This paper considers fuzzy logic and proportional integral derivative based multi-objective optimization of a non-linear active suspension system of a 4 × 4 in-wheel motor-driven electric vehicle by using the non-dominated sorting genetic algorithm II. The active suspension system of the electric vehicle and its controllers are optimized to achieve International Organization for Standardization2631-1 ride comfort and health criteria, also providing the actual working conditions such as roll angle and tire load transfers simultaneously for driving safety. In this regard, a non-linear full electrical vehicle model with quadratic tire and cubic suspension stiffnesses with 11 degrees of freedom and a seat-driver model with 5 degrees of freedom are implemented and optimized regarding seven objective functions determined from the root mean square of head and seat accelerations, crest factor , vibration dose value , the ratio of head and seat accelerations, the ratio of the upper torso and seat acceleration, root mean square upper torso acceleration, and root mean square of suspension, tire, and in-wheel motor displacements. The design variables of the optimization problem are chosen as the stiffnesses and damping coefficients of the suspension, in-wheel motors, and seat, as well as the parameters of the proportional derivative and fuzzy logic controllers. The obtained results demonstrate that significant improvements can be achieved by using a controller over the passive systems. It is also noted that the fuzzy logic controller improves ride comfort and the health criterion over proportional derivative system up to 13%, while the load transfer ratio index showed no adverse change between models concerning the rollover condition. The outcomes of this work clearly state that significant improvements, in terms of vibration exposure, can be achieved with the help of reducing the vibration amplitude of an in-wheel motor-driven electrical vehicle active suspension system by using multi-objective optimization considering a non-linear full vehicle model and realistic working conditions such as tire load transfer and vehicle body roll during cornering circumstances. Thus, obtained results are of utmost importance for manufacturers about the active suspension design process providing both a safe and comfortable driving of in-wheel driven electric vehicles.

Fuzzy logic and proportional integral derivative based multi-objective optimization of active suspension system of a 4×4 in-wheel motor driven electrical vehicle

This article studies the Takagi-Sugeno (T-S) fuzzy delayed sampled-data $$\mathcal {H}_\infty $$
 control problem for a class of intelligent suspension systems with varying vehicle load and frequency-domain constraint. The T-S fuzzy model is utilized to characterize the varying vehicle load. Considering the transmission delay, a robust fuzzy delayed sampled-data control mechanism is newly propounded for suspension systems. According to the Lyapunov stability theory, a useful theorem is proposed based on the Wirtinger inequality to guarantee the states of the active suspension system being asymptotically stabilized with the required $$\mathcal {H}_\infty $$
 performance by the proposed controller. Moreover, the suspension constrained requirements are also satisfied within the finite frequency domain. Finally, simulation examples are presented to attest to the usefulness and superiority of the proposed controller.

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Robust fuzzy delayed sampled-data control for nonlinear active suspension systems with varying vehicle load and frequency-domain constraint

This paper provides a systematic method to design robust tracking controllers of reference signals with bounded derivatives of order ν for uncertain multi‐input multi‐output (MIMO) systems...

Robust tracking design for uncertain MIMO systems using proportional–integral controller of order v

Energy harvesting shock absorbers (EHSA) have made great progress in recent years, although there are still no commercial solutions for this technology. This paper addresses the question of whether, and under what conditions, an EHSA can completely replace a conventional one. In this way, any conventional suspension could be replicated at will, while recovering part of the wasted energy. This paper focuses on mimicking the original passive damper behavior by continuously varying the electrical parameters of the regenerative damper. For this study, a typical ball-screw EHSA is chosen, and its equivalent suspension parameters are tried to be matched to the initial damper. The methodology proposes several electrical control circuits that optimize the dynamic behavior of the regenerative damper from the continuous variation of a load resistance. The results show that, given a target damper curve, the regenerative damper can adequately replicate it when there is a minimum velocity in the damper. However, when the damper velocity is close to zero, the only way to compensate for inertia is through the introduction of external energy to the system.

https://www.mdpi.com/1424-8220/21/13/4378/pdf

Can a Semi-Active Energy Harvesting Shock Absorber Mimic a Given Vehicle Passive Suspension?

This paper presents an optimal proportional-integral-derivative-accelerated (PIDA) controller design for a quarter car suspension system to improve the ride comfort and road handling. Based on the modern optimization, the proposed PIDA controller design framework is based on the intensified current search (ICuS) optimization which is one of the most efficient trajectory-based metaheuristic optimization techniques. By comparison, a passive quarter car suspension system controlled by the PID and PIDA controllers optimized by the ICuS are tested against four different road profiles, i.e. bumpy road, pothole road, ramp road and random road. As results, the PIDA controller can provide very satisfactory responses with smoother and faster than the PID controller, significantly.

Optimal PIDA Controller Design for Quarter Car Suspension System by Intensified Current Search

Background, Modelling and Problem Statements of Active Suspensions -- Constrained H∞ Control for Active Suspensions -- Finite Frequency H∞ Control for Active Suspensions -- Constrained Active Suspension Control via Nonlinear Feedback Technology -- Actuator Saturation Control for Active Suspension Systems -- Active Suspension Control with the Unideal Actuators -- Active Suspensions Control with Actuator Dynamics -- Energy Saving Control Strategies: Motor-driven Active Suspension.

Advanced Control for Vehicle Active Suspension Systems

In the previous chapters, the dynamic process of the actuator is neglected by us. In this chapter, we mainly look at actuator dynamics when designing control scheme, and electro-hydraulic systems are typically chosen as the actuators. However, the main drawback of electro-hydraulic systems is their highly non-linear behavior. In addition, there exists model uncertainties when establishing the mathematical model. All these factors make it difficult to design the controller and influence the effectiveness of active force tracking.

Active Suspensions Control with Actuator Dynamics

Actuator saturation is very common in an actual control system, and has proved a source of performance degradation and even instability. In practice, it is not always possible to ensure that all signals are small, particularly for high-performance application, and meantime, actuators which deliver the control signal in physical applications are always subject to the magnitude or rate limits. This chapter provides some control strategies about saturation problems.

Actuator Saturation Control for Active Suspension Systems

One of the disadvantages of the active suspension is its high energy consumption, which limits its application. To overcome this problem, in recent years, researchers pay much attention to reducing energy consumption of active suspensions to make active suspensions widely used, and there are many remarkable results. A great deal of energy is dissipated in the form of heat through the viscous damper and the actuator. In other words, most of the vibration energy excited by road is transferred into useless heat energy. If we can recycle vibration energy excited by the uneven road in some way, it is attainable to consume less energy, even to achieve a self-powered suspension. So energy saving control strategies of active suspensions is a research field worth studying.

Energy Saving Control Strategies: Motor-Driven Active Suspension

In this chapter, the background knowledge of the suspension systems is demonstrated. We mainly introduce three categories of suspension systems: two degree-of-freedom (DOF) quarter-car model, four DOF half-car model, and seven DOF full-vehicle model, whose mathematical models are established. The road excitement model is given in time domain and in the form of spectrum as well. In addition, control objectives of active suspension systems are illustrated.

Weichao Sun

Papers

Advanced Control for Vehicle Active Suspension Systems

Active Suspensions Control with Actuator Dynamics

Actuator Saturation Control for Active Suspension Systems

Energy Saving Control Strategies: Motor-Driven Active Suspension

Background, Modelling and Problem Statements of Active Suspensions