Active Control for an Electric Vehicle with an Observer for Torque Energy-Saving
Abstract
:1. Introduction
2. Mathematical Model of the Vehicle
2.1. Definition of the Mathematical Model of the Vehicle
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- When studying stability and maneuverability, the analysis focuses on the dynamics of lateral velocity and yaw angular velocity.
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- The active brake actuator, denoted Mz, is responsible for creating differential braking forces, generating a moment around the z-axis, which further impacts the dynamics of lateral velocity.
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- The dynamics of the pitch angle are not considered. Since the system is a rigid body, Figure 1 can be utilized to depict the nonlinear dynamics of the system.
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- is the angular velocity of turn (rad/s), which is in synchrony with [39].
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- R > 0 is a constant gain that is chosen so that the angular velocity of the turn is not saturated. It relates the input voltage on the actuator with the angular velocity obtained from [40].
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- , are the tire angle components imposed by the driver and controller (rad), is the angular velocity response of the actuator on the power steering wheel (rad/s), where is the input voltage to actuator (V), is an estimated back electromotive force constant (V/(rad/s)), is the resistance of the actuator (Ω), and I is the current (A), considering the simplified mathematical model of the cc motor where its values are obtained experimentally [41].
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- m is the mass of the car (kg).
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- J expresses the moment of inertia of the vehicle (kg·m2).
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- h is the height of the center of gravity (C.G) with respect to the ground (m).
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- β denotes the chassis side-slip angle (rad).
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- lf, lr, are the lengths from the center of the vehicle to the front and rear tires (m).
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- r indicates the rolling radius of the tire (m).
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- vx signifies the longitudinal velocity (m/s).
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- vy represents the lateral velocity (m/s).
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- ωz is the angular rate of turn (rad).
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- x = [vx, vy, ωz] is the compact vector of the vehicle state.
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- αfy = αfyl = αfyr, αry = αryl = αryr denote the front and rear side-slip angles of the left and right tires (rad).
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- αf,0 = αrx0 are the uncontrolled front lateral and rear longitudinal slip angles respectively (rad).
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- αfx = αfxl = αfxr, αrx = αrxl = αrxr signify the front and rear longitudinal slip angles of the left and right wheels (rad).
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- Mz means the turning moment resulting from the active brakes (N·m).
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- μ is the coefficient of friction between the tire and the ground.
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- Fdx, Fdy are the longitudinal and lateral aerodynamic forces (N).
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- Mdz is the external aerodynamic yaw disturbance (N·m).
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- Ff,x, Fr,x are the front and rear longitudinal forces on the wheels (N).
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- Ff,y, Fr,y the front and rear lateral forces (N) as a function of the angle imposed on the front tires (δ = δd + δce).
2.2. Aerodynamics
2.3. State Feedback Controller Design
2.4. Design of the State Feedback Observer
2.5. Design of the Active PID Controller
3. Experimental Results and Discussion
3.1. Maneuver ISO 7401
3.2. Maneuver ISO 3888-2
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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González-López, J.M.; Pérez, S.S.; Betancourt, R.O.J.; Barreto, G. Active Control for an Electric Vehicle with an Observer for Torque Energy-Saving. World Electr. Veh. J. 2023, 14, 288. https://doi.org/10.3390/wevj14100288
González-López JM, Pérez SS, Betancourt ROJ, Barreto G. Active Control for an Electric Vehicle with an Observer for Torque Energy-Saving. World Electric Vehicle Journal. 2023; 14(10):288. https://doi.org/10.3390/wevj14100288
Chicago/Turabian StyleGonzález-López, Juan Miguel, Sergio Sandoval Pérez, Ramón O. Jiménez Betancourt, and Gilberto Barreto. 2023. "Active Control for an Electric Vehicle with an Observer for Torque Energy-Saving" World Electric Vehicle Journal 14, no. 10: 288. https://doi.org/10.3390/wevj14100288