Electrical – When to use analog PID

analogconstant-currentoperational-amplifierpid controller

So I am building a rather simple constant current load to test power supplies. I am using an INA138 for high-side current measurement with only 5V power (and I have reasons for that, unfortunately) and a couple of opamps to control the current through the Q1 mosfet. On the schematic, VCC is 5V power, CURSENSE is the voltage proportional to the current passing through the R1 resistor and Q1 mosfet and CONTROL is some voltage setting the constant current (e.g. DAC output or well-filtered PWM straight from a uC). The power input is on the left.

At first, I tried to simply put an opamp in a comparator mode. The schematic started oscillating and crashing in the simulation. Then I tried to lower the error amplifier gain to 100 V/V (second schematic). This schematic kinda works in the simulation, however, that raised a number of questions in my head.

Since I've essentially created an analog PID controller with only proportional coefficient in the second schematic – do I need to implement a full-scale analog PID controller (like the one in this question) with an integrator and differentiator or will the second schematic be sufficient?
When exactly (excluding cases with mechanical systems and such) do I need to implement a PID controller or lower the error amplification gain? For example, a simple opamp voltage follower is also essentially a controller that tries to set it's output voltage equal to the input one and somehow it is fine without PID or gain reducement.
If I only need to lower the gain – how should it be selected?
What could be the requirements for the error amplifier opamp?

Best Answer

Since I've essentially created an analog PID controller with only proportional coefficient in the second schematic - do I need to implement a full-scale analog PID controller (like the one in this question) with an integrator and differentiator or will the second schematic be sufficient?

If you don't need to adjust the I or D component, then don't include them. Many controllers are only PI controllers. The question is, "what do you need to be adjustable?", and "what controller is suitable for the final design?". No two components are created equal, if component tolerances affect the operation of the controller (which they almost always do) then you'll most likely need to adjust the gain. If the pole is changing with component tolerances then it might be wise to include I to compensate for changes in frequency.

The best thing to do would be to include the full PID controller for testing, and then reduce it to a bare minimum for production.

If I only need to lower the gain - how should it be selected?

Either by trial and error, preferably with a variable resistor or by actually calculating what the gain should be with a controller/plant model and by using control theory.

When exactly (excluding cases with mechanical systems and such) do I need to implement a PID controller or lower the error amplification gain? For example, a simple opamp voltage follower is also essentially a controller that tries to set it's output voltage equal to the input one and somehow it is fine without PID or gain reducement.

The feedback path of a simple voltage follower has a gain of 1, and the plant has a gain of 1 which makes it a stable system. The problem with control systems is they go unstable when the phase on any given frequency reaches -180, then you get positive feedback.

Related Solutions

PID controller algorithm for sr90 digital controller

The key to good engineering is to keep it simple. In your case, you can use something very simple to turn on/off a relay to control a heater. A psuedo code:

int temperature;
int setpoint;
int status = 0;
int pulses = 0;
int integral = 4;
int derivative = 5;
int upperTemp = 1000; //100.0C
int upperLimit = 100; //pulses per time frame
int counter = 0;

//NO PULSING
runtime //make a timer that runs and updates temperature value
{
  read temperature; 
  temperature *= 10; //still keeping in int for faster processing
  status = ((setpoint - temperature)*integral)/derivative; //EX: (800-400)*4/5 = 320
                                                           //EX: (800-780)*4/5 = 16
  status = abs(status); //get absolute value, this for for within range
                        //(800-850)*4/5 = -40 -> ABS(-40) = 40
  if(status < 16)  //from example, 16 means that value is within 2*C, you can always 
    Relay Off;     //change this value to something else (e.g: (800-795)*4/5 = 4
  else             //4 gives 0.5*C tolerance range...which is a bit tight for temp.
    Relay On;      //anyway, play around with this value;
                   //you can also change integral and derivative if you wish.        
}

//WITH PULSING
runtime //make a timer that runs and updates temperature value...lets say every second
{
  read temperature; //every second
  temperature *= 10; //multiply by 10 for decimal place, but still keeping in integer
  pulses = map(temperature, upperTemp, 0, 0, upperLimit); //when temperature increases, 
                                                          //pulses decreases...vice versa
  //take this value of pulses to update the timer interval
  //timer's interval = pulses per second or minute
}

timer
{
  if(Relay On)
    Relay Off;
  else
    Relay On;   
}

//borrowed from arduino
long map(long x, long in_min, long in_max, long out_min, long out_max)
{
  return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}

//PWM method: still need the runtime with pulsing from above. Let's say you get 75 pulses, this means that the relay will be on for 75% of the duration of each pulse and off for the other 25%. Let's say that you want to have a frequency of 1s (1000mS). Relay will be on for 750mS and off for 250mS. If the temperature is very far away from setpoint, then it might even be on for 100% of the time.

//choose entire duration by tick_interval*percentage: 100mS*100 = 10000mS or 10seconds. Back to example. If you have 75 pulses, then relay will be on for 7.5 seconds and off for 2.5 seconds.

timer //example 100mS per tick
{
  if(counter > 100) //has reached the end of time period
    counter = 0;
  if(counter > pulses) //pulses from above is now the duty cycle
  {
    if(Relay is On)
      Relay off;
  }
  else
  {
    if(Relay is Off)
      Relay on;
  }
  counter++; //increment by 1
}

//this method is more flexible than using a fixed number (30 minutes) because different heater controllers respond differently

Electronic – Astrom-Hagglund Relay PID tuning – relay transfer function

Your second PlantInput description is correct.

Relay tuning relies indeed on input steps whose sign depend on the sign of the error. An IEEE Control System Society file also graphically shows it.

The diagram you posted is ambiguous, but interpreting the relay block as a sign function rather than a gain (which is usually of triangular shape) would dissolve your confusion and have it agree with your intuition.

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Related Solutions

PID controller algorithm for sr90 digital controller

Electronic – Astrom-Hagglund Relay PID tuning – relay transfer function

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