Module2 - session - Local session 2

Here it is assumed that you have completed the Module2 - project - Setup and configuration and up and including section all of section 4 in Module2 - proj - Project phase 1.

Assuming that one covers this in a 3h lecture the suggested schedule would be

When	What
0:00-1:00	Introduction and section 1 below , do not get stuck on 1.1! (session leader shows)
1:00-1:30	Initial experiment part from section 2 below (i.e. Project phase 1 - Section 5.2) performed together (experiments by session leader)
1:30-	Controller design, experimentation and make video to show off milestone1 (in groups)

Reminder to session leader

Bring

Drone
USB radio dongle
Micro USB cable to charge drone
Stick / pen / something
2 coffee mugs with good ears for experiments in Module2 - proj - Project phase 1
Tape or rubber band to attach stick to drone
Computer running
- Bitcraze software so that you can run Crazyflie client and connect to a drone
- Matlab

1. Modelling, simulation and height control of a UAV

You will play with a Matlab program called uav_height_control.m Download uav_height_control.m

which is aimed at giving you a basic understanding for automatic control and PID-controllers in particular.

You find controllers everywhere. Most of them are simple but they share a common structure. You have some objective you want to achieve. You measure something which is connected to this objective and you calculate a control signal based on this measurement.

Below is a block diagram for a so called PID-controller. You can read more about them on Module2 Control or talk to a WASP colleague that knows all about them. You want to control the output, $y (t)$ $y(t)$ , of the system (process/plant) such that it reaches the reference signal $r (t)$ $r(t)$ . In the example below we will look at the Crazyflie and the output will be the height of the UAV. The reference is the desired height.

Your task is to figure out how to control the height of the Crazyflie.

The UAV is assumed to be on the ground when we start, i.e. h=0, and we want it to get to height 1m, i.e. hRef=r=1.

We assume that

we only have to care about the motion up/down i.e. the height
we give the same control signal to all 4 rotors
we can control the lift force (thrust) directly (i.e. without delay)
the drone will come to an immediate rest at h=0 if h<0

Looking a bit at the system we know that there are two main forces acting on the Crazyflie that influence the height: gravity which pulls down with a force m*g and the thrust from the propellers that generate an upward force F.

The resulting force up is therefore

F = F_thrust - m*g;

Newton's second law will tell us how the UAV moves

F = m * a --> a = F / m

Start matlab and look at the program uav_height_control.m

Try to run it on the command line with uav_height_control(1). This should bring up two windows. One will show the UAV as a blue blob which moves up and down and the other will show the height as a function of time. The simulation will terminate if the drone flies too high. The ground in the simulation is very nice and causes no damage and simply makes the drone come to a rest h=0, hdot=0

Your tasks is to experiment with the controller which is around line 90 in uav_height_control.m.

1.1 Add a model for the thrust as function of PWM duty cycle

The control signal that is used on the UAV is a PWM signal. You give the duty cycle between 0 and 1 of the signal. On a low level you actually give an integer value between 0 and 65535.

Start by performing the experiment in Section 5.1 in Module2 - proj - Project phase 1.

This should give you a model that you can add at line 106 in uav_height_control.m. (A crude model will do for now, such as a linear mapping. If you haven't done the experiment, you can assume the Crazyflie can lift an additional load that equals its own weight.).

Make sure to comment out the warning message on line 105 as well to stopping the massive spamming in your window.

1.2 Constant control action

How large does the PWM duty cycle, ie. the control signal u, have to be for it to compensate for gravity? You should be able to calculate this based on the function you found in the previous section.

Can you come up with a constant control signal that will make the UAV move from h=0 to h=1? Why, why not?

This would corresponds to using a control law that looks like

u=constant

on line 92.

1.3 P-controller

Now we will experiment with a P-controller. Comment out the commands on line 91 and 92

Make sure that line 90 reads

u = kP*e + kD*dedt + kI*eInt;

and that kD=0 and kI=0 just above. This will give you a P-controller where the control signal is proportional to the control error, i.e. the difference between the reference height (1m) and the current height.

How big does kP have to be for the UAV to take off? Could you calculate this?

