## Materials and Methods
### Evaluation of the Model Performance  
All the Equations from (1) to (8) for the coulter dynamics and the hysteresis model of the MR damper were applied and simulated in MATLAB and Simulink. The acquired field surface profiles (Figure 4) and the vertical forces (Figure 5) from the dynamic measurements at the speeds of 10 km h\({}^{-1}\) and 12 km h\({}^{-1}\), when the MR damper was excited with 0.3 A, 0.5 A, and 0.7 A, were used as inputs to the simulation model. The acquired strains were utilized to determine the vertical forces and the damper forces that were acting on the coulter time and the fixed shank. To define the field profiles, the geo-referenced coordinates of the active prism were transformed to the ground touching point of the wheel. The detailed formulas on calculating all the forces and transformations, in terms of rotations and translations for the profile determination, are given in reference [27]. The outputs of the model were the pitch angle of the assembly movement and the damper force. All parameters and constants of the Bouc-Wen model, as well as the coulter model, can be found in reference [24]. The real-life test of the assembly performance was performed with different current input values loaded on the MR damper (0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0 A). Two different traveling speeds of 10 km h\({}^{-1}\) and 12 km h\({}^{-1}\) were set for all performed experiments. The field tests with the current values 0.3 A, 0.5 A, and 0.7 A had the best performance, in terms of coulter dynamics [27], thus they were chosen to be further analyzed in the present work. In order to validate the correctness of the simulation model, its outputs such as the simulated pitch angles of the assembly vertical motion and the damper forces were compared with the measured ones. The comparison analyses were carried out by calculating the RMSE in percentage, absolute RMSD, and the correlation coefficient between the simulated and the measured data. The RMSE estimated the relative error in percentage between the measured and the simulated datasets. Taking into account the effect of the neglected lateral forces on the tire dynamics, the value of 20% for the RMSE in percentage was considered as a threshold that should not be exceeded [34; 35]. The formula of the RMSE in percentage that was used is the following:  
\[\varepsilon_{RMS}=\frac{Z_{RMS}^{m}-Z_{RMS}^{s}}{Z_{RMS}^{m}}\times 100\% \tag{9}\]where \(Z_{RMS}^{m}=\sqrt{\sum\limits_{i=1}^{N}{{{{(z_{m}(t))}^{2}}}/{N}}}\); \(Z_{RMS}^{s}=\sqrt{\sum\limits_{i=1}^{N}{{{{(z_{s}(t))}^{2}}}/{N}}}\); \(z_{m}(t)\) and \(z_{s}(t)\) are the measured and the simulated data, respectively, within the time \(t\) that was needed to travel the specified distance. N is the total number of samples. Subsequently, the average difference between the measured and the simulated outputs was evaluated by determining the RMSD value. This was defined by the following expression:  
\[\mu_{RMSD}=\sqrt{\frac{{\sum\limits_{i=1}^{N}{{{({(z_{m}(t))}^{2}}-{{(z_{s}(t)) }^{2}})}}}}{N}} \tag{10}\]  
In addition to the error estimation, the fitting accuracy, in terms of similarity relationship, of the simulated data to the measured data were also addressed with a correlation coefficient. The values higher than 0.6 could be considered as practically acceptable based on the same reasons as above. The correlation coefficient \(\rho\) was based on the following equation:  
\[\rho=\frac{1}{N-1}\sum\limits_{i=1}^{N}{{{(z_{m}(t)-\mu_{z_{m}}})}\over{{ \sigma_{z_{m}}}}}(\frac{{z_{s}(t)-\mu_{z_{s}}}}{{\sigma_{z_{s}}}}) \tag{11}\]  
where \(\mu_{z_{m}}\) and \(\sigma_{z_{m}}\) are the mean value and the standard deviation of \(z_{m}(t)\), respectively, and \(\mu_{z_{s}}\) and \(\sigma_{z_{s}}\) are the mean value and the standard deviation of \(z_{s}(t)\), respectively. Figure 4: The measured field surface profiles at the speeds of (**a–c**) 10 km h\({}^{-1}\) and (**d–f**) 12 km h\({}^{-1}\), when the MR damper was supplied with 0.3 A, 0.5 A, and 0.7 A.