Semi-active Suspension Control Research Articles

Tuning Parameters of the Fractional Order PID-LQR Controller for Semi-Active Suspension

In order to further improve the control effect of proportion integral differential (PID) control and linear quadratic regulator (LQC) control, and improve vehicle ride comfort and enhance body stability, the 7 DOF semi-active suspension model was established, and the fractional order PIλDμ-LQR controller was designed by combining fractional order PIλDμ control theory and LQR control theory. The semi-active suspension model in this paper is more complex, and there are many parameters in the controller. The optimal weighting coefficient of 12 vehicle smoothness evaluation indicators and parameters Kp, Ki, Kd, λ and μ in the controller were founded by NSGA-II algorithm. After optimization, the optimized parameters were brought into the controller for random pavement simulation. Compared to the traditional passive suspension, fractional order PIλDμ individual control and LQR separate control, the simulation results show that the effect of fractional order PIλDμ-LQR control is very significant. The evaluation index of vehicle smoothness has been significantly improved, and the use of fractional order PIλDμ-LQR control has significantly improved the working performance of the suspension and improved the smoothness of the vehicle. At the same time, the adjusting force output of the actuator is very balanced, which inhibits the roll of the body and improves the anti-roll performance. After simulation, the excellent performance of the designed fractional PIλDμ-LQR controller was verified, and the introduced NSGA-II algorithm played an important role in the controller parameter tuning work, which shows that the fractional order PIλDμ-LQR controller and NSGA-II algorithm cooperate with each other to achieve good control effects.

Nonlinear dynamic modeling and analysis of magnetorheological semi-active suspension for tracked vehicles

The magnetorheological technology has been widely used in automotive applications, whereas less research has been done on tracked vehicles. Hence, this research focuses on the dynamic modeling of the whole system of a tracked vehicle, for analyzing the effect of magnetorheological semi-active suspension on track tension and chassis vibration during driving. Applying the multibody system transfer matrix method and a dynamic recursive method, the dynamic models of the chassis subsystem and the double track subsystems are developed, respectively. These three subsystems are coupled by nonlinear contact forces, where the meshing shock, polygon effect, and rolling effect during contact are also taken into consideration. Subsequently, the normalized Bouc-Wen model is adopted to describe the nonlinear characteristics of rotary magnetorheological dampers. Then, a semi-active suspension control of the tracked vehicle is implemented with rotary magnetorheological dampers and the independent skyhook control method. Finally, numerical simulations are performed under different operating conditions. Comparing with the case of passive suspension, it reveals that, the magnetorheological semi-active suspension not only improves the distribution of the track tension but also effectively reduces the chassis vibration. It provides a theoretical basis for the design and application of magnetorheological semi-active suspensions for tracked vehicles.

Semi-active Suspension Control with PSO Tuned LQR Controller Based on MR Damper

As the Linear Quadratic Regulator (LQR) approach is applied extensively in the system control of automobile suspension, the accuracy improvement of the weighting Q and R matrices is getting concern. The Particle Swarm Optimization (PSO) algorithm is being introduced to identify parameters and optimize matrix Q and R in order to fix the insufficiency of these experienced values because of the fast convergence and a more accurate solution. In this article, a quarter car model and a Bouc-Wen-based magnetorheological (MR) damper model are developed to combine the control of PSO identification and PSO-LQR controller in the semi-active suspension system. The MR damper was performed with an experimental test for running identification using experimental data as input into the Bouc-Wen model to obtain six unknown parameters, where the parameters were estimated with the PSO algorithm. Since the numerical model has been done with all parameters clear, the need for damping force from suspension is obtained by means of running the model using an input current. In the employment of PSO for damper model and vehicle control, the dual applications succeeded in verifying the feasibility of parameter identification in the MR damper and successfully tuned the LQR controller in the semi-active suspension, which decreases the vehicle body acceleration and displacement so that the improvement of ride comfort and drive stability achieved.

Optimal Control of Semi-Active Suspension for Agricultural Tractors Using Linear Quadratic Gaussian Control.

