Implementation of PID

STANDARDS: Next Generation Science Standards (NGSS) and International Society for Technology in Education (ISTE)

Modified 2020-09-16 by Rachel Ma

ISTE: 1. d.: Understand the fundamental concepts of technology operations, demonstrate the ability to choose, use and troubleshoot current technologies and are able to transfer their knowledge to explore emerging technologies.

Assessments and Evidence of Understanding

Modified 2020-09-16 by Rachel Ma

By the end of this assignment, students will be able to implement a 1D PID Controller.

AGENDA (Brief Summary of Activities)

Modified 2020-09-16 by Rachel Ma

10 min: teach what a python class is for

40 min: Implement the 1D controller

Differentiation (strategies for grouping, ELL, and inclusion)

Modified 2020-04-16 by Garrett Warren

Advanced preparation/Materials/Set Up (Including Misconceptions)

Modified 2020-09-16 by Rachel Ma

Materials needed

Teacher Materials

• Projector for displaying videos or slides
• Look under resources section for more information about coding and classes

Modified 2020-04-16 by Garrett Warren

Introducing The Lesson

Modified 2020-09-16 by Rachel Ma

• Explain what classes in python allow you to do
  • allows to have multiple copies of code running at once

Main Lesson

Modified 2020-07-21 by Rara Ma

• Students will inmplement a PID controller for a simulated drone that can only move in 1D, the vertical dimension. You can control the speed the motors spin on the drone, which sets the thrust being generated by the propellers.

Modified 2020-07-21 by Rara Ma

Exercises

1. Implement the step method to return the constant . At what value of does the drone takeoff? What could happen if were set too high on a real drone? Set to 1300 for the remainder of the questions.
2. Implement the P term. What happens when the absolute value of is very large? What happens when its absolute value is very small? Can you tune the P term to stop oscillations? Why or why not?
3. Implement the D term. Set to zero. What happens when is 50? 500? 5000?
4. Now tune and so that the drone comes to a steady hover. Describe the trade-off as you change the ratio of to . Can the drone stabilize at its target (zero steady-state error)? Why or why not?
5. Implement the I term and observe the difference between PD and PID control. What role does the I term play in this system? What happens when and are set to zero?
6. Implement the reset method and test its behavior. If implemented incorrectly, what problems can you anticipate reset causing?
7. Finally, tune the constants in your PID controller to the best of your abilities. When the setpoint is moving, the drone should chase the setpoint very closely. When the setpoint is still, the drone should converge exactly at the setpoint and not oscillate. Report your tuning values.

Modified 2020-07-21 by Rara Ma

Now, we introduce latency! Run the simulation as python sim.py -l 6 to introduce 24 milliseconds of latency (six steps of latency running at 25 hz).

Exercises

1. Tune the constants in your PID controller to the best of your abilities. The drone should chase the setpoint very closely, but will converge more slowly when the setpoint is still. Report your tuning values.
2. Compare your tuning values to the values you obtained in problem 1.
3. Explain the effect of latency on each control term.

Modified 2020-07-21 by Rara Ma

In the most realistic mode, you will tune a controller with latency, noise, and a drag coefficient. You can do this with the command line arguments python sim.py -l 3 -n 0.5 -d 0.02 to be most realistic to real-world flight.

Exercises

1. Tune with these arguments to be as good as possible. Report your tuning values.
2. Compare your tuning values to the values from problems 1 and 2.

Run python sim.py -h to see the other simulator parameters. We encourage you to experiment with those and observe their effects on your controller.

Tuning 1D Controls: Part 1: Planar Tuning

Modified 2020-07-21 by Rara Ma

In this portion of the project, you will be tuning the low rate integral terms of the PID controllers that we’ve provided.

Modified 2020-07-21 by Rara Ma

Due to differences in the weight distribution and other factors that cause asymmetries, the drone will tend to initially drift in a particular direction. In order to tune your altitude PID, the planar motion of the drone needs to be controlled. This is important so that the drone does not fly uncontrollably across the room while you’re trying to tune its altitude controller. To control the drone’s planar motion while you’re tuning the altitude, we’ve created and tuned PIDs to do this for you, but you will need to tune the initial low-rate integral terms to account for the uneven weight distribution specific to your drone. You will first use the provided altitude PID to tune the planar controllers, and then you will tune your altitude PID with the tuned planar controllers.

