Simulation-based comparison of robust control and deep reinforcement learning control techniques for active suspension systems

Solenoid Valve CDC Damper is one of mainstream commercial solutions for Active Suspension.For most of Active Suspension control strategy, CDC dampers are treated as force generator [1].For getting desirable damper force, CDC Damper performance is necessary.There are two way to describe to CDC damper performance, data lookup and model building.Because of unpredictable extensionality, Data lookup require large of experiment data to maintain accuracy that effect efficiency of lookup algorithm.CDC damper model building involve in field of mechanism, hydrodynamics and electronic.Although model building have high quality of extensionality.But complex algorithm make it hard to implement on control unit.I propose a new way, compressing CDC experiment data by fitting basic valve model.By understanding about construction of one type of Solenoid Valve CDC damper, I build basic damper model based on valve theory, then using experiment data to tune model parameter to fit experiment data.Basic damper model I build is simple and easy to implement on controller unit.

Suspension system is used to fulfil the criteria of ride comfort and road handling. In this paper, a quarter car active & semi-active suspension systems are designed using Matlab/Script software. Comparison of active & semi-active suspension systems are done using robust control theory for the control targets suspension deflection, body acceleration and body travel. H infinity controller is selected to compare the two suspensions using time domain analysis. Finally the simulation result prove the effectiveness of the active suspension system by decreasing the body acceleration & sustaining the suspension deflection and body travel outputs.

A passive suspension system is used by the automotive industry to control the motion of the vehicle. Nowadays, semiactive and active suspension systems are a requirement of commercial vehicles to improve performance characteristics and road comfort. The objective of the paper is to present a comprehensive analysis of passive, semiactive, and active suspension systems. The fuzzy logic controller is used to present the active suspension system. The characteristic of the shock absorber (damper) is non-linear and hysteresis in nature. Hence, a Magneto-rheological (MR) damper-based Bouc-Wen model is utilized to present the semiactive suspension. The comparative analysis of vehicle suspension characteristics has been carried out by using a bump road profile. The modeling of the Bouc-Wen model and quarter car system is carried out in the Simulink environment. The simulated results show that the semiactive and active suspension systems can be a better option for vehicle suspension systems to provide passengers with road comfort.

The active suspension system faces an inherent conflict between body acceleration and suspension deflection: reducing body acceleration to improve comfort often results in increased suspension deflection, while suppressing suspension deflection to enhance stability may exacerbate body vibrations. To address this issue, a nonlinear dual-objective cooperative control strategy (NCDOC) is proposed in this paper, which enhances the overall performance of the active suspension system by coordinating conflicting control terms. For body dynamics, a specialized quasi-sliding mode control method is employed, utilizing body acceleration information to reduce body acceleration and regulate body displacement. Meanwhile, for the faster-changing suspension deflection dynamics, a saturated PD sliding mode tracking control term is introduced to regulate suspension deflection and counteract disturbances in the suspension deflection. Based on Lyapunov stability theory, the finite-time convergence of the closed-loop system is proven. A comparative analysis with the nonlinear disturbance observer (NDO) method reveals that the proposed control scheme achieves excellent control performance while reducing the control input by more than 50%. The effectiveness of the designed control scheme is verified through simulations and experiments. Multiple results demonstrate that the designed controller can achieve improved active suspension performance with smaller control inputs, including reducing body acceleration by more than 40% and more effectively regulating suspension deflection.

<div class="section abstract"><div class="htmlview paragraph">The design of the conventional passive suspension has always been a compromise between vehicle handling and comfort, which led to the development of the modern active and semi active suspension systems. Amongst these, semi-active suspension has been focus of research in recent years owing to its lesser complexity and less power consumption as compared to active suspension.</div><div class="htmlview paragraph">Semi active suspension uses real time variation in damping coefficient which can be achieved by using various control strategies. It is observed from available literature that Skyhook (for better ride comfort), Groundhook (for better vehicle handling) and Hybrid are most widely used strategies. These strategies use ‘On-Off’ control strategy (i.e. two preset values of damping co-efficient) but a better control over damping coefficients can be achieved using Continuous Control strategy. This paper aims to implement Continuous control strategy using Fuzzy logic for the semi active suspension. For the analysis, Two degree of freedom Quarter car model is used which is excited by three road profiles namely Bump, Sine Wave and Swept Sine wave. Comparison is done on the basis of vehicle parameters: Body displacement, Wheel displacement, Suspension working space and Dynamic tire deflection. Also frequency response of system is analysed using Fast Fourier Transform. Simulation is done using MATLAB SIMULINK and results of ‘Continuous control strategy’ are compared with the results of ‘On-Off control strategy’ and ‘Passive suspension’. Continuous control strategy using Fuzzy Logic control was found to provide better overall performance with 22.1% reduction in body displacement, 11.66% reduction in dynamic tire deflection and 31.77% reduction in suspension working space. Also Fuzzy logic control retained its stability over whole frequency range.</div></div>

