Lab4_jaleti

Lab 4: The swing up pendulum. (Answer Sheet) ∗ Name: ∗ Part of this write-up and figures were taken directly from Quanser’s lab manuals, Quanser Inc. 1 Joshita Alexi

1 Total energy 1.1 Experiment: the controller using E . Figure 1: Simulink model used with QUARC to run swing-up controller In this experiment, we will design a controller of the form u = sat u max ⇣ k e ( E - E r ) ˙ ↵ cos( ↵ ) ⌘ . (1.1) 1. Run the setup swingup.m file in Matlab. 2. Open and run the QUARC Swingup.slx in Matlab. This should look like Figure 1. 3. Be ready to hit the stop button at any time in case the pendulum goes wild. Place your critical value (minimum value to make the pendulum stand up) E r with k e = 1 here: Place your best k e and E r here: 2 Er = 3500 m5 ~ 34 seconds for pendulum to stand up We = 60 M5s Er = 50 mJ

1.2 Experiment: the controller E with the sign function. In the final experiment, we will design a controller of the form u = sat u max ⇣ k e ( E - E r )sign( ˙ ↵ cos( ↵ )) ⌘ . (1.1) 1. Run the setup swingup.m file in Matlab. 2. Run the QUARC file Swingup sign.slx in Matlab. This should look like Figure 1. 3. Be ready to hit the stop button at any time in case the pendulum goes wild. Place your best k e and E r here: For your best k e and E r place the graph of the pendulum angle here: 4 ke = 30 M5/5 Er = 85M]

2 Kinetic energy 2.1 Experiment: the controller using E c . Figure 2: Simulink model used with QUARC to run swing-up controller In this experiment, we will design a controller of the form u c = sat u max ⇣ k e ( E c - E r ) ˙ ↵ cos( ↵ ) ⌘ (2.1) 1. Run the setup swingup.m file in Matlab. 2. Open the Swingup center.slx in Matlab. This should look like QUARC model presented in Figure 2. Hit monitor and tune to run this file. 3. Be ready to hit the stop button at any time in case the pendulum goes wild. Place your critical value (minimum value to make the pendulum stand up) E r with k e = 1 here: Place your best k e and E r here: 5 Er = 50 ~ 13 . 922 seconds for pendulum to stand up Ke = 10 M5 , s Er = 20 m5

2.2 Experiment: the controller using E c and sign function. In this experiment, we will design a controller of the form u = sat u max ⇣ k e ( E c - E r )sign( ˙ ↵ cos( ↵ )) ⌘ . (2.1) 1. Run the setup swingup.m file in Matlab. 2. Run the QUARC file Swingup center sign.slx in Matlab. This should look like Figure 2. 3. Be ready to hit the stop button at any time in case the pendulum goes wild. Place your best k e and E r here: For your best k e and E r place the graph of the pendulum angle here: 7 We = 45 M5/5 Er = 41MI

3 Potential energy 3.1 Experiment: the controller using E p . Figure 3: Simulink model used with QUARC to run swing-up controller In this experiment, we will design a controller of the form u p = sat u max ⇣ k e ( E p - E r ) ˙ ↵ cos( ↵ ) ⌘ (3.1) 1. Run the setup swingup.m file in Matlab. 2. Open the Swingup PE.slx in Matlab. This should look like QUARC model presented in Figure 3. Hit monitor and tune to run this file. 3. Be ready to hit the stop button at any time in case the pendulum goes wild. Place your critical value (minimum value to make the pendulum stand up) E r with k e = 1 here: Place your best k e and E r here: 8 Er = SOmJ ~ 2 . 8 seconds for pendulum to stand up ke = 3 M5/s Er = 305

3.2 Experiment: the controller using E p and sign function. In this experiment, we will design a controller of the form u = sat u max ⇣ k e ( E p - E r )sign( ˙ ↵ cos( ↵ )) ⌘ . (3.1) 1. Run the setup swingup.m file in Matlab. 2. Run the QUARC file Swingup PE sign.slx in Matlab. This should look like Figure 3. 3. Be ready to hit the stop button at any time in case the pendulum goes wild. Place your best k e and E r here: For your best k e and E r place the graph of the pendulum angle here: 10 Pre = 20 MT/s N2 . b seconds Er = 80 m5

Present a short discussion on which one of the controllers you think performed the best. Explain what di ↵ erences you observed (if any) when using the sign function version of the controllers. 11 I think the controller using kinetic energy and sign function is the best. This is because the pendulum took the shortest time of approximately 2.2 seconds to stand up compared to the other controllers. The pendulum was also more stable and in the graph you can see that there is minimal noise and even oscillation to portray that the controller was stable before standing up. One of the differences I observed when using the sign function version of the controllers is that the time it took the pendulum to stand up was much shorter than the base controller of that particular energy. Also I noticed the Er value for the sign version of the controller is greater than its base controller.