Merge pull request #57 from TTK4130/assignment-8

Added assignment 8 to the page

docs/assignments/assignment-8.rst

@@ -0,0 +1,89 @@
+=============================
+Assignment 8 - Bond Graphs II
+=============================
+
+.. note::
+
+    Submit your assignment as a single PDF, including plots and source code (if any).
+    We expect academic honesty. Collaboration is encouraged, but must be declared. Any use of AI must be declared along with any other sources used.
+    This is not an exam. Do your best and show that you put in effort and the assignment will be approved.
+
+In this assignment we will develop bond graphs for three different systems. A mechanical system, an electrical system and a hydraulic system.
+
+Problem 1 - Pendulum on an oscillator
+-------------------------------------
+
+.. figure:: ./figures/assignment_8/pendulum_osc.png
+    :width: 100%
+    :align: center
+    :name: assignment_8_pendulum
+
+    Pendulum on a vertical oscillator.
+
+We will revisit the oscillating pendulum one last time. 
+This time we will use bond graph to model the system.
+
+Figure  :numref:`assignment_8_pendulum` shows a sketch of the system. 
+A pendulum with a point mass :math:`m_2` is attached to a mass :math:`m_1` that can oscillate along a vertical axis. 
+The pendulum rod has a length :math:`L` and the rod can be considered mass-less 
+(i.e. the pendulum can be considered as a point mass at the end of a mass-less rod).
+
+The oscillating mass is connected to a stationary construction through a spring with stiffness :math:`k`. 
+The vertical position :math:`z` of the mass is defined such that :math:`z = 0` when the spring is in its neutral position.
+The angular displacement of the pendulum rod is :math:`\theta`, as shown in the figure. 
+For simplicity we also constrain body one to only move up or down, i.e no movement along the :math:`y_0` or :math:`z_0` axis.
+
+.. admonition:: Tasks
+
+    a. Draw a bond graph for the system, as described above. Include gravity force on the two masses.
+
+    .. hint::
+        :class: dropdown
+
+        A good starting point is to place a 1-junction for each relevant velocity.
+        In this case, you will need a velocity representing the vertical movement of the oscillating mass, and two 1-junctions representing the horizontal velocity and the vertical velocity of the pendulum mass.
+        In addition, you will need a 1 junction for :math:`\dot{\theta}` because the vertical and horizontal velocity of the point mass on the pendulum is a function of :math:`\dot{\theta}`.
+        You then need to establish a relationship between them using MTF-elements and 0-junctions.
+
+    b. Now include linear friction on the motion of oscillating mass and the pendulum hinge.
+
+    c. Assume now that the mass at the end of the pendulum is not a point mass but a sphere with mass :math:`m_2` and moment of inertia of :math:`J_2`. Update the bond graph to account for this.
+
+
+Problem 2 - Electrical circuit with a battery
+---------------------------------------------
+
+.. figure:: ./figures/assignment_8/electrical.png
+    :width: 100%
+    :align: center
+    :name: assignment_8_electrical
+
+    Electrical circuit with a battery.
+
+Figure  :numref:`assignment_8_electrical` show an electrical circuit powered by voltage source :math:`u(t)`. 
+The task is to develop a bond graph for this system. 
+The parameters for the two resistors, two capacitors and the inductance, are :math:`R_1` and :math:`R_2`, :math:`C_1` and :math:`C_2`, and :math:`L` respectively.
+
+
+.. admonition:: Task
+
+    Make a bond graph for the circuit.
+
+
+Problem 3 - Single acting spring return hydraulic actuator
+----------------------------------------------------------
+
+.. figure:: ./figures/assignment_8/hydraulic.png
+    :width: 100%
+    :align: center
+    :name: assignment_8_hydraulic
+
+    A single acting spring return hydraulic actuator powered by a hydraulic pump.
+
+Figure  :numref:`assignment_8_hydraulic` shows a hydraulic system were fluid can be pumped from a reservoir and into to single acting hydraulic actuator, or back to the reservoir via a controllable valve.
+The opening area of the valve can be controlled though the signal :math:`u(t)` to return fluid to the reservoir and hence reduce the pressure on the hydraulic actuator.
+When the pressure is low enough, the spring will return the hydraulic actuator piston back to the position :math:`x = 0`.
+
+.. admonition:: Task
+
+    Draw a bond graph for this system where :math:`P_a`  is the atmospheric pressure.

docs/assignments/index.rst

@@ -14,3 +14,4 @@ Assignments
     assignment-5
     assignment-6
     assignment-7
+    assignment-8