###### Abstract  
This paper presents a double sky-hook algorithm for controlling semi-active suspension systems in order to improve road-holding property for application in an in-wheel motor. The main disadvantage of the in-wheel motor is the increase in unsprung masses, which increases after shaking of the wheel, so it has poor road-holding that the conventional theoretical sky-hook algorithm cannot achieve. The double sky-hook algorithm uses a combination of damper coefficients, one from the chassis motion and the other from the wheel motion. Computer simulations using a quarter and full car dynamic models with the road conditions specified by ISO2631 showed the effectiveness of the algorithm. It was observed that the algorithm was the most effective in the vicinity of the wheel hop frequency. This paper also proposed the parameter set of the double sky-hook algorithm to differentiate the driving mode of vehicles under advanced development.  
sky-hook; in-wheel motor; semi-active suspension 2021 21 September 20  
In order to overcome the above-mentioned problems, a practical double sky-hook algorithm was proposed [18], which can effectively control the unsprung mass resonance as well as the sprung mass resonance. The proposed algorithm utilizes an additional sky-hook damper in the wheel combined with a conventional sky-hook damper that is attached to a sprung mass. In other words, the damper coefficient in a real physical semi-active damper is adjusted according to the principle of the sky-hook algorithm not only in the vicinity of the sprung mass resonant frequency, but also in the vicinity of the unsprung mass resonant frequency. In the algorithm, hardware components such as a semi-active damper and a chassis vertical accelerometer and a relative distance sensor for the proposed algorithm are the same as those of the conventional sky-hook algorithm. However, average damping force transmitted to the sprung mass can be increased due to larger value of an additional sky-hook damper at unsprung mass, which in turn, will increase the sprung mass acceleration levels. Therefore, there has been a great deal of research on determining the contribution of the sky-hook damping at unsprung mass for a semi-active suspension system [19; 20; 21].  
This paper focused on the robust trade-off performance of ride comfort and handling by guaranteeing ride quality in every driving situation regardless of the value of the sky-hook damping coefficient at unsprung mass. For practical proof, trade-off performance analysis using cross-plot of RMS (root mean square) tire normal force variation, and RMS body acceleration using the proper model was used. The analysis was performed with the model of the in-wheel motor vehicle under development and with enough fidelity model for ride comfort simulation, which consists of actuator delay, suspension friction, and damper nonlinearity.  
The rest of this paper is organized as follows. In Section 2, modeling of the suspension dynamics of a quarter and a full car is described. Section 3 explains the principle of the double sky-hook algorithm and suggests a design method to select suitable damping coefficients. In Section 4, computer simulations with a quarter and a full car suspension dynamics model are presented with a discussion of some the results for the purpose of comparison with a passive and the conventional sky-hook suspension system in the RMS of the suspension performance measures. Conclusions are made in the final section.