To improve the performance of the magnetorheological (MR) semi-active suspension system, a fractional-order sliding mode control (FOSMC) strategy is proposed to address the nonlinear problems caused by the external disturbances and changes in parameters of system. Firstly, The MR damper designed by the research team is applied to the vehicle’s MR semi-active suspension, and a one-fourth semi-active suspension dynamic model is established. Mechanical performance tests of the MR damper are conducted through tensile experiments, confirming its satisfactory mechanical characteristics and suitability for meeting the output damping force requirements of the vehicle’s semi-active suspension. To accurately convert the computed control force into the MR damper’s control current, an adaptive neuro-fuzzy inference system (ANFIS) inverse model of the MR damper is constructed. Comparative data analysis demonstrates the inverse model’s high accuracy and its ability to effectively meet the controller’s requirements. The proposed FOSMC strategy effectively reduces the chattering phenomenon associated with sliding mode control, leading to improved vibration-damping performance of the suspension. Subsequently, a simulation model and experimental platform are utilized to evaluate the performance of the proposed controller. Experimental results indicate that the FOSMC-controlled suspension outperforms the passive suspension, achieving significant reductions in body acceleration, suspension dynamic travel, and tire dynamic displacement by 27.4%, 7.3%, and 17.39%, respectively. Similarly, the semi-active suspension controlled by sliding mode control (SMC) also shows improvements compared to the passive suspension, with reductions in body acceleration, suspension dynamic travel, and tire dynamic displacement by 20.9%, 4.3%, and 5.2%, respectively. In summary, the FOSMC-controlled MR semi-active suspension exhibits superior damping performance compared to both the passive suspension and the SMC-controlled semi-active suspension, demonstrating the effectiveness of the proposed FOSMC controller.

The optimal control design of the ground-vehicle active suspension system is presented. The active suspension system is to improve the vehicle ride comfort by isolating vibrations induced by the road profile and vehicle velocity. The vehicle suspension system is approached by a quarter car model. Dynamic equations of the system are derived by applying Newton’s second law. The control law of the active suspension system is designed using linear quadratic regulator (LQR) method. Performance evaluation is done by benchmarking the active suspension system to a passive suspension system. Both suspension systems are simulated in computer. The simulation results show that the active suspension system significantly improves the vehicle ride comfort of the passive suspension system by reducing 50.37% RMS of vertical displacement, 45.29% RMS of vertical velocity, and 1.77% RMS of vertical acceleration.

This paper presents a new approach for intelligent fuzzy logic (IFL) controller tuning via firefly algorithm (FA) and particle swarm optimization (PSO) for a semi-active (SA) suspension system using a magneto-rheological (MR) damper. The SA suspension system’s mathematical model is established based on quarter vehicles. The MR damper is used to change a conventional damper system to an intelligent damper. It contains a magnetic polarizable particle suspended in a liquid form. The Bouc–Wen model of a MR damper is used to determine the required damping force based on force–displacement and force–velocity characteristics. The performance of the IFL controller optimized by FA and PSO is investigated for control of a MR damper system. The gain scaling of the IFL controller is optimized using FA and PSO techniques in order to achieve the lowest mean square error (MSE) of the system response. The performance of the proposed controllers is then compared with an uncontrolled system in terms of body displacement, body acceleration, suspension deflection, and tire deflection. Two bump disturbance signals and sinusoidal signals are implemented into the system. The simulation results demonstrate that the PSO-tuned IFL exhibits an improvement in ride comfort and has the smallest MSE for acceleration analysis. In addition, the FA-tuned IFL has been proven better than IFL–PSO and uncontrolled systems for both road profile conditions in terms of displacement analysis.

The performance of active suspension systems is directly related to the mechanical design and control of the system. The stable operation of the controller improves driving comfort and handling. The quarter car model is frequently used in the analysis of suspension systems due to its simple structure. In this study, Matlab Simulink software was used in the modeling, control and simulation of the quarter car active suspension model. System performance was investigated for four different road profiles with PID and fuzzy logic control methods. Two of the road profiles used are in the form of impact signals consisting of pits and bumps. The other two road profiles are random road disturbances with high frequency. The effects of active and passive suspension systems on driving comfort are compared by taking into account the control methods used. As a result of the study, it has been determined that the fuzzy logic controller gives better results in pulse signals consisting of bumps and pits, and the PID controller gives better results in high-frequency random road disturbances. In addition, with the use of fuzzy logic control method in the active suspension system, a significant decrease in the actuator force has occurred. This result is very interesting in terms of minimizing energy, reducing actuator sizes and reducing costs.

