Saturday, October 17, 2015

Fun with PIDs

PID?  What the heck is a PID?

According to Wikipedia, PID is a Proportional-Integral-Derivative controller (PID controller) which is any kind of control loop feedback mechanism.  These controllers find common usage in industrial control systems.

What a PID controller does is continuously calculate an error value as the difference between the measured value of something that is changing and the desired value.

Perhaps a simple example is in order.  Let's say you want to fill a pan of water at a specific temperature from the tap.  You have two sources of water, cold and hot.  You will need to control the mix of hot and cold water to obtain the desired temperature which you are going to measure with your finger.  So you start with a guess of the hot and cold water settings, measure the result and adjust the hot and cold flow until satisfied.  Making a change that is too big may result in overshooting or undershooting the desired temperature.

Lets call the water temperature sensed by your finger the "process variable" or PV.  The temperature that is desired, let's call the "set point" or SP.  The amount of change of the water flow mix of hot and cold, let's call the "control variable" or CV.  And lastly, the difference between the measured temperature and the desired temperature is the "error" or e.

The most obvious way to change the water flow is in proportion to the current error.  The bigger the error, the bigger the change.  A slightly more complex methodology might want consider the rate of change of the error adding more water flow control depending on how fast the error is approaching zero (a derivative action).  Another refinement might be to consider some historical accumulated error information to detect whether the temperature is settling out too low or too high and make the appropriate corrections (an integral action).  Another way to perform this integral action would be change the current water tap position in steps proportional the current error.

When making changes that result in overshoot or undershoot of the desired set point, continuing to do so will result in oscillations around the desired set point that either grow or decay with time.  If the oscillations decay, the system is stable.  If they grow, the system is unstable.  If they remain at a constant amplitude, the system is marginally stable.  The desired goal is a gradual convergence to the desired set point, so the controller may try to dampen future oscillations by tempering its adjustments by a process called reducing the loop gain.

When the controller starts from a stable state with no error (PV = SP), any changes made by the controller will be in response to changes in other inputs to the process that affect it.  These changes are known as disturbances.  An example of a disturbance in our simple system described above would be a change in the tap water temperature caused by an external event such as the water heater deciding to turn on its heating element.

In theory, a PID controller can be used to control any process which has a measurable output (PV), a known ideal for that output (SP) and an input to the process (CV) that will affect the PV.  So, as you can see PID controllers find uses in any problem domain that needs to regulate temperature, force, speed, pressure, flow rate, weight, position and just about any other variable for which a measurement exists.

So, now just a little bit about the theory of PID controllers.  The name as we have seen above comes from its three terms (Proportional, Integral and Derivative) which are summed to calculate the ouput of the controller.

The clasasic formula for the algorithm (from Wikipedia) is:

   Kp - Proportional gain.  These first three are algorithm tuning parameters
   Ki  - Integral gain
   Kd - Derivative gain

   e   - Error = SP - PV

   t   - Time or instantaneous time (the present)
   T  - Variable of integration (takes values from time 0 to present time t)

What is desired is a controller that will smoothly make adjustments to the desired set point with minimal over-shoot and under-shoot.  Directly implementing this formula in code would lead to some simple solutions that would most likely suffer from a number of short-comings such as the following:

