Optimal sliding mode control design using a genetic algorithm for electric power steering control

This article presents a robust control strategy for Electric Power Steering (EPS) to enhance overall performance. The proposed approach integrates Backstepping Control (BSC) and Sliding Mode Control (SMC) techniques, with the input signal finely tuned using a Proportional-Integral-Derivative (PID) controller. An Extended State Observer (ESO) is utilized to estimate the system’s state variables, including the effects of external disturbances, through an augmented state variable. This work’s novelty lies in designing an integrated control mechanism that effectively eliminates steady-state error and sensor noise while reducing overshoot and chattering, which commonly affect traditional control methods. The numerical simulation method is conducted to compare the proposed controller’s performance with existing algorithms. The results show that the controlled state variables closely track their desired values with minimal errors. The Root Mean Square Error (RMSE) for most state variables is insignificant (below 0.37%), except for motor current signals (9.93% for v 1 and 25.65% for v 2 ). The ESO demonstrates high accuracy in estimating both the state variables and disturbances. In conclusion, the proposed control approach significantly outperforms conventional methods in EPS system control.

This paper studies integrated control of chassis control systems to achieve the goal of functional integration of the control systems. A two-layer hierarchical control architecture is developed for integrated control of Electric Power Steering (EPS) system and Anti-Lock Brake System (ABS). The upper-layer controller is designed to coordinate the interactions between the EPS system and the ABS. In the lower layer, the two controllers including the EPS system and the ABS are designed independently to achieve their local control objectives. Both a simulation investigation and an on-vehicle experimental study are performed to demonstrate the effectiveness of the proposed hierarchical control system. Simulation results show that the system is able to improve the lateral stability of the vehicle, and at the same time ensure the steering agility and braking performance of the vehicle. Moreover, on-vehicle experiment results conform to the simulation results.

This article presents the design of a high-performance, robust algorithm used to control an automotive electric power steering system. Compared with previous studies, this algorithm provides several novel achievements: reducing system error, eliminating the influence of chattering for a multi-input and multi-output system, and ensuring automotive dynamic stability based on a complex spatial dynamic model. This new algorithm is established by combining backstepping control, sliding mode control, and a fuzzy computing technique based on state variables observed by an extended state observer. The theoretical stability of the system is evaluated according to the Lyapunov criterion, while the algorithm’s performance is validated through numerical simulation results. According to the research findings, output signals closely track ideal values with negligible errors if the proposed algorithm is applied to control the system. The root mean square error between observed signals and actual values does not exceed 2.0%. In addition, the vehicle dynamics behaviors are maintained with minimal errors when applying the proposed technique, compared to other control algorithms. In conclusion, the algorithm’s performance is guaranteed even when the vehicle speed changes and the system is subjected to external disturbances.

During the last two decades, parallel robots have become more ubiquitous, employed in a great variety of sectors, from food to aerospace industries. In fact, they are much more efficient than their serial counterparts in terms of performing fast motions and consuming less energy. However, due to their mechanical complexity, they present a highly complex non-linear dynamics, which makes the modelling and control tasks difficult. Aiming to improve the performance and robustness of the control laws already used to control this type of mechanisms, this paper proposes two hybrid control techniques. The first hybrid control is derived from the combination of a pure PD control with a modified Sliding Mode control. The second hybrid control, in its turn, combines a pure Computed Torque with the altered Sliding Mode control. The proposed modifications in the Sliding Mode control aim to achieve a considerable reduction of the tracking errors and chattering. A stability analysis of the proposed control techniques and an experimental validation are carried out, comparing the performance of the pure and hybrid control laws in a 5R parallel mechanism. Moreover, simulations are also conducted to evaluate the behaviour of a 3-dof spatial parallel robot, when performing a 3D-path. Analysing the simulations and the experimental results, it is possible to observe a significant reduction of the path tracking and steady-state errors in both hybrid control strategies.

Integrity of electric power steering system is vital to vehicle handling and driving performance. Advances in electric power steering (EPS) system have increased complexity in detecting and isolating faults. In this paper, we propose a hybrid model-based and data-driven approach to fault detection and diagnosis (FDD) in an EPS system. We develop a physics-based model of an EPS system, conduct fault injection experiments to derive fault-sensor measurement dependencies, and investigate various FDD schemes to detect and isolate the faults. Finally, we use an SVM regression technique to estimate the severity of faults.