Can you find a value for kP that make the UAV reach 1m and stay there? If not can you make it reach at least a constant height? What are the limitations?

1.4 PD-controller

Now add the D-part to the controller. This part adds to the control signal a term which is proportional to the derivative of the error. This mean that the control signal will be reduced when the error is reduced and vice versa. This will dampen the system.

Can you make it come to a constant height with proper values for kP and kD? Can you make it reach exactly 1m?

There might be practical challenges with using a D-part: For example, what happens if you increase the noise level (y_std) on the measurements? What happens if you change the reference signal during the run?

1.5 PID-controller

Now add the I-part to the controller. This part is proportional to the integral of the error. The slower the system is when reducing the error the larger this part will become and vice versa.

Can you get rid of the error completely?

Assuming that you managed to get the system to reach a steady state, what can you say about the term kI*eInt? Is it constant? If so, what would that constant be?

It is useful to do an estimate on how fast the UAV in theory can change height from h=0 to h=1. What is the minimum time, assuming the limits on vertical acceleration are -g and +g respectively, and assuming zero velocity at start and stop? (Answer: $t_{m i n} = 2 \sqrt{h / g} = 0.64 s$ $t_{min} = 2\sqrt{h/g}=0.64s$ ).

If time permits: Try to find a PID controller that settles to within h=[0.99,1.01] in less than 1 second.

For control PhD students: If time permits, describe to your colleagues some improvements to the PID control code that you would consider in a real implementation (antiwindup, filter on derivative part, dont derivate reference signal, ...)

1.6 Test on the real UAV

Naah, we cannot do that because

We need a controller to stabilize the position in x,y as well if we are to fly and
we need measurement information about the height y to feed into our controller, such as from a local positioning system (LPS)

2. Modeling and control of the yaw angle (Milestone1)

Now let us turn our attention to controlling the yaw angle of the drone.

We will start by performing the modelling experiment in Section 5.2 in Module2 - proj - Project phase 1. The experiments performed there will have given you the information you need to figure out how to use the PWM signal to the motors to generate torques. For the rotational motion of the drone, Newton's second law for rotation states that $T = I \frac{d ω}{d t}$ $T = I \frac{d\omega}{dt}$ , where $T$ $T$ is the torque, $I$ $I$ is the moment of inertia and $ω$ $\omega$ is the angular rate (yaw rate in our case) and thus $\frac{d ω}{d t}$ $\frac{d\omega}{dt}$ the angular acceleration (second derivative of the yaw angle).

We could proceed and measure the moment of inertia $I$ $I$ but we will not in this case. We will show that one can design a controller without detailed knowledge of the process. We know how the control signals influences the state of the system, and as you will hopefully show soon, this is enough. As you will soon find out a bigger limitation of the model as described so far is that we have neglected friction. Friction will be quite significant when the UAV is standing on the table.

How can you reduce the influence of friction in our case? Think of what you need to do to make it fly and what that would do to the friction.
We need to be able to rotate the platform in both directions. How would you make the platform rotate clockwise? And counter clock-wise? Ideally we would want the drone to stand still and rotate. Does your strategy take that into account?
How to accomplish both 1 and 2 above?

We have prepared a new version of stabilizer.c that you can start from. It is called stabilizer_session2.c Download stabilizer_session2.c

. Make sure that you are standing in the directory with the crazyflie-firmware. Make a backup of the previous version by executing

cp src/modules/src/stabilizer.c stabilizer_backup.c

Now download the new version of stabilizer and replace stabilizer.c with this version. Assuming that you have it in your Download folder this would mean executing

cp ~/Downloads/stabilizer_session2.c src/modules/src/stabilizer.c

Take a look at the code so that you understand it. Adjust the section in the code around lines 231. You can make that code run by changing yawCtrlMode the Parameter tab in the Crazyflie Client to 2.

We suggest that you first test your ideas from above with a simple if-then type controller to show that you can make the Crazyflie rotate in the right direction.
Then you can try to implement a PD controller. The yaw rate is measured by the gyro and you access it via sensorData.gyro.z.

Document a successful series of yaw changes with a short movie showing the Crazyflie and the logging screen and submit it in Canvas.

Congratulations, you have now passed Milestone 1 !