  • Sample Time - The formula requires recalculation at a regular interval since both integration and derivatives are a function of time.
  • Derivative Kick - Any time the set point (SP) is changed, the error is changed (SP-PV) and the derivative of this change is infinity.  In practice however, since the change in time is never zero, it ends up being a very big number which when fed into the calculation results is an undesirable spike in the output.
  • On the fly Tuning Changes - Changes in the three tuning parameters affect the integration of the error value over time.  Any change in Ki will be multiplied by the entire error sum that has been accumulating when we really only want it to affect the result going forward.
  • Reset Wind-up - Most controllers have some limit on operational ranges.  For example a water valve can only be set in the range of completely closed to completely open.  If the PID controller does not know about these ranges, it may calculate an output value that is out of range.  Over time when it tries to continue to add more water flow beyond maximum, only to have it clamped by the physical size of the pipe, the algorithm will continue to ask for more and more beyond the limit.  The result is that the output gets "wound up" way beyond the maximum limit.  Where the problem reveals itself is when the set point (SP) is dropped, the algorithm needs to wind back down again to the maximum before it will even affect the output.  This results in what looks like a lag in response of the controller to the new set point.
  • Switching the PID Controller on/off - This occurs when you validly decide that regardless of what the PID controller is doing, you want to override its decision for a period of time.  Now, when you stop overriding it's decision, you get a sudden, huge change in the output.  The controller keeps trying to adjust the output to get the desired result, but it doesn't see any change, so it adjusts the output a little more and so on.  It would be like externally overriding a volume control of a stereo system while trying to adjust the volume internally.  No change internally has any effect.  Then you switch off the external override and suddenly you have a huge volume change.
  • Initialization - While it is useful to be able to turn off the PID and set your own override, when you turn it back on, the PID jumps back to the last output value it had set resulting in another spike in the output.  These transitions need to be seamless.
  • Changing Direction - The PID algorithm may be used to drive a system that is either "direct acting" (an increase in the output causes an increase in the input) or "reverse acting" (an increase in the output causes a decrease in the input).  A refrigeration system for example is a reverse acting system as an increase in the cooling results in a decrease in temperature.  Changing the sign of Kp, Ki and Kd allows proper control of a reverse acting systems.
Rather than detail the solutions for all of these potential issues, let me refer you to a most excellent blog by Brett Beauregard detailing the improvements one-by-one starting with the most basic code example.  It is a great read and not one I could not improve upon.

There is a great PID implementation for the Arduino also available at the Arduino Playground which will be the subject of my next posting.

Sunday, October 11, 2015

Postage Stamp Micro-controller

I have updated my ATMega328 controller board with a new layout to fix the previously posted deficits and have sent the gerbers off to OshPark for production.  Hopefully I will have the set back in a week or so.  After validation, I will make the design public at OshPark so anyone interested can purchase the boards.  This is a one inch square PCB with an ATMega328 processor, full set of IO pins and programmable via an ISP connector.

See my previous postings for the schematic and further details.  This was originally a project done for purposes of learning how to use KiCAD.

Sunday, September 20, 2015

Arduino Satellite/Sun Tracking

I have put together the recent bits and pieces of test code that I have been playing with to control my AZ/EL servo camera mount and an Arduino port of the old Plan13 code, originally written in Basic back in 1983 by James Miller G3RUH.  You can read about his efforts over on the AMSAT web site here.  Jim gives a great treatment of the math involved and example code in Basic.

A port of the code described on the page above has been made to the Arduino and I leveraged this code from the QRPTracker project web site.  With some simple changes, I have pulled together a simple satellite tracker to drive my AZ/EL camera mount.  It should be simple to scale this up to drive an actual satellite antenna array.

Here you can see the project pointing to the point in the sky where the ISS would be located at a point in time today.  I took the AMSAT Keplerian elements and processed the six passes today where the satellite was above the horizon at my location.  The code currently processes the entire 24 hour period in a day, and tracks in real time each of the passes.

The implementation of Plan13 is not particularly accurate due to the limited precision available in single precision floating point on the Arduino, but with the broad bandwidth of most amateur 144 and 440 MHz antennas, it is of little consequence even if the accuracy was only to the degree level.  In fact most low earth orbital satellites can be worked with a fixed elevation on a standard yagi, but the project has been interesting.  If there is interest, I will post my code, though most of it was gleaned from the efforts of others.

Beyond the code I have previously published, I have changed the mapping of the azimuth servo to be clockwise from north to match a magnetic compass.  I limit the calculated elevation values to those angles physically possible with my AZ/El mount.  I prevent movement of the servos if the satellite is currently below the horizon.

I would like to put a real-time clock in the circuit and have it calculate and pre-position the antenna to the point where the satellite rises, add a simple display, add the ability to load Keplerian elements from a wifi connection to the internet and provide for calibration of the servos.

On an Arduino Uno, I am able to load the entire two line elements (TLE) set from here into flash.  I have written a routine that will print out the start of every visible pass for my location for every satellite in the list (89 of them).  I suspect that it will be unusual to have the entire set in flash at any given time, but it can be done and still have room for the code.  Alternatively a storage card could be used to store the data.

On the mighty Arduino Uno, this table fills much of the flash and calculating the position of all 89 satellites for every minute of a 24 hour period takes quite a while.  A better approach might be for the process that grabs the KEPS also pre-calculate the start of pass and just generate a table along with the KEPs table.  This table could then drive a higher level process  to allow the selection a which satellites you want to track today.