Modified 2020-07-21 by Rara Ma

Our controller is a dual I-term (integral term) PID controller. The high-rate I-term changes quickly, allowing fast response to changes. The low-rate I-term changes slowly, allowing the drone to adjust to systemic sources of error. The provided PID gains have been pretuned to this drone hardware, and should not need significant modification for your specific drone. But, the initial low I-terms do need to be adjusted based on the static error of your specific drone.

Exercises
1. Name a source of static error that the low-rate I term can correct for.
2. Name two sources of dynamic error that the high-rate I term can correct for.

Modified 2020-09-16 by Rachel Ma

The first step in the tuning process is finding an initial throttle value that allows your drone to have a smooth and controlled takeoff. To do this, you’ll be adjusting the value of throttle_low.init_i in pid_class.py. This is the initial value of the low-rate (slow changing) integral term for the throttle, which controls altitude. The default value is 100. you will tune this value by having the drone take off, observing its behavior, and modifying the value accordingly. Each time you wish to change the value, you will need to restart pid_controller.py to use the new value.

Setup
1. Prepare your drone to fly over a highly textured planar surface¹.
2. Navigate to `4 of the screen.
3. Quit the program by pressing ctrl-c.

Exercises
1. In this screen (`4), use a text editor (such as vim or nano) to modify throttle_low.init_i in pid_class.py to test out different values for throttle_low.init_i. Be cautious when modifying this value because the drone could take off abruptly with a value that is too high. The specific throttle_low.init_i value is drone specific, but typical values range between 50 and 150. Try both of these values and two more values between then. In one sentence, describe the drone’s behavior as a result of changing the value up and down.
2. Now find the value for which your drone is able to have a smooth and controlled takeoff. The goal is to reduce the overshoot and undershoot for the drone to takeoff and fly stable at 0.3m. Try changing this value in increments of 10 and then 5 until you find a value that allows the drone to take off at a reasonable rate. Record this value in your answers.

Modified 2020-07-21 by Rara Ma

Next you will set the trim on roll and pitch. You will do this by tuning the low I-terms to adjust for the static errors that exist on your drone. The default value is 0, and positive values will move the drone to the right or forward, and negative to the left or backward, depending on the axis you’re modifying. Note that you may need to repeat this process periodically, for example after a crash or the like. When performing this process, each time make sure that you:

• Place the battery in the same place each time as much as possible so the weight is distributed the same.
• Plug the flight controller while the struts are fully engaged and the drone is level, so the gyros are well calibrated.
• Always place the drone so that the camera is closer to you and the skyline is farther away.

Setup
Modify pid_controller.py to print out the low rate integral terms of the PIDs by finding the block of code shown below and uncommenting the following print statements

print 'roll_low.init_i', pid_controller.pid.roll_low.init_i
print 'pitch_low.init_i', pid_controller.pid.pitch_low.init_i

You will also need to set the verbose variable in this file to zero so that these print statements will not be overridden by the other print statements: verbose = 0

While flying, the low-rate I-terms will change to account for the static flight error, and when you disarm the drone, the initial low-rate I terms will be set to these changed values, thus allowing the low-rate I terms to start at this corrected value. Eventually, these values will converge, and your drone will no longer drift. Once converged, you will save the values by modifying the variables self.roll_low.init_i and self.pitch_low.init_i in pid_class.py to the corresponding value printed in `4 of the screen after disarming. This will store the initial low-rate I-terms between flights.

Exercises

1. Perform one flight. After the drone takes off, do not give it movement commands but allow it to drift.
2. Disarm the drone before it flies too far in any direction.
3. Write down the low-I values printed in `4 of the screen.
4. Pick up and move the drone by hand back to the center of the flying area.
5. Repeat steps 1-4 until the values that are printed out after disarming have converged (roughly when the change in magnitude is less than 1).
6. Once these values have converged, record these values in your answers.

