How to stabilize this control system?

Question

I have a control problem with saturation. It is nearly linear in the non-saturation zone.

Problem:

Occasionally I measure huge error spikes. They must not disturb my control routine. I want to get down to 50% (of the reference voltage) in my output voltage. In the moment I do this by stepping one step up or down depending on whether the output is bigger or smaller than 50%. This leads to oscillations.

Oscillations:

If I wait some bigger time before measuring the output voltage and then adjust the control voltage the oscillations go down. But this also extends my start-up time which is a problem as I don't know which control voltage value delivers 50% output voltage. I have to search quite a time.

How can I control the oscillations without slowing down my sampling rate?

In PID control it is said that the stationary error is reduced to zero if an integral part is added but how can I do something similar here?

Otherwise what would your approach to control this thing be?

Answer 1

If you have huge transient error spikes, then you need a derivative part (i.e the D in PID) to handle these.

A simple PID system is not hard to write in code, it's the tuning that's the difficult part - you need to know roughly. The integral part will handle the DC offset, the proportional part the gain, and the derivative the reaction to change.

Here's some code I wrote for a temperature controlled etching tank I made with a PIC16F and a DS18B20 temp sensor ages ago (it used some nichrome wire driven via PWM wrapped round a couple of ceramic tiles for the heating element, so it had a large thermal capacity)
The results, once tuned, were an overshoot a of less than 2 degrees on power up, and a variation of less than a degree or so thereafter. It's very old code for a one off project thrown together quickly, so it can probably be improved a fair bit.
I found this document "PID without a PHD" quite helpful. Also, Matlab, Scilab or Octave can be used to simulate and tune PID systems.

/** Control variables **/

int DEADBAND = 0;   // Range where no change will be made

// PID gain values 
double Kp = 10;
double Ki = 0.02;
double Kd = 5;

// Accumulator variable for Integral calculation
double I_acc = 0;

// Returns out the proportional term
double get_prop(int error)
{
    double p;
    p = (Kp * error); 
    return p;
}

// Returns the integral term
double get_int(int error)
{
    double i;
    I_acc += (error);

    i = (double)(Ki * I_acc);
    if(i > 1000) i = 1000;
    if(i < 0) i = 0;
    return i;
}

// Returns the derivative term
double get_deriv(int error)
{
    double d;
    static int prev_error;
    d = (Kd * (error - prev_error));
    prev_error = error;
    return d;
}

double get_pid(int error)
{
    double result;
    double p, i, d;

    p = get_prop(error);
    i = get_int(error);
    d = get_deriv(error);
    result = p + i + d;
    return result;
}