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Technical Awards : 2021 JSAE Award The Outstanding Technical Paper Award - An Approach to Exploring Vehicle Motion to Enhance Ride Quality of Passenger3.2 Converting motion perceived by passengers into state variablesFig.4　 Acceleration and jerk detection with soft sensor (physical image of state observer) : Acceleration and jerk at the attached body are approximated to state variables.Fig.5　 Frequency response characteristic of state observer: Four cases of translational and angular accelerations.mass of the upper body and are expressed in equation (4):The equation of motion of the upper body about the pivot in the roll direction, caused by the forces FyB and FzB acting on the upper body CG, is expressed as equation (5). For the roll stiffness and damping, the effects of the supporting force acting between the passenger and the seat surface, friction, etc. are included as approximate values:In the last step, equations (3) and (4) are substituted into the equation of motion of the upper body (equation (5)) to determine the roll angle acceleration of the upper body , as shown in equation (6):The differential quantities of the state variables of the , are included in the vehicle model, derived passenger model, as shown in equation (6). However, if equation (6) is converted from the equation of motion to the equation of state and if the converted equation and the vehicle model are considered as a set of simultaneous equations, replacement with the state variables can be performed such that the equation will converge to the form of equation (2). In this manner, the formulation of the optimal control used for the inverse vehicle dynamics analysis was realized.The physical quantities that can be expected to be related to the ride quality may include the translational and angular accelerations applied to the passenger body. However, as mentioned in the previous section, quantities other than the state and input variables cannot be and incorporated into the evaluation function.The acceleration can be converted into a state variable by differentiating the equation of motion, which is expressed as a second-order differential equation, once more to a third-order differential equation (and to the fourth order for conversion to the jerk state variable). However, this increases the number of equations that need to be solved, leading to a calculation burden and making this approach unsuitable for inverse vehicle dynamics calculations. To address this problem, a state observer is used to derive the approximate state variables that can be incorporated in the evaluation function.To formulate optimal control by combining the vehicle and passenger models, the state observer is used as a soft sensor, as shown in Fig. 4. Specifi cally, the state equation described in equation (7) is employed, and the acceleration at the passenger body or at the measurement target . position of the vehicle body is used as input Utilizing this method, the translational acceleration, roll acceleration, and jerk at the mounting position can be observed as approximate state variables The approximation accuracy of the state variables is determined by setting the c and k values in equation (7). Fig. 5 shows the characteristics corresponding to different natural frequencies when the set values are altered. The set values are selected such that the gain, which represents the degree of approximation, is close to 1; this implies that the characteristics will be fl at. :73112No.88 (2022) NISSAN TECHNICAL REVIEW