Footnotes

1A flat posterboard scribbled or written on with marker will work.

Tuning 1D Controls: Part 2: Altitude Tuning

Modified 2020-07-21 by Rara Ma

In this part, you will be transferring the altitude PID you created in part 1 onto your drone. You will then tune the PID gains on your drone as you did in the simulator.

Modified 2020-07-21 by Rara Ma

Now that the planar PIDs are tuned, and you have found a value for throttle_low.init_i that allows the drone to take off at a reasonable rate, you will be using your altitude PID to control the height of the drone. To tune your altitude PID, you will first use the Ziegler-Nichols tuning method to generate an initial set of tuning parameters. You will then fine tune these parameters similar to how you tuned the drone in simulation.

To use your PID, you’ll be running student_pid_controller.py instead of pid_controller.py. This will allow your PID to run alongside our planar PIDs, and on top of our throttle low-rate I-term which you found previously. Your PID will be responsible for keeping the drone flying steady vertically.

Setup
Change directories to ~/ws/src. Run git clone https://github.com/h2r/project-pid-yourGithubName.git. In your repo, change “pidrone_project3_pid” to “project-pid-yourGithubName” in package.xml and “project(pidrone_project3_pid)” to “project(project-pid-yourGithubName)” in CMakeLists.txt. Also remove the msg folder, and comment out “add_message_files” in CMakeLists.txt. Then change directories back to ~/ws/ and run catkin_make --pkg project-pid-yourGitHubName.

OR

Use the scp command to transfer student_pid_class.py, student_pid_controller.py, and z_pid.yaml from the repo on your base station to the scripts folder of your drone (~/ws/src/pidrone_pkg/scripts/). In the instructions below, instead of using rosrun, you may use python to execute your scripts.

Change directories into ~/ws/src/pidrone_pkg and modify pi.screenrc to start up with your altitude pid by changing python pid_controller.py\n to rosrun project-pid-yourGitHubName student_pid_controller.py\n. Prepare your drone to fly and then navigate to `4 of the screen. Press ctrl-c to quit student_pid_controller.

In this screen (`4), modify ~/ws/src/project-pid-yourGitHubName/z_pid.yaml by setting to 1250 and the rest of the gain constants to 0. Now run rosrun project-pid-yourGitHubName student_pid_controller.py to fly with your altitude PID.

Exercises

Fly your drone and observe its flight. Tune by slowly increasing its value between flights until you can see the drone moving up and down with uniform oscillations. Each time you will need to quit the controller, edit ~/ws/src/project-pid-yourGitHubName/z_pid.yaml, and then run rosrun project-pid-yourGitHubName student_pid_controller.py again to use the new PID gains.

1. Record your final value that causes uniform oscillations as , the ultimate gain.
2. Fly your drone and pause the altitude graph on the web interface when you see two peaks. Find the time difference between these two peaks and record this value as , the ultimate period.
3. Use your and values to compute , , and . Refer to the equations in the Ziegler-Nichols section in the introduction to this project. Record these values and change z_pid.yaml accordingly.
4. Fly your drone with the set of tuning values generated by the Ziegler-Nichols method. Note that the Ziegler-Nichols method should enable safe flight, but will probably not control your drone’s altitude very well! Empirically tune the gain constants in z_pid.yaml on your drone as you did in the simulator portion of this project. ² Record your final tuning values.

Take a video of your drone flying first using our altitude pid by running pid_controller.py in `4, then take a video of your tuned pid by running student_pid_controller.py in `4. See if you can get yours to track the altitude setpoint better than ours! The drone should get to the setpoint quickly and stay there without bouncing up and down. Submit these videos in Github Classroom as ‘original_controller’ and ‘student_controller’

Footnotes

2 Use the graph on the web interface to observe the drone’s behavior as it oscillates around the 0.3m setpoint the drone’s ability to hover at the setpoint. When observing the drone itself, try to get eye-level with the drone to just focus on the the altitude and ignore the planar motion; it is easier to focus on one axis at a time when tuning the PIDs. The planar axes can be re-tuned after you tune your altitude pid if need be.

