# Analytical Investigation of Vertical Force Control in In-Wheel Motors for Enhanced Ride Comfort
## 1 Introduction
Then, to address these challenges, researchers have explored advanced control strategies for active suspension systems in in-wheel motor-driven electric vehicles (IWMD-EVs). One notable approach is the mixed \(H_{2}/H_{\infty}\)-based robust guaranteed cost control system, which integrates dynamic vibration absorbers into the active suspension model to significantly improve ride comfort and handling stability. Ref. [20] demonstrated through simulations that this controller can outperform traditional passive suspensions and standalone \(H_{\infty}\) controllers, offering a marked improvement in overall vehicle dynamics. Additionally, decentralized dynamic event-triggered communication mechanisms have been developed to enhance control efficiency in IWMD-EVs. Ref. [21] has proposed a decentralized dynamic event-triggered control approach that not only improves ride comfort but also reduces the communication load. Adaptive control strategies, such as sliding mode control and fuzzy logic systems, also have shown significant effectiveness in addressing the nonlinearity and time-varying dynamics inherent in active suspensions. Refs. [14; 22] have developed robust adaptive controllers that ensure consistent tire-road contact and vehicle stability under varying load conditions and road profiles. Furthermore, regenerative active suspension systems have been explored to harness residual energy from suspension movements. Ref. [23] demonstrated that such systems can improve energy efficiency while maintaining or enhancing ride comfort and handling. Model predictive control (MPC) has emerged as a promising approach for real-time optimization of suspension performance. Ref. [24] showed that MPC can effectively balance ride comfort and handling by predicting future states and optimizing control inputs accordingly. Despite these advancements, practical implementation challenges persist, particularly due to limited wheel space and the need for robust control systems [25; 26; 27]. Further research and development are required to fully realize the potential of these advanced suspension technologies in IWMD-EVs. One promising solution to the suspension issue is the ride-blending control method. Simulations by Ref. [3] showed that this technique effectively reduces the pitch response of the vehicle body by leveraging the vertical component of the driving force, all while keeping the tire dynamic force within safe limits. Ride-blending control works by integrating vehicle dynamics through electronic brake distribution and active suspension systems, coordinated in a decentralized manner [28]. Essentially, when one system is active, the other minimizes its force, ensuring a balanced and efficient performance. This method offers a more refined approach to handling the challenges posed by increased unsprung mass in IWM vehicles. Ref. [1] demonstrates the development of ride-blending control, a strategy that utilizes the vertical component of IWM driving force to enhance ride comfort and handling. Simulation tests on a vehicle model with coupled dynamics showed a 31.8% improvement in ride comfort without impacting tire load or longitudinal dynamics. The method also confirmed stable lateral dynamics. It seems that ride-blending control has significant potential to improve ride comfort, as demonstrated by various studies [1; 3; 28]. However, most of these studies present results in the time domain and in terms of sprung mass acceleration. This research extends the findings of Ref. [1] and aims to develop a proportional ride-blending controller for a vehicle and analyze the results in the frequency domain to better understand how well ride-blending control can improve suspension performance. Additionally, frequency-weighted acceleration will be calculated to compare ride comfort. The contribution of this research lies in the investigation of proportional ride-blending control in the frequency domain and its impact on enhancing ride comfort for EVs with IWMs.