Extended State Observer-based Backstepping Sliding Mode Control for Wheel Slip Tracking.. Advanced Motion Control of a Quadrotor Unmanned Aerial Vehicle based on Extended State Observer.
Motivation
Electric cars are revolutionizing the automobile industry by utilizing electric motors instead of traditional internal combustion engines These electric motors offer numerous advantages, including noise-free operation, zero emissions, enhanced performance, and the capability for advanced control methods, which collectively improve the dynamic quality of electric vehicles Essential components of electric vehicles include the electric traction motor, power electronics controller, DC/DC converter, thermal system, traction battery pack, auxiliary battery, charge port, transmission, and onboard charger.
Electric Traction Motors are essential for electric and hybrid vehicles, offering advantages like rapid torque response, high torque at low speeds, compact size, and lightweight design Major automotive manufacturers, including Honda, BMW, Tesla, Toyota, Holden, and Ford, utilize various types of traction motors, such as brushless DC motors, switch reluctance motors, induction motors, and permanent magnet synchronous motors, in their electric models This technology enables electric vehicles to deliver impressive dynamic performance, as illustrated by their typical speed-torque characteristics.
Base speed ed Maximum speed
Constant torque region n Constant power region Reduce power region
Figure 1.2 Typical speed-torque characteristics of EVs [2]
In recent decades, active safety technologies like anti-lock braking systems, traction control systems (TCS), and electronic stability control have gained popularity, significantly enhancing vehicle traction, stability, and safety TCS specifically manages wheel traction torque to achieve optimal vehicle motion by minimizing slip through the tire-road interaction By reducing torque on the driven wheels, TCS ensures that control is maintained, allowing for safe maneuvering around obstacles Typically functioning as a secondary feature of electronic stability control, TCS is designed to prevent traction loss in various road conditions, with wheel slip being a nonlinear factor influenced by both wheel and vehicle velocity.
Main research question
Urgency of the topic
1 The need to improve safety and comfort when driving is increasing, and the trend of self-driving cars is developing strongly in the world but is not yet popular in the Vietnam.
2 The requirement to build a complete knowledge base on electric car motion control to develop domestic electric car human resources is especially meaningful for car manufacturers.
Novelty and applicability of the topic
1 Mastering the full 14-DOF mathematical model of a car facilitates the development of control algorithms to improve safety and driving experience, thereby making the project highly practical in training human resources for Vietnam’s electric car industry.
2 Building a testing platform for car models and comparing and testing, combined with specialized software Carsim, will create a solid basis for designing control algorithms for cars The full 14-DOF model of the car will help analyze and control the vehicle’s motion and transmission in more detail and more completely.
Main contributions
The main contributions of the thesis can be summarized as follows:
A two-loop control strategy enhances ride quality by enabling the system to effectively absorb vibration energies from road surface disturbances transmitted to the vehicle body.
The active suspension system utilizes an electro-hydraulic servo actuator, characterized by high nonlinearity due to the spring and damping properties, as well as parameter uncertainties To address these challenges, an Extended State Observer (ESO) combined with Backstepping Sliding Mode Control (BSMC) is developed to accurately estimate lumped disturbances and ensure the stabilization of the vehicle body.
3 In Chapter 3, novel high-gain-based observers are proposed to estimate unknown system dynamics, driving forces, and external disturbances such as driving resistance.
Unlike the approach in [17], which faces implementation challenges due to the time derivative of control torque being used as the control input, Chapter 3 simplifies the system by requiring only the control torque.
5 A quarter electric vehicle model using IPMSM with an anti-slip controller and observers as a slip-ratio observer and driving force observer is completed.
A nonlinear control system has been developed for four in-wheel motor electric vehicle models, incorporating driving force distribution, driving force control, and observers This system demonstrates effective performance across various simulation scenarios.
7 This chapter proposed backstepping control using the barrier Lyapunov function method to guarantee the constraint for the lateral error and avoid the chattering phenomenon.
The proposed method is validated through simulation tests using the high-fidelity dynamic simulator Carsim and Matlab/Simulink Results indicate that the efficiency of the proposed controller surpasses that of sliding mode control, achieving lower error rates.
Limitations
This study primarily emphasizes the design of motion control and electric drive systems in electric cars, intentionally setting aside a comprehensive exploration of power electronic control and energy management to streamline the research focus.
2 The results are based on simulations No experimental verification was performed for the proposed control algorithms However, the developed vehicle mathematical models were verified using experimental data.
3 This thesis assumes that the information about the surrounding environments, as well as the required feedback signals, is available.
VERTICAL MOTION 7
Introduction
The suspension system plays a crucial role in vehicles by effectively absorbing vibrations from road disturbances, ensuring riding comfort, and maintaining system stability There are three main types of suspension systems: passive, semi-active, and active.
Passive suspension, characterized by its simple design of springs and dampers, is widely used in vehicles due to its effectiveness in enhancing ride quality and road holding While independent passive suspension offers notable improvements, active suspension systems stand out for their superior stability and performance By generating independent forces based on relative suspension motion, active suspension control has emerged as a promising approach However, developing an effective control strategy to balance ride comfort, handling, and road adherence remains a significant challenge, as highlighted by numerous researchers in the literature.