Tuning 1D Controls: Part 3: Position Control

Modified 2020-07-21 by Rara Ma

Thus far, the planar PIDs have been used to control the velocity of the drone; now, you will use cascaded PIDs to control the position of the drone. The cascaded PIDs are set up so that the position controller forms the outer loop which uses the position error to provide setpoint velocities for the inner loop velocity controller.

How to Engage Position Control

Modified 2020-07-21 by Rara Ma

Engaging position control involves two steps. First you have to tell the drone to “remember” a frame. You can do this using the r key. This will save the frame which the drone will attempt to fly directly above. Next you have to engage position control. You can engage this mode with the p key, and disengage with v for velocity control. So the procedure is to first save a frame (target location for position hold) using r and then shortly after (before drifting too much) type p.

Note: Position hold works best over a textured surface with lots of visual contrast. Even when doing position hold, always be ready to kill in case of a mishap. Especially be careful when looking at other windows.

Position Control Demo

Modified 2020-07-21 by Rara Ma

This video demonstrates the drone doing a zero velocity hover and drifting in the scene. Then we turn on position hold (you can tell when it is engaged when the drone’s throttle drops) and it holds its position for several minutes.

Then we turn off the position hold so you can see it drift again, and then turn it on again at the end and land. You can tell when it is turned on because we move the drone back to the center of the flight area before each hold.

Modified 2020-07-21 by Rara Ma

First, you are going to experiment with flying your drone in velocity control and controlling its motion with the keyboard keys. Based on observations and knowledge of the controllers, you will then explain the inner workings of the velocity PIDs in your own words.

Setup
Prepare your drone to fly over a highly textured planar surface. Make sure there is space for the drone to fly around.
Exercise
Fly your drone in velocity control (the default control) and make sure there is room to fly to the right. Press and hold ‘L’ and observe the drone’s motion, and release ‘L’ to stop the drone from moving.

1. Explain what the following key terms are in this controller, and how they change to cause the drone to move when you press ‘L’ and stop when you release: setpoint, error, control variable, process variable, proportional term, integral term, derivative term. We are looking only for a higher level description to demonstrate understanding of the PID controllers.
2. Try flying in velocity mode over a blank white poster board. Be careful! What do you notice about the drone’s behavior, and what do you suspect causes this?

Modified 2020-09-16 by Rachel Ma

Now you are going to fly your drone in position control and experiment with controlling its motion with the keyboard keys. Based on observations and knowledge of the controllers, you will then explain the inner workings of the position PIDs in your own words.
Setup
Prepare your drone to fly over a highly textured planar surface. Make sure there is space for the drone to fly around.
Exercises
1. Engage position hold using the procedure described above. Observe the drone’s behavior. How is it different from just velocity control?
2. How long are you able to hold position? Ideally you should be able to do this in one spot for an entire battery. If not, try re-tuning your I-term preloads above. If you’re flying on the power supply instead of a battery, the drone should stay in place indefinitely, but you can stop it after 5 minutes.
3. While flying in position control, make sure there is room for the drone to fly to the right and then take note of the desired position in `4 of the screen. Now press the ‘L’ key in the user interface and note the new desired x-position of the drone; it should be 0.1m to the right of the drone’s last position. Explain what the following key terms are in the outer loop position controller, and how they change to cause the drone to move and stop 0.1m to the right after you press ‘L’ in position control: setpoint, error, control variable, process variable, proportional term, integral term, derivative term. We are looking only for a higher level description to demonstrate understanding of cascaded PID controllers.
4. Try flying in position control over a uniform surface such as the floor in 121, or un-patterned carpet. Echo the state of the drone by typing rostopic echo /pidrone/state into an empty window in the screen. Note the position data, and explain your observations of how well the drone is able to estimate its position. How long is it able to hold position? Does the drone move correctly when you use the arrow keys?

Take a one minute video of your drone flying in velocity control, and then engage position control.

Ending The Lesson

Modified 2020-09-16 by Rachel Ma

• Students now should be able to tune their PID loops!

Useful Resources and References

• Teachers can see EdX lectures on PID Control

• Basics of python here