# The Tractor-Cart System Controller with Fuzzy Logic Rules
## 6 Results and Discussion  
In order to evaluate the proposed algorithm based on fuzzy logic rules to control the motion of the tractor and cart, computer simulations of the derived models of system were performed [31; 32; 33] in a MATLAB/Simulink environment [34]. Reference patterns of plant rows to analyze performances of designed controllers, velocity of tractor are given in Table 5.  
The influence of uneven and off-road terrain profile, time delays due to friction, and steering loads have been neglected. Simulation results showed that the proposed controller was able to move the hitch arm to keep a cart in a correct path within \(-0.06\) to \(0.06\) rad with respect to the given plant rows. For relatively small values of \(\alpha\), oil flow rates of 6 GPM was enough to make the required change in time for any speed of 1 to 10 m/s. Figure 10 shows the time delay for changing the pump flow rate and changing the cart position. The analytical and numerical results showed that time delay was relatively small, and the pump flow rate (max 44 GPM) was sufficient to make the hitch arm move without considerable delays. A more complex pattern with sharp changes along the rows was also tested. The system response of the tractor-cart controllers in this pattern were accurate for more than 96% at lower speeds (1-5 m/s). At higher speeds, the accuracy of the controller dropped slightly and was between 61% to 96% (Table 6). Figure 12 shows the simulation results at 3 m/s and the accuracy of the cart with the designed active controller was about 92% success in adjusting the position of cart according to the reference pattern with very marginal offsets. The third pattern tested to evaluate the controller performances was a Zigzag pattern with more abrupt changes along the path. The position control of the cart in comparison with passively controlled system improved significantly, but the combination of increased speed and complex pattern reduced the accuracy far more than in the aforementioned patterns Figures 11 and 12. The simulation results of the zigzag pattern at 5 m/s is shown in Figure 13. This demonstrates the reciprocal relationship between speed of running agricultural operations and accuracy of performing. Figure 13 shows that the proposed controller corrects the cart position for average of over 90% (at all speeds). The controller performance degrades in the peaks and valleys of pattern to \(\sim\)2-3 cm. Without the proposed controllers, the cart had an average offset of 5-10 cm from the reference pattern and about 50% of accuracy. The last generated pattern was a pattern with a combination of three previously considered patterns to assess the performance of the system control in a more complex pattern of plant rows. Figures 14-16 indicate the cart behavior with and without a controller at three different speeds (2, 4 and 9 m/s). Figure 14 demonstrates that, in the case of a complicated pattern in lower speed (\(<\)5 m/s), the controller could adjust the cart position according to the given path with the accuracy of \(\sim\)2-3 cm and over 90% of accuracy for the whole simulation duration. Figure 15 shows the effect of higher speeds in reducing the accuracy of controller. The performance of the controller deteriorates, as it gets closer to the end of the pattern and almost loses a track of the row pattern in the final 25 m of simulation. Simulations in the highest speed at 9 m/s shown in Figure 16 show that the efficiency of the controller dropped significantly. The position accuracy of the cart with the controller dropped to 5... 10 cm in magnitude and the accuracy without a controller was about 7-13 cm. A low controller accuracy with the increase of tractor's driving speed and in abrupt row pattern changes were in agreement with the study results of [PERSON] et al. [35]. [PERSON] et al.