Ecp Executive Program System

1. Objectives

The objective of this experiment was to serve as an orientation of the ECP Executive program system for first time users.

1. Procedure

Before commencing the self-guided tour the ECP Executive program was verified to be in working condition. The ECP program was ensured to have found the real time controller and the disk was checked to be able to rotate freely. To begin the tour, a configuration file named default.cfg through the File menu must be loaded. This file contained the controller gain parameters and other trajectories necessary for this particular tour. To continue, the Controller needed to be implemented. Through the Setup Control Algorithm in the Setup menu an algorithm was set that used the following gains:

kp = 0.20

kd = .010

ki = 0

Using these values, the next step involved executing a Step trajectory and plotting it. Under the Command menu, selecting Step and Setup a step size of 400, a dwell time of 100ms and a total of 1 repetition was selected. After the trajectory was executed the plot was set through the Plotting menu, a plot of a critically damped system with a natural frequency of 6Hz was obtained. With the same general instructions as the critically damped system, a plot of Underdamped Step Response was obtained by changing the gains to:

kp = 0.20

kd = .002

ki = 0

By changing the kd to 0.002 the velocity feedback gain was reduced. The gains were then reset in preparation for the next plot. To demonstrate the ECP Executive programs ability to track responses a Ramp trajectory was selected. A distance of 1000 counts, a velocity of 1000 counts per second, dwell time of 100ms and a total of 1 repetition were selected. The plot obtained from this trajectory showed a velocity move of 10,000 counts followed by a dwell of 100ms and then a return to motion was shown.

Frequency Response was also tested. The Sinesweep trajectory was used, with an amplitude of 500 counts, minimum frequency of 0.1 Hz, max frequency of 12Hz and a sweep time of 30 seconds were selected. Two plots were obtained, one which required changing kd to 0.002, which imitated that of an underdamped system, and one with a kd to 0.010 imitating a damped system.

The last plot obtained was that of a system experiencing viscous damping. Selecting Disturbances under the Command Menu, Viscous Friction¸ was selected. A disturbance of 1.0 volt/radian/second was used. The plot showed the effect of viscous friction and its addition to a damped system.

3. Results and Discussion

The data acquired from this experiment showed the difference in measurements of three different controller functions: step, ramp, and sine sweep.

When kd was set equal to 0.010 the controller simulated a critically damped response. As Figure 1 shows, the encoder 1 position eventually reached the commanded position quite soon after the function was executed. This is an example of a closed loop system which means that it tries to correct the output to the set or desired value.

Figure 1-Critically Damped Step Response

Figure 1 reached its eventual position because it was critically damped with a relatively high value kd.

Another example of a step function in a closed loop system is shown in Figure 2 which showed the type of oscillation problems that arose with a closed loop system due to an underdamped response when kd, derivative gain, was set to a value of 0.002. However, the controller managed to reach the target values after seven oscillations.

Figure 2-Underdamped Step Response

After implementing the ramp function and executing the function the group observed that the function had a delayed response, which is expected from a feedback control system. Figure 3 shows encoder 1 tracking the commanded position while surpassing its position by a barely visible margin of 15 counts.

The following two parts of the self-guided demonstration measured the frequency response of the controller; one was measured with a derivative gain of 0.010 and the other with a derivative gain of 0.002. For the first frequency response measurement the derivative gain was set to 0.010 which meant that the signal was critically damped. As shown in Figure 4 this resulted in an increasingly stable response as time increased.

Figure 4- Frequency Response (Critically Damped)

The second frequency response measurement was measured using a derivate gain of 0.002, which meant that the signal is underdamped and is vulnerable to larger frequency oscillations than that of Figure 4. As seen on Figure 5, the frequency signal increases at around eleven seconds into the measurement of data and began to stabilize twenty seconds after data was measured. However, it is not as stable as Figure 4 because the error signal is not corrected as quickly as if the signal was damped.

The last part of the self-guided demonstration recreates the effects of viscous damping on the closed loop controller with a viscous friction coefficient set to 1.0 volts/radian/second. Figure 6 shows a very similar effect to that of Figure 5, the encoder's response became stable after reaching the commanded position, which was the desired value for the controller.

Figure 6-Viscous Damping

4. Summary

Through usage of the ECP Executive Program and the inputs for the ramp, step and sine sweep functions, it was observed that when the derivative gain kd was set to a relatively high value such as kd=0.010 the data set proved to be critically damped, thus, it stabilized almost immediately. For the under-damped closed loop systems that were setup it took more oscillations to reach the target value of the commanded position proving that error does arise when using a closed loop system with a derivative gain that is relatively small. This only applied to the step, sine sweep, and viscous damping setups. As for the ramp function as predicted by the