In this study, a semi-active suspension based on a hydro-pneumatic mechanism was designed to minimize the ride vibration using a suspension control algorithm. The performance of the algorithm was critical for controlling the characteristics of the target tractor. A linear-quadratic-Gaussian (LQG) optimal control algorithm was designed as a semi-active suspension control algorithm. The plant model for developing this algorithm was based on the parameters of an actual tractor. The rear suspension deflection was represented by a Kalman-filter-based state observer feedback to estimate the state variables that were difficult to measure. The designed state observer of the LQG controller was validated in terms of an accuracy index. The estimated vertical velocity and acceleration accuracies of the cabin were 83% and 79%, respectively. The performance of the designed controller was validated in terms of a performance index by comparing the performance of a tractor equipped with a rear rubber mount with that of one equipped with a semi-active suspension. The peak and root-mean-square values of the vertical acceleration of the cabin were reduced by up to 48.97% and 47.06%, respectively. This study could serve as a basis for the application of the control algorithm to systems with similar characteristics, thereby reducing system costs.

Model predictive control of a semi-active suspension with a shift delay compensation using preview road information

This paper presents a model predictive control of a semi-active suspension with a shift delay compensation using preview road information. A Model Predictive Control (MPC) methodology has been developed to optimize both ride comfort and road handling performance, where suspension states have been estimated through a model-based Kalman filter. The use of MPC in semi-active suspension control has proven to be suitable due to its ability to consider constraints when optimizing the objective function. A feasible region for the control inputs into the semi-active suspension has been determined from its mechanical limitations. However, the proposed Model Predictive Controller carries a sizeable computational load. Occurrences of “shift time delays” have been observed from the vehicle’s Electronic Control Unit processing the algorithm. To combat this, a model prediction system, in which a full-car dynamic model and road preview information are utilized to predict vehicle suspension states, has been further proposed to compensate for the shift time delay. Preview road information has been obtain through the computation of relative vehicle motion and a temporal–spatial conversion. The overall algorithm has been evaluated via computer simulation studies. Simulation results have shown that the shift compensation algorithm provides considerable improvements with regards to ride comfort. A noteworthy section of this study is the successful implementation of the proposed algorithms into an actual vehicle, where the real world performance of the proposed algorithms have been assessed. It has been shown via vehicle tests that significant improvement in ride comfort can be obtained by the proposed MPC damping control.

Vibration analysis and control of semi-active suspension system based on continuous damping control shock absorber

Vibration analysis and control of semi-active suspension system based on continuous damping control shock absorber

A novel semi-active suspension algorithm based on a high-precision frequency selector

This study proposes a novel semi-active suspension control algorithm based on a high-precision frequency selector. The algorithm focuses on the phenomenon of redundant switching in frequency domain judgment. Furthermore, the working principle of realizing high-precision selection is explained. The behavior of window sample number N is analyzed theoretically, and the gray prediction theory is used, together with a formerly sampled signal, to predict and obtain advanced output. This can compromise time delay in the control strategy and improve the accuracy of the selector. Using the combined sky-hook and acceleration-driven damper control algorithm and the MIX algorithm as the benchmark, the improved frequency selector is verified under sweep road environments. The results demonstrate that the improved algorithm significantly reduces the number of switches that occur while driving the vehicle, without deteriorating the comfort, thus improving the energy efficiency and service life of the damper.

Sliding Mode Control of Vehicle Semi-active Suspension System Based on Magnetorheological Damper

Given the fact that the passive suspension of the vehicle cannot adapt to the changing road excitation and replace conventional suspension with damping-adjustable semi-active suspension, based on the 1/4 vehicle model, sliding mode controllers are designed for two different error vectors respectively, and the simulation is carried out through Matlab/Simulink. The results show that the semi-active suspension controller can effectively improve the stability and safety of the vehicle when driving.

