## 2 Control Strategy
### Active Seat Suspension Control Strategies  
In order to design a practical and cost-effective active seat suspension, the cost and number of sensors that provide the controlling signals have to be considered. Accordingly, in this study five simple control strategies have been designed to attenuate the vertical vibration at the driver's seat. The concept inherent in these control strategies is that the control force is assumed to be a linear function of the preview information from the vehicle suspension combined with feedback states, as given in Table 1.  
All of the controllers, A1 to A5, use preview signals from the vehicle suspension, namely, the vehicle suspension displacement \((x_{s}-x_{us})\) and velocity \(\big{(}\dot{x}_{s}-\dot{x}_{us}\big{)}\). Controller A1 employs only preview information while A2 uses the preview information and the acceleration of the sprung mass in the QvM. A3 uses preview information together with the acceleration of the seat, whereas both the seat and the sprung mass accelerations are used in the controller A4. Finally, instead of using acceleration signals, the controller A5 utilises the preview information as well as the feedback states of the seat suspension's travel and velocity. \begin{table}
\begin{tabular}{c c} \hline \hline
**Control Strategy** & **Control Force (\(\ddot{x}_{s}\))** \\ \hline A1 & \(F_{a}=q_{1}\;\big{(}\dot{x}_{s}-\dot{x}_{us}\big{)}+q_{2}\;\big{(}x_{s}-x_{us} \big{)}\) \\ A2 & \(F_{a}=q_{3}\;\big{(}\dot{x}_{s}-\dot{x}_{us}\big{)}+q_{4}\;\big{(}x_{s}-x_{us} \big  
The parameters (\(q\)'s) and (\(r\)'s) in Table 1 refer to the gains of the feed-forward (preview information) and feedback states for each control strategy, respectively. These were obtained by optimising a fitness function to improve the vibration isolation performance of the seat and subsequently to provide improved ride comfort for the driver. As a result of the improved attenuation of the seat acceleration, the controllers increased the travel of the seat suspension which, itself, is physically limited [26; 27] and, consequently, both the suspension travel and actuator force limitations were included in the optimization process. There are many methods for assessing ride comfort either using the time or the frequency domains, such as the root mean square (RMS) of the seat acceleration or the power spectrum density (PSD) function, respectively. However, the human body sensitivity to acceleration depends on the vibration frequencies and directions [1; 28]. For instance, it is well known that the human body is most sensitive to vertical vibration in the frequency range of 4-8 Hz. Consequently, in this study, the fitness function that was used in the gain optimisation process was based on the seat effective amplitude transmissibility (SEAT) factor, which is defined as the ratio between the acceleration at the seat to that at the base of the seat [1]. This is mathematically given by ([PERSON], [PERSON] et al. 2009) [29]:  
\[SEAT=\frac{\left(\ddot{x}_{se,w}\right)_{rms}}{\left(\ddot{x}_{s,w}\right)_{ rms}} \tag{5}\]  
where \(\left(\ddot{x}_{se,w}\right)_{rms}\) is the RMS of the seat acceleration and \(\left(\ddot{x}_{s,w}\right)_{rms}\) is the RMS of the sprung mass acceleration. The subscript \(w\) means that these acceleration values are weighted according to the frequency weighting function \(W_{k}\) in the vertical direction given by the ISO-2361-1 standard.