**Physics 37100
Advanced Physics Laboratory I**

**Lab #5**

(PART I: PID---The Process Function)

1)
The process
function V(n) of a PID controller maps the control
variable n to the process variable V. That
is V=V(n). You will make a PID controller to control
the average brightness of an LED as measured by a photoresistor. In this system the process variable V will be
the measured average brightness of the LED in counts 0-1023, and the control
variable n will be the value sent to analogWrite() to
change the brightness of the LED. To
begin you will measure the process function V(n). From lab 3 and 4 we know that the LED driven
by analogWrite() is pulse-width-modulated (pwm). That means that it is actually turning on and
off, but at a high enough rate to not be noticed by
our eyes. In lab you found that the
frequency is ~490Hz. Use the function getPhoto() (below) to measure the average brightness. getPhoto(na,dta) takes 2 arguments. na
is the number of averages and dta is the sampling
time. The exact period of the pwm output is 2040us so we take 15 samples at 136us each to
give 2040us total. By averaging over
exactly one cycle we eliminate some noise.
Briefly explain why?

a. Use getPhoto() to measure and plot V=V(n) for every value of n [0,255],
where n is the input to analogWrite(n) and V is the
value of getPhoto().
You should pause about 100ms between changing analogWrite() and measuring
the brightness using getPhoto().

float getPhoto(int na
= 15, int dta = 136) {

int n;

unsigned
long dt;

float
vS = 0;

for
(n = 0, dt = micros(); n < na; n++) {

while (micros() - dt < dta);

dt = micros();

vS += analogRead(inPin);

}

return
(vS / na);

}

b. From the plot of the process function V(n) estimate
the maximum value of the variable P in a proportional controller given by the
equation n=P*e, where e=Vset-V is the error and Vset is the control set point. Use Vset=V(10) for the estimate.