moved library code back to root from sub-folder

when github was adding a hash to the library download zip, there was confusion from beginners about needing to rename the unzipped folder before moving into the arduino ide.
this library has been prepped (thijse) for the arduino library manager, which requires the library to be in the root directory.  Having the library in the manager also removes the "beginner user hash" concern.

examples/PID_AdaptiveTunings/PID_AdaptiveTunings.ino

@@ -0,0 +1,53 @@
+/********************************************************
+ * PID Adaptive Tuning Example
+ * One of the benefits of the PID library is that you can
+ * change the tuning parameters at any time.  this can be
+ * helpful if we want the controller to be agressive at some
+ * times, and conservative at others.   in the example below
+ * we set the controller to use Conservative Tuning Parameters
+ * when we're near setpoint and more agressive Tuning
+ * Parameters when we're farther away.
+ ********************************************************/
+
+#include <PID_v1.h>
+
+//Define Variables we'll be connecting to
+double Setpoint, Input, Output;
+
+//Define the aggressive and conservative Tuning Parameters
+double aggKp=4, aggKi=0.2, aggKd=1;
+double consKp=1, consKi=0.05, consKd=0.25;
+
+//Specify the links and initial tuning parameters
+PID myPID(&Input, &Output, &Setpoint, consKp, consKi, consKd, DIRECT);
+
+void setup()
+{
+  //initialize the variables we're linked to
+  Input = analogRead(0);
+  Setpoint = 100;
+
+  //turn the PID on
+  myPID.SetMode(AUTOMATIC);
+}
+
+void loop()
+{
+  Input = analogRead(0);
+  
+  double gap = abs(Setpoint-Input); //distance away from setpoint
+  if(gap<10)
+  {  //we're close to setpoint, use conservative tuning parameters
+    myPID.SetTunings(consKp, consKi, consKd);
+  }
+  else
+  {
+     //we're far from setpoint, use aggressive tuning parameters
+     myPID.SetTunings(aggKp, aggKi, aggKd);
+  }
+  
+  myPID.Compute();
+  analogWrite(3,Output);
+}
+
+

examples/PID_Basic/PID_Basic.ino

@@ -0,0 +1,31 @@
+/********************************************************
+ * PID Basic Example
+ * Reading analog input 0 to control analog PWM output 3
+ ********************************************************/
+
+#include <PID_v1.h>
+
+//Define Variables we'll be connecting to
+double Setpoint, Input, Output;
+
+//Specify the links and initial tuning parameters
+PID myPID(&Input, &Output, &Setpoint,2,5,1, DIRECT);
+
+void setup()
+{
+  //initialize the variables we're linked to
+  Input = analogRead(0);
+  Setpoint = 100;
+
+  //turn the PID on
+  myPID.SetMode(AUTOMATIC);
+}
+
+void loop()
+{
+  Input = analogRead(0);
+  myPID.Compute();
+  analogWrite(3,Output);
+}
+
+

examples/PID_RelayOutput/PID_RelayOutput.ino

@@ -0,0 +1,60 @@
+/********************************************************
+ * PID RelayOutput Example
+ * Same as basic example, except that this time, the output
+ * is going to a digital pin which (we presume) is controlling
+ * a relay.  the pid is designed to Output an analog value,
+ * but the relay can only be On/Off.
+ *
+ *   to connect them together we use "time proportioning
+ * control"  it's essentially a really slow version of PWM.
+ * first we decide on a window size (5000mS say.) we then 
+ * set the pid to adjust its output between 0 and that window
+ * size.  lastly, we add some logic that translates the PID
+ * output into "Relay On Time" with the remainder of the 
+ * window being "Relay Off Time"
+ ********************************************************/
+
+#include <PID_v1.h>
+#define RelayPin 6
+
+//Define Variables we'll be connecting to
+double Setpoint, Input, Output;
+
+//Specify the links and initial tuning parameters
+PID myPID(&Input, &Output, &Setpoint,2,5,1, DIRECT);
+
+int WindowSize = 5000;
+unsigned long windowStartTime;
+void setup()
+{
+  windowStartTime = millis();
+  
+  //initialize the variables we're linked to
+  Setpoint = 100;
+
+  //tell the PID to range between 0 and the full window size
+  myPID.SetOutputLimits(0, WindowSize);
+
+  //turn the PID on
+  myPID.SetMode(AUTOMATIC);
+}
+
+void loop()
+{
+  Input = analogRead(0);
+  myPID.Compute();
+
+  /************************************************
+   * turn the output pin on/off based on pid output
+   ************************************************/
+  if(millis() - windowStartTime>WindowSize)
+  { //time to shift the Relay Window
+    windowStartTime += WindowSize;
+  }
+  if(Output < millis() - windowStartTime) digitalWrite(RelayPin,HIGH);
+  else digitalWrite(RelayPin,LOW);
+
+}
+
+
+