# Comparative Analysis of Different Model-Based Controllers Using Active Vehicle Suspension System  
[PERSON] and [PERSON]  
1 College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; [EMAIL_ADDRESS]  
Footnote 1: email: [EMAIL_ADDRESS]  
deflection [7]. An additional benefit of the active suspension is that unlike passive and semi-active suspension systems, it gives dynamic compensation [8]. Active control forces can be implemented by hydraulic, pneumatic or electromagnetic actuators commonly located in parallel with a spring and a damper [9]. Pneumatic actuators are simple, which is their greatest advantage. Hydraulic actuators are well known for their performance in high-power applications. In contrast to hydraulic and pneumatic, accuracy is always much higher in electromagnetic [10]. A new cascade control approach to the active suspension of forest machines using pneumatic actuators and parallel mechanical structure is proposed in [11]. However practically, the force of suspension cannot act directly as the suspension system, thus the suspension force is applied using the hydraulic actuator dynamics in [12]. The electromagnetic actuator replaces the damper and the hydraulic actuator, forming with the spring an oil-free suspension in [13]. A modified energy-saving skyhook for active suspension based on a hybrid electromagnetic actuator is developed in [14]. An active vehicle suspension control approach with electromagnetic and hydraulic actuators is presented in [15]. It is well known that an active damping suspension is an efficient way to enhance the suspension performance and has arduously studied [16]. Various active control strategies are presented based on control methods to improve ride performance. The more effective the control strategy, the better the performance will be. Thus, the selection of control approach for suspension has major impact on the system efficiency. PID controllers are not well suitable as they are incompetent of handling built-in uncertainties [17]. Also, the system robustness reduces with structural uncertainties, so adjusting the gains of PID control law is challenging issue [18]. Many studies concerning active control strategies have been presented during last decades, such as fuzzy logic control [19], \(H_{\infty}\) control [20], and backstepping and control [21]. To attain high level of precision, robust control laws are required. Thus, it draws special attention to more advanced active control strategies, for example FOSMC, ISMC, and HOSMC with variant algorithms that can offer an efficient systematic approach to monitor the desired trajectories accurately [22]. LQR is entirely a linear control method whereas FOSMC is a robust control strategy for handling complex systems. Terminal sliding mode control and ISMC are robust techniques of control system, but there is always a discrepancy between the mathematical and physical model, due to mismatched disturbances that cause disparities in the physical model [23; 24; 25]. It is well known that FOSMC is insensitive to parameter variations and external disturbances. Whereas, HOSMC is robust against system structure changeability unlike other active control strategies. It reduces harmful oscillation to its maximum level [26]. Hence, HOSMC has all the qualities of SMC and it provides the sliding variable and its derivatives a finite time convergence [27]. Furthermore, the STA algorithm offers finite time stabilization for all the states [28]. In this paper, mathematical model of active suspension system and active model-based dynamic control approaches, i.e., SMC, ISMC, HOSMC are presented. This study deals with theoretical, qualitative and quantitative analysis. The performance of SMC, ISMC and HOSMC are compared with each other, and with conventional LQR, PID, and passive suspension system by using road profile with bump and pothole.