Takagi–Sugeno Fuzzy Model-Based Control for Semi-Active Cab Suspension Equipped with an Electromagnetic Damper and an Air Spring

Variable damping shock absorbers have received extensive attention for their efficient vibration reduction performance, and air springs have also been widely used in high-end commercial vehicles due to their nonlinear stiffness characteristics. This paper presents a novel semi-active cab suspension integrated with an air spring and a variable damping electromagnetic damper (A-EMD). The electromagnetic damper (EMD) prototype was designed, manufactured and tested. Then, due to the interference of nonlinear stiffness characteristics of the air spring with the controller in the subsequent design, the Takagi–Sugeno fuzzy method was adopted to segmentally linearize its nonlinearity, based on which an H∞ state feedback semi-active controller was designed to control the EMD to generate variable damping force. Furthermore, a Luenberger state observer was designed to provide immeasurable state parameters for the controller. Numerical simulations were carried out to validate the effectiveness of the proposed approaches, and the results show that the proposed control strategy can significantly improve the ride comfort of the A-EMD system. The vibration dose value (VDV) acceleration under the bump road and the frequency-weighted acceleration root mean square (FWA-RMS) under the random road decreased by 36.05% and 19.77%, respectively, compared with the passive suspension system.

Intelligent Road-Adaptive Semi-Active Suspension and Integrated Cruise Control

The availability of road and vehicle data enables the control of road vehicles to adapt for different road irregularities. Vision-based or stored road data inform the vehicle regarding the road ahead and surface conditions. Due to these abilities, the vehicle can be controlled efficiently to deal with different road irregularities in order to improve driving comfort and stability performances. The present paper proposes an integration method for an intelligent, road-adaptive, semi-active suspension control and cruise control system. The road-adaptive, semi-active suspension controller is designed through the linear parameter-varying (LPV) method, and road adaptation is performed with a road adaptivity algorithm that considers road irregularities and vehicle velocity. The road adaptivity algorithm calculates a dedicated scheduling variable that modifies the operating mode of the LPV controller. This modification of operation mode provides a trade-off between driving comfort and vehicle stability performances. Regarding the cruise control, the velocity design of the vehicle is based on the ISO 2631-1 standard, the created database, and the look-ahead road information. For each road irregularity, the velocity of the vehicle is designed according to previous measurements and the table of ISO 2631-1 standard. The comfort level must be selected in order to calculate dedicated velocity for road irregularity. The designed velocity is tracked by the velocity-tracking controller evaluated with the LPV control framework. The designed controllers are integrated, and the operation of the integrated method is validated in a TruckSim simulation environment.

Deep Reinforcement Learning of Semi-Active Suspension Controller for Vehicle Ride Comfort

Among the controllable suspension systems, the control of the semi-active suspension is mostly based on optimal control. Recently, deep reinforcement learning is widely used as a method to solve the optimal control problem. Control strategies developed using reinforcement learning have shown performance beyond conventional control algorithms in some fields. In the current study, we have proposed a near optimal semi-active suspension ride comfort controller using deep reinforcement learning. An algorithm suitable for a semi-active suspension control environment was selected based on deep reinforcement learning theory to increase convergence in training. Furthermore, a state normalization filter was designed to improve the generalization performance. When compared with the ride comfort oriented classical control algorithms, our trained controller showed the best performance in terms of ride comfort. Policy map comparison with mixed SH-ADD (Skyhook-Acceleration Driven Damping) algorithm suggested the direction to the design of the semi-active suspension control algorithm.

A novel preview control for MLD models and its neural network approximation for real‐time implementation: Application to semi‐active vibration control of a vehicle suspension

Advances in image processing technology have made it possible to measure the surface shape of the road ahead while driving. A new semi-active suspension control method considering the forward road surface shape is proposed. A vehicle model equipped with a semi-active suspension can be expressed as an mixed logical dynamical model. When the shape of the road ahead can be measured, the information on future disturbances is available before the vehicle undergoes. In this paper, the finite time optimization problem for the mixed logical dynamical model is formulated to consider the future disturbances as a mixed integer quadratic programming problem in the same way as the conventional control problem without future disturbance. However, the mixed integer quadratic programming problem is hard to obtain the control action within the control cycle period required in the real-time vibration control with general computers for vehicles. In this paper, the reduction of the computational load is achieved by constructing an approximation function of the designed controller. A neural network is adopted for the approximation. The performance evaluation of the proposed method is evaluated by simulations. In the simulation study, the proposed method achieves better ride comfort with the equivalent suspension stroke compared to the traditional methods.

