailer on manoeuvrabil- the eective wheelbase of the vehicle in order to improve ity and stability of tractor-semitrailer combinations is in- low-speed turning ability, while large weights and high vestigated. A linear bicycle model and a nonlinear version Centre of Gravity (CG) of AHVs reduce the high-speed sta- are used for controller design and vehicle dynamic simula- bility in three dierent potentially unstable motions: jack- tion in MATLAB environment. The Linear Quadratic Regu- kning, trailer swing, and rollover [4]. Trailer swing and lator optimal state feedback control is used to minimise the rollover are directly related to the amplication of lateral tracking error at low-speed, and regulate Rearward Am- acceleration experienced at semitrailer’s centre of gravity plication ratio and roll at high-speed. Quantum Particle which is known as the Rearward Amplication (RA) ratio. Swarm Optimisation is used for optimising the weighting The RA ratio is dened as the ratio of peak lateral accelera- factors. Three dierent control algorithms are introduced tion of the semitrailer CG to that of the tractor unit during a and it is demonstrated through simulations that the vehi- high-speed single lane change manoeuvre [1, 5]. This hap- cle with the proposed steering control exhibits desirable pens due to the generation of semitrailer tyre lateral forces improvements compared to the baseline vehicle. with a time delay with respect to those of the tractor, result- ing in larger yaw motion and higher lateral acceleration of Keywords: Articulated Vehicle, Tractor-Semitrailer, Active the semitrailer [6]. Steering, Optimal Control, Vehicle Safety There have been many attempts to minimise the ex- cessive yaw and roll behaviours of the AHVs including the use of variable damping ratio for the fth wheel, dier- ential braking, active and passive semitrailer steering sys- 1 Introduction tems, and roll control. Among such control strategies, the semitrailer steering system seems to be the most eective Being cost eective due to reduction in labour require- approach to regulate the lateral acceleration of the semi- ments and fuel consumption, and large load carrying ca- trailer resulting in more desirable yaw and roll motions pacity compared to single unit vehicles, Articulated Heavy with the relatively small amount of energy requirement. Another reason that makes the semitrailer steering sys- tems interesting is that they could also be used to improve low-speed manoeuvrability of the vehicle by improving Sina Milani, School of Engineering, RMIT University, Melbourne, Australia, E-mail: [email protected] the tracking ability of the towed unit by means of proper *Corresponding Author: Y. Samim Ünlüsoy, Mechanical Engineering steering strategies. Department, Middle East Technical University, Ankara, Turkey, Passive semitrailer steering systems have been devel- E-mail: [email protected] oped at the earlier stages of AHV researches and studied Hormoz Marzbani, School of Engineering, RMIT University, Mel- in detail by Jujnovich and Cebon [7]. Command steering, bourne, Australia, E-mail: [email protected] Reza N. Jazar, School of Engineering, RMIT University, Melbourne, self-steering axle, and pivotal bogie systems are among Australia the most common passive steering systems. Studies on School of Civil Engineering and Architecture, Xiamen University of the passive semitrailer steering systems have concluded Technology, Xiamen, China, E-mail: [email protected] Open Access. © 2019 S. Milani et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License. S. Milani et al., Semitrailer Steering Control for Improved Articulated Vehicle Manoeuvrability and Stability Ë 569 that the passive steering systems improve low-speed ma- Linear Quadratic Regulator (LQR) technique has been noeuvrability and tyre-road scrub; however they appear to used in the design of the active semitrailer steering sys- diminish the high-speed lateral performance of the vehi- tems as the optimal feedback structure in a number of re- cle [1, 4, 8]. searches such as [1, 12–16] with dierent minimisation ob- Active steering systems enable the designer to elim- jectives. This method has been proved to be a simple yet inate complex mechanisms required for passive systems eective approach in dealing with active control of AHV and, if tuned properly, are also capable of providing proper dynamics. steering for dierent purposes regardless of vehicle speed. Based on the discussion related to the articulated ve- However, the low and high-speed requirements of the hicle behaviour to understand how tracking ability, lat- AHVs naturally conict with each other due to dierent eral accelerations, and roll motion are correlated; a new side-slip behaviour of the vehicle at dierent speeds [9, approach to semitrailer active steering strategy is intro- 10]. duced. The control strategy is expected to provide a sim- In a recent study [11], kinematics of the turning vehi- pler yet suciently accurate approach to semitrailer steer- cle in low speed is studied; a two-layer control strategy us- ing, in comparison to the more sophisticated methods ing fuzzy control and PID control is introduced to calculate requiring intensive mathematical calculations and hard- desired steering angles of tractor and semitrailer axles as ware requirements. The LQR control together with Quan- well as adjusting angular velocities of individually driven tum Particle Swarm Optimisation (QPSO) method is used wheels. The method works in a limited range of vehicle to ensure the optimal solution avoiding manual tuning of speeds when the side-slip is small. design parameters. In a novel approach, Jujnovich and Cebon [4] provided Current studies on the subject have mostly concen- a perspective by which both low and high-speed dynamics trated on a specic vehicle speed for low or high speed op- could be investigated in the same manner. They suggested eration of the articulated vehicles. The proposed control that the tracking ability of the towed unit may be consid- strategy is developed for a wide range of vehicle speeds ered as the main objective for the active steering control and a table of feedback coecients is obtained, so that design. This approach, despite its great level of accuracy, dierent requirements in varying travel speeds can be met requires a complicated set up to achieve the control objec- smoothly in an adaptive manner. Gain-scheduling for PID tive. control of trailer steering has been used in [17] with man- As far as the high-speed manoeuvre is concerned, it ual tuning of gains. The objective in this study is to avoid has been shown by Islam [1, 12], that the regulation of RA manual tuning of parameters as much as possible and en- ratio could be used to minimise the high-speed tracking sure optimal performance of the control strategy at the error and the roll stability at the same time. During a high- same time. A couple of variants of the controller to improve speed transient manoeuvre, the time delay between gen- the roll and the yaw stability of the tractor-semitrailer com- eration of tyre forces for the tractor and the semitrailer binations at high-speed manoeuvres, as well as the low- causes the semitrailer to travel slightly outwards due to speed cornering ability of the vehicle are also investigated. its large inertia. This, in turn, results in larger tyre slip an- gles for the semitrailer trying to bring it back to the steady- state conguration. Consequently, larger lateral forces are 2 Vehicle modelling generated at the semitrailer tyres causing larger lateral ac- celeration. In steady-state high-speed turning, the vehicle Selection and development of a vehicle model for a spe- units travel with equal yaw velocities and the semitrailer cic vehicle dynamics study is a crucial task. An over- experiences larger radius of curvature due to its large mass complex model will increase the simulation time and the resulting in larger lateral acceleration. So, in both tran- risk of unwanted errors. On the other hand, an excessively sient and steady-state conditions, the RA ratio is deeply re- simple model causes information loss. Thus, the most im- lated to the tracking behaviour of the vehicle. On the other portant factors in modelling include the level of complex- hand, the roll motion of the semitrailer unit is directly re- ity (assumptions), Degrees of Freedom (DOF), linearity, lated to its lateral acceleration as a consequence of the cen- and the expandability of the model. There are many AHV tripetal force. Thus, the excessive high-speed oscillation of modelling approaches introduced in the literature, each of the semitrailer along with its excessive roll motion, as the which has its own advantages and disadvantages. Never- most important high-speeds concerns, may be treated by theless, a very comprehensive modelling approach for ar- regulation of the RA ratio as a single criterion.
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