# Optimal Sliding Mode Control for an Active Suspension System Based on a Genetic Algorithm
## 1 Introduction  
The suspension system is one of the most important parts of the vehicles, which can reduce the impact loads from the road to improve the automotive ride comfort and stability. Compared with the passive and semi-active suspension systems, the active suspension system can supply energy from an external source and generate force to achieve the desired performance [1]. The active suspension system is widely used in vehicles because of its outstanding control characteristic and performance. The performance indicators for the vehicle suspension mainly consist of the ride comfort, suspension deflection, and road holding; however, these three indexes usually conflict with each other. For instance, improving the ride comfort leads to the increase of the suspension deflection and the decrease of the tire road holding [2]. As a result, it is essential to find an appropriate control strategy for the active suspension system to balance the relationships among the above three performance indexes effectively. [PERSON] [3] proposed the minimum time controller design using singular perturbation method for a quarter car active suspension system. [PERSON] [4] proposed a new design method of fractional skyhook damping control for full-car suspension based on the principle of modal coordinate transformation. [PERSON] [5] presented a novel control strategy for a nonlinear uncertain vehicle active suspension system without using any function approximators. [PERSON] [6] designed a robust predictive control for a nonlinear active suspension system. [PERSON] [7] introduced the self-tuned robust fractional order fuzzy PD (proportion and differential) controller for uncertain and nonlinear active suspension system, but their tuning method requires human experience to construct the fuzzy rules [8]. [PERSON] [9] proposed the linear quadratic regulator (LQR) and fuzzy logic controller for activesuspension system, however, the SMC can remove the chattering which had been the main defect of the LQR control [10]. SMC is gradually applied in control fields, which has the advantages of good robustness to external disturbance and fast dynamic response, etc. [PERSON] [11] applied the adaptive sliding mode controller on the experimental validation for electro-pneumatic system. [PERSON] [12] presented the adaptive super twisting extended state observer-based sliding mode control for diesel engine air path subject to matched and unmatched disturbance. [PERSON] [13] put forward the robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input. [PERSON] [14] designed a sliding mode controller for MIMO (multi-input-multi-out) nonlinear systems so as to improve control performance. [PERSON] [15] presented the high order sliding mode control for active suspensions, which attenuates chattering effectively while preserving its robustness. However, it adds complexity to the calculations [16]. The switching function and control law are the critical parts of the sliding mode control according to the principles of variable-structure control [17]. Actually, these two parts determine the extent of chattering and the control effect of the SMC controller. Some scholars have applied the SMC on the control of various systems. [PERSON] [18] presented the adaptive neural network sliding mode control of shipboard container cranes considering actuator backlash. [PERSON] [19] proposed a sliding mode controller for active suspension system with data acquisition delay. [PERSON] [20] used the fractional order sliding mode controller to solve the vibration problem of full car active suspension system. [PERSON] [21] designed a robust sliding mode controller of a DC/DC boost converter (DC--direct current) with switching frequency regulation. However, most of the scholars only provided the range of values for parameters of the switching function and control law, and the final values of which are given straight away without any explanations and selection methods.