This chapter presents an extended state observer for accurately estimating system disturbances, demonstrating its effectiveness in state and disturbance estimation Most active suspension control studies assume known actuator dynamics, leading to the ideal force generation assumption However, actuator dynamics often involve uncertain parameters and unmodeled nonlinearities The electro-hydraulic servo has proven to be an effective actuator for isolating vibrations transmitted to passengers A two-loop control design is introduced, featuring a force loop control and a main loop control, where the H ∞ control law ensures system stability based on Lyapunov theory while achieving desired performance Additionally, an adaptive robust control is proposed in the force loop to accurately track the desired force from the main-loop controller, although the nonlinearity of basic suspension components, such as nonlinear springs, is overlooked.
This chapter examines a nonlinear full-car model featuring a nonlinear spring and seven degrees of freedom, incorporating uncertain parameters A backstepping sliding mode control method, as proposed by [27], is utilized in the main control loop The backstepping approach is favored for its systematic process in constructing Lyapunov functions, ensuring system stability This method not only guarantees stability but also enhances performance metrics such as ride comfort Furthermore, an extended state observer is implemented to accurately estimate disturbances, allowing for robust control designed to effectively track the desired force using force actuators.
Problem formulation
Figure 2.1 The model of the full-car active suspension system [26]
This study examines a nonlinear suspension system for a full car, characterized by a 7-degree-of-freedom (DOF) model that accounts for heave, pitch, roll motions, and the dynamics of four unsprung masses The tire is represented as a simple linear spring, with the assumption that the movements of the four wheels are independent The dynamic suspension is analyzed within the frequency range relevant to vertical vehicle dynamics (0–25 Hz) The model, extensively utilized in this research, includes parameters such as the mass of the sprung mass (M), the masses of the four unsprung components (m_i), and the inertia values for roll (I_y) and pitch (I_x) motions Forces generated by the nonlinear spring (F_si) and linear damper (F_di), along with tire stiffness (k_ti), are also incorporated In this context, z, θ, and φ denote the heave, pitch, and roll motions, while y_i and y_o represent the displacements of the sprung mass and road input, respectively Additionally, f_i indicates the force input produced by the electro-hydraulic servo actuator.
Assumption 2.1 The pitch and roll angles are small It can be considered as:
Assumption 2.2 The suspension with uncertain parameters is assumed that:
(2.2) where M max ,I xmax ,I ymax and M min ,I xmin ,I ymin are the upper and lower limit of the sprung mass and the inertia for the roll and pitch motions, respectively.
According to the model in Fig 2.1, the suspension deflectionΔ i (i = 1, ,4) are defined: Δy 1=y+aθ+cφ−y 1 Δy 2 =y+aθ−dφ−y 2 Δy 3=y−bθ+cφ−y 3 Δy 4=y−bθ−dφ−y 4
The dynamic equations of active suspension with electro-hydraulic servo actuators are as follows [26]: z¨=−1
(F di +F si −f i )) y¨ i = 1 m i [F di +F si −k ti (y i −y oi )−f i]
The dynamic equation of active suspension, incorporating the effects of uncertainty and disturbance, can be expressed as z¨ = -4, where the forces generated by the nonlinear spring (F si = kΔy i + k n Δy 3 i) and the linear damper (F di = bΔy˙ i) play crucial roles in the movement of the sprung mass.
(2.5) whereg i (i=z,θ,φ)are the non-linearity of the suspension itself and f z ,f θ ,f φ is stood for the equivalent control forces on the vertical, pitch, and roll motions as follows: f z = ∑ 4 i = 1
The active suspension system incorporates nonlinear suspension components, model uncertainties, and the effects of road surface conditions on the wheels The lumped disturbances in heave, pitch, and roll motions are represented as d_i (where i = z, θ, φ), with d_z defined as ΔM.
(2.6) where g i (i = z,θ,φ) are the non-linearity of the suspension ΔM,ΔI x ,ΔI y are uncertainty parameters of mass, moment inertia I x , and I y ; Δk,Δb are uncertainty parameters of non-linear springs, and dampers, respectively.
Assumption 2.3 The unknown disturbances d z ,d θ ,d φ are assumed that vary slowly and bounded From which, exist that: d˙ z 0) The slip ratio (λ) and friction coefficient (μ) are also critical factors Additionally, the driving torque (T g ear) and total resistance load (F dr) play significant roles in vehicle dynamics.
Figure 3.1 The quarter-vehicle model
The aerodynamic force (F aero) acting on a vehicle is influenced by several key factors, including air density (ρ), drag coefficient (c w), frontal area (A f), vehicle speed, and wind speed (v wind) Additionally, the equation incorporates the gravitational acceleration (g z) and the sine of the angle (α), represented as 4g z sin(α) Understanding these components is essential for analyzing vehicle performance in varying conditions.
Rolling resistance F roll can be expressed as a function of tire normal force F z and rolling resistance coefficient f r as follows:
F roll = f r F z (3.7) with the normal force on the driven axle is determined by:
The equation for the force acting on a vehicle during acceleration is given by 4g z cos(α), where α represents the incline angle of the road The slip ratio of the vehicle wheel is defined by the formula λ = (v ω - v max(v ω, v, ξ)), where the small constant ξ is introduced to avoid zero denominators To finalize the dynamic model of the system, it is essential to understand the concept of effective radius, defined as v_eff = r_eff ω_w = b_t.
R stat