Minor formatting edits

Author: alchemyst

2_Control/6_Discrete_control_and_analysis/Discrete PI.ipynb

@@ -191,7 +191,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Reconstruction\n",
+    "## Reconstruction\n",
     "Here is the direct reconstruction of Figure 11.10. Turns out they use a continuous PI controller with the parameters for a discrete controller."
    ]
   },
@@ -244,7 +244,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Discrete responses"
+    "## Discrete responses"
    ]
   },
   {
@@ -295,14 +295,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This looks different from the given figure, but the position form and velocity form look identical. Note that the analog PI controller gets better results than the digital approximations with the same controller parameters."
+    "This looks different from the given figure, but the position form and velocity form look identical. Note that the analog PI controller gets better results than the digital approximations with the same controller parameters. \"Better\" in this context means that in general the error is smaller (note the worst case error in the analog case is about 5, while in the digital case it's almost 7."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# With output limits\n",
+    "## With output limits\n",
     "Now, let's include limiting behaviour"
    ]
   },
@@ -354,14 +354,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The windup on the position form PID is very clear."
+    "The windup on the position form PID is very clear. In the \"wound up\" case, the output is stuck at the limit for a long time as the controller has to unwind the integral before moving away from the limit. In the velocity form, the output comes away from the limit much faster."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# With setpoint tracking"
+    "## With setpoint tracking"
    ]
   },
   {
@@ -373,7 +373,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -436,7 +436,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.6"
+   "version": "3.7.9"
   }
  },
  "nbformat": 4,