Implementation of semi-active suspension control methods in a full car model and a comparative study in terms of ride comfort and road holding

Semi-active suspension systems are becoming increasingly common in the automotive industry due to their low energy consumption and cost advantages. A significant milestone in semi-active suspension control is the emergence of the skyhook control method. Then, the active driven damper method was introduced to bring the semi-active control closer to the optimum limit of the system. Later, power driven damper was introduced to reduce the jerk of the active driven damper and skyhook. The active and power-driven damper are mixed with skyhook control to be optimal throughout the entire frequency range. However, the methods mentioned above have been developed using the quarter car model, and no comparative studies have been found on the full car model effectiveness and the application of the methods, realistically. In this study, the above methods, which have been used in the literature, frequently, were compared first, on the quarter car model to reveal the system response characteristics. Then, a curved regular grid road profile and a high-fidelity full car model were used to compare the centralised skyhook continuous and four quarter car approaches.

On an enhanced back propagation neural network control of vehicle semi-active suspension with a magnetorheological damper

To improve the ride quality of a vehicle, an enhanced vibration control method is presented for semi-active suspension (SAS) with magnetorheological (MR) damper by combining back propagation neural network (BPNN) and particle swarm optimization (PSO). Based on the test data of MR damper, a non-parametric model of MR damper using adaptive neuro-fuzzy inference system (ANFIS) is first established, and based on that, a dynamics model of the SAS system is derived. Next, a BPNN controller is designed to fulfill the effective control of the current in MR damper. Meanwhile, the improved PSO with adaptive weight and dynamic acceleration constant is introduced to optimize the weights and thresholds of the BPNN controller, which can avoid the designed BPNN falling into the local optimum and then improve the convergence rate of the designed controller. Besides, the stability of the developed controller is analyzed via Lyapunov stability theory. Different from the existing models and methods, the established model can well describe the dynamics behaviors of the actual MR damper, and the proposed control method has better adaptability, convergence speed and precision. Finally, a simulative investigation is performed to validate the effectiveness and feasibility of the proposed controller, compared to existing BP-PID control and the passive suspension, the vehicle acceleration of SAS with this proposed controller is respectively improved by 10% and 30%.

Initial Pitch Control for Semi-active Suspension System

Initial Pitch Control for Semi-active Suspension System

A study on a vehicle semi-active suspension control system based on road elevation identification.

A semi-active suspension system can effectively improve vehicle ride comfort and handling stability, and the active detection of road information is key to achieving semi-active suspension. To improve the road elevation perception ability of vehicles, this study proposes a continuous multiple scanning recursive matching algorithm based on a single-line LIDAR sensor. Radar recursive scanning is used to obtain the multiple superposition data of echo signals, and coordinate matching is realized between historical scanning data and current scanning data. Simultaneously, the sensor height deviation and pitch angle deviation of the sensors are regressed to obtain an accurate pavement elevation. Considering the control effect of the active vehicle suspension, a vehicle suspension model with seven degrees of freedom is established. The semi-active suspension controller is constructed using a diagonal recursive neural network algorithm, and the neural network weight is trained using a genetic algorithm. In addition, a preview diagonal recursive neural network control strategy for semi-active suspension, based on the combination of road elevation information, is proposed. The results of a hardware-in-the-loop co-simulation, which was conducted based on the Simulink control model and dSPACE real-time simulation, revealed that the ride comfort and stability of the vehicle were improved owing to a preview of the elevation information of the road ahead and the active adjustment of the shock absorber of the suspension system.

