# Hybrid Particle Swarm Optimization Genetic LQR Controller for Active Suspension
## 5 Conclusions  
This paper mainly discusses an improved optimization of the LQR control method that adapts the hybrid particle swarm optimization and genetic algorithm for active suspension. The controller for the active suspension is crucial for effectively improving the performance in the ride comfort and handling stability of active suspension systems. However, there are unavoidable flaws, in which weight coefficients of matrix Q and matrix R are determined by experience in the tradtional LQR control method for an active suspension that cannot obtain the optimal result. Hence, the traditional LQR controller for active suspension is imprecise and unperfect. Based on these shortcomings, in this paper, an improved optimization LQR control method that adapts the hybrid particle swarm optimization and genetic algorithm is presented, and then this controller is applied to the active suspension to overcome these limitations.  
The quarter car suspension model and road input model are considered at first. Then, the hybrid controller is conducted. After that, a simulation is conducted within a Matlab Simulink environment. Finally, the performance of the proposed controller in this paper is compared with the passive suspension and active suspension under the traditional LQR control. Moreover, a full-order state observer is designed to feedback on the state of the suspension system.  
The simulation based on the random road input model, quarter car suspension model, passive suspension, LQR controller, and optimization controller is conducted. From the simulation results, it is confirmed that the sprung mass vibration and deflection are well reduced, which are regarded as important characteristics to evaluate the performance of ride comfort. The tire dynamic load used to evaluate the performance of the road holding is restrained.  
Thus, all of the above simulation results provide a foundation, with which the control method proposed in this paper can significantly improve the performance of ride comfort and road holding stability. On the one hand, the proposed hybrid control algorithm in this paper can overcome the limitation of the traditional LQR controller for active suspension. On the other hand, the proposed controller is efficient and very promising in order to guarantee the performance of the active suspension.  
Moreover, this paper also applies the full-order state observer to monitor the state of the active suspension system. The simulation results indicate that the observer can effectively reflect the true state of the active suspension system.  
The experimental validation is an important part of the conducted research and is better for revealing the application in real suspension systems. However, our current study is limited in experimental conditions, and relevant research could not help to conduct the experiments. Thus, our future research will focus more on the experimental validation of controllers and mainly include the following points. First, we hope to apply the proposed control method to the nonlinear active suspension, which is more precise for a real suspension model. Second, we hope to establish an adaptive controller for a full car active suspension dynamic model and apply it to real suspension.  
Methodology, W.Z.; Writing--original draft, W.Z.; Writing--review & editing, L.G.; Supervision, L.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The authors appreciate the support from [PERSON] and the editor and the reviewers for their constructive comments. The authors declare no conflict of interest.