The code calculates the effects of doppler and provides a tuning frequency for both the uplink and downlink if the frequencies are provided prior to the calculation.  For now I am passing in zeros, but a table of satellite frequencies and a bit of glue code to drive tuning a transceiver could fully automate tracking and tuning tasks.

This has been lots of fun and a precursor to building a LEO satellite station, but for this particular hobby AZ/EL mount, my next task will be to calculate the position of the sun and use this mount to keep a small solar panel array pointed at the sun for battery charging.  For that particular task, I am thinking of trying out a couple of approaches.  The first would be to calculate the position of sun relative to me as an observer.  The second would be to use an analogue approach where the output of the solar panel is used as feedback to drive a correction to the AZ/EL servos to keep the panel at maximum output regardless of the position of the sun.  I suppose in theory, I could just set the device out in the sun and let it figure out where to point to maximize output.  Who knows, it might decide to point at a white wall rather than at the sun when currently behind tree cover for example.  Should be fun!

Sunday, September 13, 2015

Arduino and Servos

This little project has been lying around waiting to be done for far to long, so I have resurrected it on a rainy Sunday and hope to make something useful out of it.

I have this little AZ/EL camera mount pair of servos that are quite stout.  They have external feedback potentiometers for the servo position, so even though they are geared down, they can be accurately positioned.

Coupling these up to an Arduino UNO is trivial.  I need one signal pin, power and ground.  Do not try to power servos from the USB power on the Arduino, use an external power supply.

The first task at hand was to decide on the range of pulse widths that would be allowed for the servo.  The defaults are 544 us to 2400 us.  The APIs decide that if you set a pulse width less than the minimum, then it must be an angle in degrees 0-359.  I didn't take the time to sort this out.  Instead, I decided arbitrarily that angle zero is 500 us. and everything is counterclockwise from there.

I placed a mark on the Azimuth gear right at the servo gear and through experimentation determined that a change of 768 microseconds would rotate the gear 360 degrees.

From there, it was simple to create a function that would convert an angle in degrees to the required microseconds pulse width to position the servo as desired.

// For the azimuth servo, angle is mapped 0-360 degrees to 500-128 us
int deg2usAZ(int angle)
  return map(angle, 0, 360, 500, 1268);


Now in the case of the elevation servo, we have some limitations to the range of motion due to the physical characteristics of the assembly.  I decided first to figure out where level was and call this zero degrees of elevation.

Next I determined the setting for negative 45 degrees of elevation (pointing down).

And finally, I determined the setting for pointing straight up.  Now it was trivial to create a function to map degrees to these settings.

// For elevation servo, angle is mapped from -45-90 to 1112 to 2220 us
int deg2usEL(int angle)
  return map(angle, -45, 90, 1112, 2220);


Now with the addition of a button, I have a simple test application that will postion to zero degrees azimuth and elevation when started and then move to 90 degrees elevation and 45 degrees of azimuth when the button is pressed..

// Servo test code

#include <Servo.h>

int button1 = 4; //button pin, connect to ground to move servo
int press1 = 0;

Servo servoEL;
Servo servoAZ;

void setup()
  pinMode(button1, INPUT);
  servoEL.attach(7, 500, 2400);
  servoAZ.attach(9, 500, 2400); 


  digitalWrite(4, HIGH);

// For the azimuth servo, angle is mapped 0-360 degrees to 500-128 us
int deg2usAZ(int angle)
  return map(angle, 0, 360, 500, 1268);

// For elevation servo, angle is mapped from -45-90 to 1112 to 2220 us
int deg2usEL(int angle)
  return map(angle, -45, 90, 1112, 2220);

void loop()
  press1 = digitalRead(button1);
  if (press1 == LOW)


So, next I obtained the Arduino port of Plan13 which is a port of some very old basic code for determining a satellite location given the latitude/longitude/elevation of an observer, the Keplerian Elements for the satellite of interest and the date/time of interest. Keplerian Elements (or just Keps), named after Johann Kepler [1571-1630] are a set of seven numbers called satellite orbital elements that define an ellipse oriented about the earth and place the satellite on the ellipse at a particular time.

I have the Arduino port of Plan13 up and running and calculating azimuth and elevation values.  The precision is really insufficient on the Arduino to have very accurate calculations due to the fact that double precision floating point is required, but the Arduino defines double precision as a single precision value.  So the calculations do not have the precision they might otherwise have, but I find it is quite sufficient for simple experiments like this.

