The optimal control law of the power supplied to the wheeled vehicle in case of curvilinear movement

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Abstract

BACKGROUND: Highly-mobile wheeled vehicles are designed to move on roads and terrain in various road and soil conditions, which is accompanied by frequent and significant changes in traction forces and rolling resistance forces. In this regard, in order to maintain vehicle mobility and to ensure low energy costs when performing transport tasks, it is necessary to continuously change the operating mode during motion from the completely locked mode to the differential mode in the case of a mechanical transmission. At the same time, the transmission operating mode selected by the driver is not always reasonable. Thus, the development of a law for controlling the power supplied to the propulsion system, ensuring minimal energy losses while maintaining vehicle mobility in widely varying road conditions, is a relevant task.

OBJECTIVE: Increasing the energy efficiency of highly-mobile wheeled vehicles by applying a control law for the power supplied to the propulsion system, adaptive to driving conditions.

METHODS: Increasing the energy efficiency of motion can be achieved by means of reducing losses due to wheel slipping by controlling the power supplied to the propulsion system. It is advisable to obtain the control law as a result of solving an optimization problem, where the loss power is chosen as the objective function, and the traction forces developed on each of the wheels are chosen as the varied values. At the same time, in order to maintain the ability of vehicle to move, it is necessary to take into account that the total traction force on all wheels must be determined by external conditions and be provided by the powertrain. To solve the optimization problem, the Lagrange multiplier method was used.

RESULTS: The conducted studies made it possible to obtain a unified law of adaptive control of the power supplied to the propulsion system in analytical form, applicable in a wide range of road conditions in both straight and curvilinear motion, ensuring the distribution of moments across the driving wheels of the machine close to optimal.

CONCLUSIONS: The application of the developed law for controlling the power supplied to the propulsion system, based on the use of information about the longitudinal and vertical forces, rotational velocities and steer angles of the wheels during the motion, will improve the efficiency of performing transport tasks when moving a vehicle in continuously changing road conditions. This is achieved due to reducing the workload on the driver in terms of controlling differential locks in comparison with a manual transmission both in straight and curvilinear motion.

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About the authors

Georgy O. Kotiev

Kazan Federal University

Email: kotievgo@yandex.ru
ORCID iD: 0000-0001-7884-157X
SPIN-code: 8963-6431

Dr. Sci. (Engineering), Professor, Director of the Naberezhnye Chelny Institute

Russian Federation, Kazan

Vasiliy A. Gorelov

Bauman Moscow State Technical University

Email: gorelov_va@bmstu.ru
ORCID iD: 0000-0002-2171-6302
SPIN-code: 1455-9984

Dr. Sci. (Engineering), Professor, Head of the Multipurpose Tracked Vehicles and Mobile Robots Department

Russian Federation, Moscow

Boris B. Kositsyn

Bauman Moscow State Technical University

Email: kositsyn_b@bmstu.ru
ORCID iD: 0000-0002-2131-2738
SPIN-code: 2005-7528

Dr. Sci. (Engineering), Associate Professor, Professor of the Wheeled Vehicles Department

Russian Federation, Moscow

Ruslan L. Gazizullin

Bauman Moscow State Technical University

Author for correspondence.
Email: rlgazizullin@bmstu.ru
ORCID iD: 0000-0002-4022-9286
SPIN-code: 3145-4190

Cand. Sci. (Engineering), Senior Lecturer of the Wheeled Vehicles Department

Russian Federation, Moscow

Konstantin E. Byakov

Bauman Moscow State Technical University

Email: byakov@bmstu.ru
ORCID iD: 0000-0002-9922-5810
SPIN-code: 7678-7778

Cand. Sci. (Engineering), Associate Professor of the Multipurpose Tracked Vehicles and Mobile Robots Department

Russian Federation, Moscow

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2. Fig. 1. Analytical scheme of stationary turn of a wheeled vehicle when moving with negligibly small slip angles: O — turn center; C — center of mass of the vehicle; xCy — the coordinate frame associated with the center of mass of the vehicle; Ri — the turn radius of the i-th wheel; θi — the steer angle of the i-th wheel relative to the longitudinal axis of the vehicle; v — velocity of the center of mass of the vehicle, ωz — angular velocity of turn of the vehicle body around the vertical axis; yкi — transverse coordinate of the i-th wheel.

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3. Fig. 2. Analytical scheme of the vehicle motion in the horizontal plane: x’iOy’i — the fixed coordinate frame associated with a supporting surface; x’’iO’’iy’’i — the coordinate frame associated with the i-th wheel of the vehicle and located at the geometric center of the contact patch Оi xкi — longitudinal coordinate of the i-th wheel.

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4. Fig. 3. Graph of changes in the rolling resistance coefficients f of the vehicle wheels depending on the number of the virtual experiment.

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5. Fig. 4. Results of a computational experiment depending on the design case: а — torques at the wheels of the vehicle; b — longitudinal reactions on wheels; c — values of wheel slip coefficients; d — power supplied to the wheels.

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6. Fig. 5. Graph of changes in the coefficient of specific power losses depending on the type of drive and the number of the computational experiment.

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7. Fig. 6. Graph of changes in slip angles of the vehicle axes depending on the type of drive and the number of the computational experimen.

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8. Fig. 7. Results of a computational experiment for a motion velocity of 7 m/s: а — difference in slip angles of the axes; b — specific power loss coefficient; c — slip angles of the axes.

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9. Fig. 8. Results of a computational experiment for a motion velocity of 9 m/s: а — difference in slip angles of the axes; b — specific power loss coefficient; c — slip angles of the axes.

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