Assistant control is the main work process of automotive electric power steering (EPS) system. The assistant target current was achieved based on the design of straight-line type assist characteristic. The flexible PID control is acted on the motor according to the driver’s input torque and the current vehicle speed. Using flexible PID control to track and control the motor current not only solved the contradiction between stability and accuracy of control system, but also enhances the system adaptability and robustness in the influence of uncertainty factors. The system with good real-time following characteristics in this paper can meet the motor performance requirements of EPS system, and provide a good platform for further research on control strategy and control algorithm at the same time.

Torque ripple in an electric power steering (EPS) system can be induced by the phase lag between steer angle and rack displacement, non-linear friction, and disturbances from road and sensor noise, especially during high-frequency manoeuvres. This paper investigates the application of robust and non-linear sliding mode control (SMC) strategies to an EPS system, based on a reference model to reduce the torque ripple and stabilize the dynamics of the EPS system. The dynamics of the EPS system is described by a non-linear state-space model with realistic non-linear friction and disturbances from road and sensor noise. Meanwhile, the ideal EPS system, in which the rack displacement tracks the steer angle perfectly, is proposed as the reference model. A non-linear sliding mode observer (SMO) is also developed to estimate the unmeasurable states. The performance and robustness of SMC and SMO are demonstrated using various simulations and compared with traditional alternatives. The results of these simulations reveal that the non-linear SMC and SMO strategies can reduce the torque ripple to achieve a better steering feel and more stable driving, and can be applied to commercial EPS systems.

Based on the established dynamic model of the electric power steering (EPS) system, the power actuation electric circuit of the EPS system and the power actuation principle of the full-bridge and half-bridge were analyzed, the mean current expression was derived, and the FB/HB switch was designed. A kind of simple practical controller of sliding mode control (SMC) was designed according to the basic principle of SMC by using the assistant motor in EPS. The simulation and experimental result indicates that this controller has very good control effect and it can give the EPS very good dynamic performance because the non-linear problem in traditional controller was solved.

The electric power steering (EPS) system is the mechatronic control system. The corrent PID control is the closed loop control with the error between the aim corrent and the motor armature backfeed corrent, and the fuzzy PID control is the mechatronic closed-loop system by the error which reflect the change of the turning-axis. In this paper we present the development of a vehicle's EPS control, based on a double layer closed-loop fuzzy-PID controller which consisted the corrent backfeed inner loop and the moment backfeed outer loop. The output of the fuzzy PID control is used as the assist-force target value, then the corrent PID control is put up so that the aim-moment can be track fastly. The simulation results show that the strategy is more effective in improving the tracing ability and stability of EPS.

In this article, a robust nonlinear torque control method using the steering wheel torque (SWT) model is proposed for electric power steering (EPS) systems. We develop an EPS model using SWT as the state variable to directly control the SWT. A robust nonlinear torque control method is designed to improve the SWT control performance of EPS. The proposed method consists of an extended state observer and a nonlinear sliding mode control (SMC) method. The extended state observer is designed to estimate the lumped disturbance, which includes modeling errors and external disturbances for robustness. The SMC is designed to track the desired SWT and suppress the estimation error. The nonlinear gain is proposed for reducing the chattering in the SMC. The proposed method is designed based on the SWT model; thus, it can improve the torque control performance while remaining robust to parameter uncertainty and external disturbances. The performance of the proposed method is validated via experiments using a pinion type EPS hardware-in-the-loop simulation.

The finite element model (FEM) for induction motors (IM) was developed and validated through experimental testing. The validated FEM provides a reliable basis for further optimization of the electric machine. A strong sliding mode technique, in conjunction with field-oriented control (FOC), is proposed for speed control of the IM. The sliding mode controller ensures steady functioning in the face of ambiguities and disruptions, while FOC enables precise control of the motor’s magnetic field. This combination enhances both the efficiency and accuracy of speed control in IM, making it a valuable tool for industrial applications. The proposed sliding mode control (SMC) was fine-tuned using the advantages produced by the ant colony optimization algorithm. This approach aids in resolving issues and delivers optimal speed and field responses. Simulation and experimental results demonstrate the effectiveness of the proposed approach. The optimized induction motor achieved a 28% reduction in rotor Joule losses, resulting in improved energy efficiency. Additionally, using Ant Colony Optimization to adjust the SMC parameters led to a 99.74% reduction in speed tracking error and a 99.59% reduction in flux error compared to traditional manual tuning. These substantial improvements confirm the superiority of the proposed method for high-performance and energy-efficient electric vehicle applications.