The remaining work is to provide a little more glue logic to have what amounts to a desktop pointer to the satellite as it passes overhead.

More to come.

Saturday, September 5, 2015

Salmoncon X QSL cards

July 10-12 this year our QRP ham radio group had our annual camp-out at Valley Camp in North Bend, WA.  We have a lot of fun hanging out together and have great technical talks as well as ham radio operating at QRP levels (low power).  We also have fun activities like hidden transmitter hunts.  Here are a couple of the participants on the hunt.

This year, the group had about 100 contacts split 75%/25% between US and DX contacts.  Since this was the 10th annual event, I decided to make up some custom QSL cards to send to all the contacts we made over the weekend.

I got all of these cards finished up today, addressed, stamped and in the post.  So if you worked K7S during the weekend of 10-12 July, look for your QSL card in the post soon.

Arduino Experiments with Serial Speed

I have been having a play around with seeing how much serial speed I can get out of a standard Arduino Uno when it isn't really doing anything else.

I decided to try 1M baud initially on the standard Serial port.  The code I used is as follows:

void setup() 

void loop()
  unsigned int a = 0;
  } while (++a > 0);  


I didn't even consider using the standard Serial Monitor application built into the IDE and instead grabbed a copy of PuTTY and set the serial port up at 1000000 baud.

At this baud rate, the Arduino had no issues and PuTTY correctly decoded the serial stream without issue.  So, if 1M is good, then 2M should be twice as good, right?

Well, not exactly.  at 2,000,000 baud the per character rate is twice the rate, but the overall throughput actually dropped visibily.  By my crude measurements, the throughput dropped by about 15%.  But, it is good to know that Arduino can push serial bits out at a respectable speed.

One side effect to note is that the IDE must override the Serial baud rate in order to program the device.  When running at these very fast serial rates, it can be a bit hit and miss.  If you have trouble, press the reset button and release it just before the compile finishes and you will help it recover.  Another alternative would be to use an external ISP programmer.

Another thing to keep in mind is that the IDE and PuTTY are both going to try and use the same COM port.  The IDE will use it for programming the chip.  PuTTY will use it to monitor the serial output.  In order for the IDE to be able to program the chip, it must be able to open the serial port.  So, you will have to terminate PuTTY before attempting to reprogram the Arduino.

I have read a lot of complaints lately about trying to debug Arduino code with the serial port output.  While upping the serial speed will not help in situations where interrupts are disabled or where time required to output debug data adversely affects the running code, being able to output the data orders of magnitude faster is certainly going to help in general.  If you are doing a lot of edit, compile, flash, run cycles, it might be better to use an ISP programmer so that PuTTY or whatever serial terminal application you use can stay connected to the debug serial port.

In my work with faster embedded processors, 2-3M baud is about the limit even on these devices with much faster core and peripheral clocks.  The Freescale K60 for example is running at 96 MHz in my configuration and at 2M baud on the debug port, I still get data loss, but it is solid at 1M baud.  I think that for high speed output or where you need to output debug information during interrupt processing, it may be a better choice to use SPI for debug output to a dedicated device that can capture and save the output such as a PC with a USB/SPI interface or another Arduino that can write to a storage device such as an SD card.

Tuesday, August 18, 2015

Android Phone (Samsung Galaxy Note 4) Power Usage

I was playing around recently with my Android phone and decided to take a look at it's power consumption when charging from my laptop USB port.

While the device comes with a quick charge power adapter, my little USB power meter is not expecting to draw a couple amps from a USB circuit, so in the interest of not damaging it, I gave it a standard USB 2.x port as a power source.  As we can see it is quite hungry and draws a consistent 2.1 watts in this mode, with only about 75 mA headroom on a standard USB charging rate of 500 mA.  The device does not seem to change its power consumption when using the device while charging or allowing it to sleep.  The device uses the typical method of various sense resistor values between the USB pins to determine if the special charger is in use or a standard one to limit current draw to USB specifications.

When charging on the quick charger, I am seeing about 1.27 amps when measured with my multi-meter, but it seems to walk around a bit from about 1.0 to 1.45 amps.

Once the charger has brought the battery up to 100% charge, I put it back on my little USB power meter and find a much more respectable 43 mA current draw.  Again, it doesn't seem to matter if the display is lit or not.