A.3.2.7.?: Test Case Analysis

A.3.2.7.?: Test Case Analysis

A.3.2.7 Nominal Simulation Results

A.3.2.7.?: Test Case Analysis

During the design process of the launch vehicle, we were given a test case of a mock launch vehicle. This vehicle was not included in the final design, but it did have all the proper inputs for our simulation. The test launch vehicle had an inertia matrix derived by the structures sub-group and a propellant mass flow rate along with burn times for each stage provided by the propulsion sub-group. This test vehicle was used to develop a design process for the final launch vehicle cases. We learned efficient ways to adjust the gain matrix to achieve an optimal orbit and we learned quick methods for modifying the steering law to follow the optimal path for the launch vehicle as given by the trajectory sub-group.

After completing our controller design, we plugged in values for our gain matrices and modified the original steering law. We shifted the third stage steering law up by one radian to try and eliminate radial velocity so that the launch vehicle would enter into a circular orbit. At this point we did not have any deviations so the case that was tested used all nominal values. We then ran the full simulation for the test case to test our controller design. The orbit of our first run is shown in Fig. A.3.2.7.?.1 below.

Fig. A.3.2.7.?.1: Actual path of launch vehicle(blue) and desired path of launch vehicle(red)

(Adam Waite, Mike Walker)

In Fig. A.3.2.7.?.1, the blue line shows the actual path of the rocket as simulated by our controller and the red path shows the desired trajectory. From this initial run, we learned that we needed to somehow lower the eccentricity of the orbit to generate a circular, stable orbit around the Earth. It was apparent that we also needed to follow the steering law much closer with sharper turns in the first and second stages. This meant limiting the error between the actual pitch angle of the launch vehicle and the desired pitch angle of the launch vehicle.

From the above data, we determined that by adjusting the values of the gain matrix and creating a modified steering law, it would be possible to circularize the orbit of the launch vehicle. We first started changing the values of the gain matrix. We gave the highest value to the first number in the gain matrix because this told the controller to place the most emphasis on the pitch angle of the launch vehicle. The other two values in the gain matrix were given smaller values because the yaw and roll rates were not as important to achieve orbit. By manipulating the gain matrix, we controlled the launch vehicle on a path much closer to the optimal trajectory to reach a circular orbit.

The second step in the design process for this test case involved modifying the original steering law. By creating smooth, continuous functions, we discovered that the launch vehicle was more stable and controlled during ascent into orbit. Modifying these original steering laws was a long and difficult process. This process involved lots of trial and error with different polynomial expressions and linear functions. Because of this, we were not able to complete the test case design to an optimal level. Time was running short and analysis needed to be started on the final design cases. The final run of the test case is shown in Fig. A.3.2.7.?.2 below.

Fig. A.3.2.7.?.2: Final orbit for test case with actual path(blue) and desired path(red)

(Adam Waite, Mike Walker)

As shown in Fig. A.3.2.7.?.2, the launch vehicle’s trajectory into orbit is much more curved in the first and second stages, which allow the launch vehicle to achieve a nearly circular orbit. The launch vehicle still deviates from the desired path in the second stage, but this is so that the launch vehicle can be controlled into a circular orbit. Since the third stage is uncontrolled, the maneuvers to circularize needed to be performed in the second stage. As can be seen, the final test case orbit is still not perfect. Time had to be devoted to the final design cases that were eventually given.

The biggest idea that was learned from analyzing and manipulating the test case was the steps for the design process for the final launch vehicles. Once given the final designs, we ran them through the simulator with all of the original gain matrix values and trajectories. After this, we adjusted the gain matrix so that the launch vehicle closely followed the desired trajectory. Next, we modified the steering law so that the launch vehicle would obtain an orbit with an eccentricity close to zero. Finally, we simulated another trial launch. Small adjustments were made again until we achieved a circular orbit with a periapsis above 300 kilometers.

Author: Adam Waite