Vertical Take-Off and Landing (VTOL) aircraft excel in their ability to maneuver in limited spaces, making them ideal for a variety of uses including urban air mobility, emergency response, and disaster surveillance. Their agility and quick deployment features are especially valuable for executing complex missions in challenging environments. This paper addresses this issue by proposing a dual-loop sliding mode control (SMC) strategy optimized for VTOL models. However, tracking errors in the inner loop can impact the performance of the outer loop, complicating the assessment of the inner loop's convergence speed to meet the outer loop's criteria, and thus hindering the achievement of absolute stability in both control loops. To tackle this issue, the paper leverages the global asymptotic stability theorem for dynamic systems and develops a closed-loop system with global Lipschitz continuity, guaranteeing robust stability across both loops. This method not only bolsters the system's dependability but also enhances its flexibility to operate effectively under complex dynamic conditions, thereby increasing the overall resilience and performance of the VTOL control systems. The implementation of the sliding mode control strategy in VTOL models significantly enhances operational stability and reduces tracking errors in complex environments. Numerical simulations demonstrate that our approach reliably improves both performance and adaptability of the system under varying dynamic conditions.

The Electric power steering (EPS) system, a typical non-linear system, is easy to be influenced by parameters perturbation and disturbance of the road. Traditional linear control method based on a simplified linear model such as PID control cannot reach good dynamic performance. To reduce the influence of parameters perturbation and disturbance of the road and enhance the robustness of the system, an Adaptive fuzzy sliding mode control (AFSMC) method is proposed in this paper. First, fuzzy sliding mode control is employed to enhance the dynamic performance of the system. Then, to improve the precision of the controller, genetic algorithm is used to optimize the control rules which are essential to fuzzy control. The experimental results on non-linear EPS model demonstrate that AFSMC is more stable than Sliding mode control (SMC) method and more efficient to the non-linear system than SFPID control method. They can also prove that AFSMC can provide a stable driving in the presence of parameters perturbation and disturbance of the road.

Sliding mode controller is a widely known robust controller, providing outstanding control performances especially in disturbance rejection. However, the chattering phenomenon that induced undesired vibration often constrained the applicability and control performance of sliding mode controller. This undesirable vibration is caused by high frequency switching, originating from signum function in mathematical formulation of the controller. This paper proposes a smoothening method in designing the sliding mode controller to reduce the chattering effect induced by the signum function. The proposed smoothening method modified and replaced the original signum function in control laws of sliding mode controller using three respective smoothening functions, namely; hyperbolic tangent function, Langevin function, and Gauss error function. The control performances of proposed algorithms in terms of tracking error reduction and chattering suppression were compared with original sliding mode controller and the popular pseudo-sliding mode controller. Simulated results showed that Langevin function is superior in both tracking error reduction and chattering suppression (94.3%). Both Gauss error function and hyperbolic tangent function able to compensate chattering but with tradeoff in tracking error reduction.

To improve the control precision of nonlinear spacecraft formation flying, the input–output linearization minimum sliding-mode error feedback controller is presented based on the linear-decoupled spacecraft formation model by input–output linearization method incorporating the sliding-mode control. This paper proposes a new strategy to estimate and offset the system-control errors, which include various kinds of uncertainties and disturbances. To facilitate the analysis, the linear-decoupled spacecraft formation model is first given; on which basis, the concept of equivalent control error is introduced to define the entire model error. Based on the minimum sliding-mode covariance constraint, a cost function is formulated to estimate the equivalent control error and fed back to the conventional sliding-mode control. It is shown that the sliding mode after the input–output linearization minimum sliding-mode error feedback controller will approximate to the ideal sliding mode with high-control precision. In addition, the new methodology is applied to spacecraft formation flying. It guarantees global asymptotic convergence of the relative-tracking error in the presence of the large perturbations. More exactly, the two input–output linearization minimum sliding-mode error feedback controller laws (continuous sliding-mode control and nonsingular terminal sliding-mode control) are developed for this spacecraft formation flying system. Several fault-tolerant scenarios are considered to verify that the input–output linearization minimum sliding-mode error feedback controller is still effective in the presence of faults in spacecraft thrusters. Numerical simulations are performed to demonstrate the efficacy of the proposed methodology to maintain and reconfigure the spacecraft formation with existence of initial offsets and large perturbations effects.