An LPV-Based Online Reconfigurable Adaptive Semi-Active Suspension Control with MR Damper

This study introduces an online reconfigurable road-adaptive semi-active suspension controller that reaches the performance objectives with satisfying the dissipativity constraint. The concept of the model is based on a nonlinear static model of the semi-active Magnetorheological (MR) damper with considering the bi-viscous and hysteretic behaviors of the damper. The input saturation problem has been solved by using the proposed method in the literature that allows the integration of the saturation actuator in the initial system to create a Linear Parameter Varying (LPV) system. The control input meets the saturation constraint; therewith, the dissipativity constraint is fulfilled. The online reconfiguration and adaptivity problem is solved by using an external scheduling variable that allows the trade-off between driving comfort and road holding/stability. The control design is based on the LPV framework. The proposed adaptive semi-active suspension controller is compared to passive suspension and Bingham model with Simulink simulation, and then the adaptivity of the controller is validated with the TruckSim environment. The results show that the proposed LPV controller has better performance results than the controlled Bingham and passive semi-active suspension model.

Experimental study of road identification by LSTM with application to adaptive suspension damping control

Road unevenness provides essential evidence for semi-active suspension control while it is difficult to estimate accurately in real time. This paper proposes a real-time method of identifying road unevenness with serial acceleration signals and unevenness-correlated adaptive suspension damping control. This new method uses Long Short-Term Memory (LSTM) network to identify the characteristics of the time domain signal and classify it into different unevenness classes. A proving ground experiment is designed and conducted to construct and validate the algorithm. The good estimation accuracy and robustness is realized at different vehicle velocities and suspension damping levels. Based on this real-time estimated road unevenness, the developed suspension controller can be enhanced by adaptive correlation of the comfort weight and adaptive damping coefficient with corresponding road unevenness. A calibration experiment is conducted to provide evidence for comfort weight selection. The validation experiment result proves that the adaptive damping control could substantially reduce RMS of body acceleration on different kinds of roads, demonstrating the effectiveness of the proposed new method.

Energy-Regenerative Semiactive Lateral Suspension Control in High-Speed Trains Using Electromagnetic Damper Cum Energy Harvester

With the increasing speeds of high-speed trains (HSTs), advanced suspension design are necessary to guarantee riding comfort and energy efficiency. In this study, a novel energy-regenerative semiactive secondary suspension system of HSTs and the corresponding control strategy, which have not been reported in the literature, were developed using the emerging electromagnetic damper cum energy harvester (EMDEH) with both vibration control and energy harvesting functions. The developed EMDEH can provide continuously tunable damping coefficients by semiactively controlling the duty cycle of an energy harvesting circuit. The mechanical behavior and energy performance of a full-scale EMDEH prototype were experimentally characterized via cyclic tests. An EMDEH simulation model was developed and verified through comparison with experimental results. A semiactive control strategy was designed to track the target force generated by a Linear–Quadratic–Gaussian (LQG) controller. Numerical simulations revealed that the semiactive EMDEH (SEMDEH) could reduce the car body vibration more effectively than the traditional passive dampers and fixed-duty-cycle EMDEH (FEMDEH) at train speeds of 200–350 km/h. Moreover, although the FEMDEH generated a greater power than the SEMDEH in the aforementioned train speed range, the SEMDEH could still generate powers of 25.89–153.19 W.

Research on time-delay-dependent H∞/H2 optimal control of magnetorheological semi-active suspension with response delay

Considering the influence of the magnetorheological damper response time delay on the low-frequency vibration (body vibration) and multi-objective control requirements of the semi-active suspension system, a novel H∞/H2 controller (time-delay-dependent H∞/H2 optimal controller) is proposed in this paper. Based on the Lyapunov–Krasovskii function and robust control theory, a time-delay-dependent H∞/H2 controller in consideration of the MR damper response time delay is designed to reduce and remove the effects of time delay on the semi-active suspension system. To obtain better suspension control performances, the optimal selection strategy of anti-interference coefficients in the time-delay-dependent H∞/H2 controller is proposed. Then, the time-delay-dependent H∞/H2 optimal controller is structured built on the optimal selection strategy. With the application of matrix properties and the cone-compensation linearization algorithm, the nonlinear matrix inequality for controller design is linearized, and the feedback gain matrix of the controller is solved iteratively. Finally, comparative simulation and experimental research are conducted to verify the effectiveness and superiority of the designed optimal controller.