# Optimal Control Method of Semi-Active Suspension System and Processor-in-the-Loop Verification
## 1 Introduction
In addition, a non-parametric model can be employed, which utilizes measured data to establish input/output relationships without requiring knowledge of the damper's internal structure. The artificial neural network (ANN) is a popular method for obtaining non-parametric models of the MR dampers. The damper coil current is generally taken as an input of the ANN model [13]. Alternatively, the damping characteristics can be changed by the section area of the throttle valve instead of the current [14]. Many different and innovative design studies are in the literature to enhance the damping capability of the MR damper [15; 16; 17]. In some studies, the damping performance was enhanced by optimizing the dimensions, which have a direct effect on the damping performance [18; 19; 20]. MR dampers use four different operating modes: squeeze mode, mixed mode, valve mode, and shear mode [15; 20; 21; 22; 23; 24; 25]. The operating mode can be selected according to the features required by the application. In this experimental study, the MR damper was used in mixed mode. Alternatively, studies using different types of dampers are also included in the literature. [PERSON] and [PERSON] put forward the critical importance of considering uncertainties in vehicle components during design to ensure passenger safety and optimal performance. They introduced a novel suspension system with inverters and asymmetric dampers, demonstrating significant improvements in ride comfort, road-holding, and rollover probability compared to conventional damper designs [26]. [PERSON] et al. studied a novel combined suspension system, incorporating a power-driven damper (PDD) and inerter-spring damper (ISD). They could address vibration issues in vehicles across a wide frequency spectrum with a fractional-order derivative sliding mode controller (FD-SMC) [27]. In addition to the design of suspension systems with different damping elements, the control of suspension systems with various controllers is also a studied subject. An adaptive controller algorithm was proposed by [PERSON] and [PERSON] to overcome parameter changes in suspension systems [28]. However, measuring changes in the parametersof the suspension system is quite difficult. Therefore, the prediction of damping force methods has been developed. [PERSON] et al. proposed a linear parameter-varying H-infinity filter based on linear matrix inequality theory dependent on parameters [29]. Prediction-based methods can also be used in controller design. In recent years, controllers using prediction-based models have become increasingly popular. [PERSON] et al. studied the prediction-based controllers for SASS and proposed an external-input autoregressive model predictive controller [30]. Model predictive controllers generate the optimal control signal for the next iteration with the designed system model. Therefore, the accuracy of the designed model is crucial. In addition, they require advanced microcontrollers for real-time applications, which increases the system's complexity and cost. [PERSON] et al. presented a robust control technique for a nonlinear vehicle suspension system dealing with uncertainties, time-delayed actuation, and bounded disturbances. They overcame these challenges by combining sliding mode and back-stepping methods, demonstrating superior performance in active suspension through MATLAB simulations [31]. [PERSON] and [PERSON] designed a SASS with multiple orifice holes and controlled it with a sliding mode controller [32]. By their nature, sliding mode controllers make the system resistant to disturbances and uncertainties. However, the chattering and variable frequency of the controller's output make it difficult to use directly for the MR damper control. Considering these challenges, the optimized PID controller is prevalent in many fields of industry. Researchers have extensively investigated the application of PSO for the fine-tuning of the controllers designed. [PERSON] et al. designed a sliding mode controller utilizing PSO by changing a sliding surface [33].