The tests were done for the closed loop system using both the right and left to control the machine to see how well the controller would perform and how much the position changes would. Closed loop system was developed later and more effort was used to tune it however, step input is not a valid input method for closed loop system as it increases the chances of oscillations because of the rapid changes in the valve spool control values as a solution a slider was inserted to control the input signal force manually.
In both joysticks test the machine is operated for 20 seconds in which the arm is moved to one direction with the control input however he machine still has minor initial movement in the first ten seconds which is why the start of the simulation time is delayed slightly. The stick calculated values were amplified by 400 and calculated boom values for 800 in order to improve the controller performance and the feedback references were amplified by 4 and 8 respectively. The value of the Kp was set to 25 for boom link controller and 20 for swing link controller during these tests while Ki is set to one.
8.2.1 Positive Y-direction
The first input given was to drive the tip in positive y-direction with maximum joystick input force from 10 seconds to 30 seconds in the simulation. Seen from the figure 8.9 below, where the solid line is the x-coordinate and dotted line the y-coordinate of the tip, the tip x-value changes from 15.50 meters to 16.06 meters and y-value from -3.27 to -1.65 meters.
Figure 8.9. Tip position change with y-direction positive input
In figure 8.10 and 8.12 are the angular velocities of the two links and the solid line is the calculated value and dotted line the sensors feedback value. As can be seen that the boom link has small over shoot of roughly 10% of the requested speed after 2 seconds of simulation however towards the end of the time the two velocities catch each other. Figures 8.11 and 8.13 have the valve control signals and their change over the course of the time simulation.
The legend of each figure shows the meaning of each line. Notable difference is the thickest line which represents the load control valve. As seen below the control signals are similar to the peaks in the reference velocity however with lower peaks. The controller can be seen reacting immediately to change in control signal however takes some time before the actuator movement has caused the manipulator arm to move. In figure 8.13 the stick control values for the three actuators are positive values described in table 6.2 however cause no movement in the manipulator and the angular velocity of the stick stays positive due to the movement of the first link.
Figure 8.10. First link calculated angular velocity and reference angular velocity
Figure 8.11. Valve control signals of first link valves
Figure 8.12. Second link calculated angular velocity and reference angular velocity
Figure 8.13. Valve control signals of second link valves
8.2.2 Negative Y-direction
The second input given was to drive the tip in negative y-direction with maximum joystick input force from 40 seconds to 60 seconds in the simulation. Seen from the figure 8.14 below, where the solid line is the coordinate and dotted line the y-coordinate of the tip, the tip x-value changes from 16.27 meters to 14.01 meters and y-x-value from -0.87 to -3.24 meters.
Figure 8.14. Tip position change with y-direction negative input
In figure 8.15 and 8.17 are the angular velocities of the two links and the solid line is the calculated value and dotted line the sensors feedback value. As can be seen that the boom link has no reaction to the initial negative velocity input however at 45.4 seconds in to the simulation the angular velocity jumps to extreme values and stabilizes over the next 4 seconds in which the tool has hit the ground and the velocity signal stops at 0. The calculated and occurring second link signals stay the same until the peak occurs. Figures 8.16 and 8.18 have the valve control signals and their change over the course of the time simulation.
Notable difference is the thickest line which represents the load control valve. In figure 8.15 there is short amount of time where the system purely oscillates from 48 to 50 seconds which is caused by the bucket reaching the ground. The tip still moves in x-direction after touching
the ground. The same oscillation is also shown in the valve control voltage plot in figure 8.16.
Figure 8.15. Second link calculated angular velocity and reference angular velocity
Figure 8.16. Valve control signals of second link valves
Figure 8.17. First link calculated angular velocity and reference angular velocity
Figure 8.18. Valve control signals of first link valves
8.2.3 Positive X-direction
The third input given was to drive the tip in positive x-direction with maximum joystick input force from 40 seconds to 60 seconds in the simulation. Seen from the figure 8.19 below, where the solid line is the coordinate and dotted line the y-coordinate of the tip, the tip x-value changes from 16.20 meters to 18.23 meters and y-x-value from -1.08 to -0.64 meters before the time of 54.7 seconds where the system has an unexpected reaction dropping the tip to the ground after which the manipulator is still able to move to x-direction however stuck in the y-direction as the system is still giving negative y-direction control.
Figure 8.19. Tip position change with x-direction positive input
The drop that occurred during the simulation was unusual and required further investigation.
The system was simulated for another 30 seconds as shown in figure 8.20 and the same behavior can be seen occurring regularly. The load control valve of the boom has a steady signal increase shown in figure 8.22 until the previously mentioned time point where the signal jumps to a point where the boom is allowed to fall down freely and the control of the
system is lost. Figure 8.20 shows that when the simulation is continued the effect occurs again at roughly 86 seconds.
Figure 8.20. Loss of control occurs twice during simulation. First at 54.7 second and again at 86 seconds.
Figure 8.21 shows that the angular velocity input for the boom link was negative however based on the sensor data the system had little to no reaction to this nevertheless the load control valve was opened and linearly increased in the control values as seen in figure 8.22.
Figure 8.23 shows the angular velocities of the stick link which follow the input signals however suffer from the major peak as explained before and start to oscillate towards the end of the simulation. The peak negative values also drive the valve control signals to be negative as shown in figure 8.24 which otherwise are not reaching the maximum values nevertheless the input is highest for that direction.
Figure 8.21. First link calculated angular velocity and reference angular velocity
Figure 8.22. Valve control signals of first link valves
Figure 8.23. Second link calculated angular velocity and reference angular velocity
Figure 8.24. Valve control signals of second link valves
8.2.4 Negative X-direction
The last input given was to drive the tip in negative x-direction with maximum joystick input force from 20 seconds to 40 seconds in the simulation. Seen from the figure 8.25 below, where the solid line is the coordinate and dotted line the y-coordinate of the tip, the tip x-value changes from 16.27 meters to 8.24 meters and y-x-value from -0.13 to 0.98. This last direction has by far the largest displacement in the tip positions compared to any other tests done.
Figure 8.25. Tip position change with x-direction negative input
Figure 8.26 shows the boom link velocities and the feedback signals are not reaching the input values until at 24.6 seconds there is a massive overshoot in the boom velocity signal from the sensors which causes the system to also undershoot as counter reaction. The boom valve signals also show the same symptoms and are displayed in figure 8.27. The second link feedback values are oscillating throughout the simulation time while trying to follow the input signal. This causes the manipulator tip to move remarkably during the simulation and the control signal is overshooting the desired values as shown in figure 8.28. The same
reaction can be seen in the valve control signals in figure 8.29 where the signals are at maximum values for a large part of the simulation.
Figure 8.26. First link calculated angular velocity and reference angular velocity
Figure 8.27. Valve control signals of first link valves
Figure 8.28. Second link calculated angular velocity and reference angular velocity
Figure 8.29. Valve control signals of second link valves,