The paper presents an optimization based sliding mode controller designed to provide the correct amount of force to the actuator of an active suspension system in order to guarantee ride comfort. First, the description of the mechanics of the active suspension system is provided. Then, the mathematical state space form of the quarter-car active suspension model is introduced. A Sliding Mode Control controller is designed to properly manage the active force production. The parameters of the proposed controller are tuned, relying on an optimization procedure, so as to improve the quality of the ride, in particular in terms of ride comfort, road holding and suspension deflection. First, the performance of the controlled active suspension are assessed in simulation using the formulated quarter-car mode. Then, the proposed optimized sliding mode controller is tested on an experimentally validated full-car model of a Range Rover Evoque in a Hardware-in-the-Loop (HiL) test rig available at the Automotive Engineering Department of TU Ilmenau, also comparing its performance with those obtained by using a standard PID controller. The HiL test rig is equipped with an active electromechanical suspension system. Simulation and HiL test results confirm that the proposed SMC controller provides better ride quality than the standard PID controller, which corroborates its suitableness for practical implementation.

Two methods which are computationally simple and easy to apply are developed by using state dependent Riccati equation (SDRE) approach and approximating sequence of Riccati equation (ASRE) approach to control active suspension system in the presence of nonlinear spring and damper. Additionally, effectivenesses of the both control methods developed by utilizing two recently introduced SDRE and ASRE techniques are compared. First, methodologies of both approaches are presented. After that, nonlinear dynamics of the vehicle suspension system is described in terms of conveniently selected state variables for better control performance. Then, a cost function is written by using suspension and tire deflections, sprung mass velocity and acceleration, and unsprung mass velocity variables to improve ride quality, suspension deflection, and tire deflection. Additionally, a convenient representation of this cost function in terms of state variables is obtained to realize better control. A bump expressed as sinusoidal function and roughness of the road expressed as white noise are taken into consideration as the disturbances from the road. Finally, quarter vehicle suspension system equivalent model of Ford Fiesta Mk2 is used as an example and simulations obtained by using the developed control methods are checked against the performance requirements and corresponding passive suspension system.

Vibration suppression is considered as a keyresearch field in civil engineering to ensure the safety and comfort of their occupants and users of mechanical structures. To reduce the system vibration, an effective vibration control with isolation is necessary. Vibration control techniques have classically been categorized into two areas, passive and active controls. For a long time, efforts were made to make the suspension system work optimally by optimizing its parameters, but due to the intrinsic limitations of a passive suspension system, improvements were effective only in a certain frequency range. Compared with passive suspensions, active suspensions can improve the performance of the suspension system over a wide range of frequencies. Semi-active suspensions were proposed in the early 1970s [1], and can be nearly as effective as active suspensions. When the control system fails, the semi-active suspension can still work under passive conditions. Compared with active and passive suspension systems, the semi-active suspension system combines the advantages of both active and passive suspensions because it provides better performance when compared with passive suspensions and is economical, safe and does not require either higher-power actuators or a large power supply as active suspensions do [2].

In this study, we investigate a robust H∞ controller for a quarter-car model of an active inerter-based suspension system under parameter uncertainties and road disturbance. Its main objective is to improve the inherent compromises between ride quality, handling performance, suspension stroke, and energy consumption. Inerters have been extensively used to suppress unwanted vibrations from various kinds of mechanical structures. The advantage of inerter is that the realized ratio of equivalent mass (inertance relative to the mass of the primary structure) is greater than its actual mass ratio, resulting in higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system were achieved for the quarter-car model with parameter uncertainties. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the robust H∞ criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the robust state-feedback controller. According to numerical simulations, the active inerter-based suspension system in the presence of parameter uncertainties and external disturbance performs much better than both a passive suspension with inerter and active suspension without inerter.

Several control policies of semi-active system, namely skyhook, groundhook and hybrid controls are presented using a half-car model, as a continuation of the previous work on quarter-car model. Their ride comfort, suspension displacement and road-holding performances are analysed and compared with passive system. The analysis covers both transient and steady state responses in time domain and transfer function in frequency domain. The results show that the hybrid control policy yields better comfort than a passive suspension, without reducing the road-holding quality or increasing the suspension displacement for typical passenger cars. The hybrid control policy is also shown to be a better compromise between comfort, road-holding and suspension displacement than the skyhook and groundhook control policies.

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.