Hi all,
This is my firs post in this forum.
I design simple PID controller (programing Microchip PIC18F2550) based on theory I have learned from Control system on college. I am newbie in PID control, so I am sorry if I ask something what is simple.

I would like whether my controller was designed correctly.
Description:
Heater element 24V 40W is in the aluminum heat sink with blades (size 6cm x 6cm x 1cm block plus 5 blades height 3cm). The temperature is controlled by micro-controller (the PID controller is programmed in the micro-controller) by 19.5V PWM (power source used from old laptop).

Output of the controller is sum of P-control, I-control and D-control. The sign of the output signal is given by the sum of those three control signals. (positive sign = heater is ON, negative sign = heater is OFF - heat sink is cooled by ambient air ). The output (sum of P-control, I-control and D-control) is fed in to PWM 10bit register. So value 0 = 0%PWM Duty cucle and 1023 = 100%PWM Duty cycle. For instance if PID controller output is 767, then PWM Duty cycle is set o 75%. If PID output is 1500 (it is more than 1023) then PWM regisr is set to 1023 (100% PWM).
Ths is how I set the realtion beteen the output signal and power signal for heater element.
Q1: Is that way right or it should be done different way?


The PID controller looks works fine, but I have one problem and I do not know whether it is normal for PID controller or not.
After many tuning tests, I have find out that if I tune the PID controller to reach e.g. 80°C from ambient temperature (system is turned ON) the setpoint is reached with no or very small overshoot, but it regulates the temperature around set-point (+5°C -5°C) slowly - response is slow.

If I tune the PID controller to control the temperature relatively fast around the set-point (+5°C -5°C), regulation works fine around setpoint Picture 2, but at system start up the temperature raise very high over 80°C (up to 120°C and it was still raising even the integral output has started to decrease Picture 1) due to very high integral control output value (area from 20°C up to 80°C is huge what causes that Integral value build up at 80°C up to around 1000 (97%PWM), so heater power 97%.

Picture 1




Picture 2





So there are two options for controller tuning
a) Controller is tuned to reach 80°C from ambient temperature with very tiny overshoot
or
b) Controller is tuned to control the temperature around 80°C

Is this behaviour normal for PID controller or not and my program code is incorrect?

This is the way how I calculate the output of my PID controller:
Error
Error = Set-point - Current temp. (Error is positive if the measured temperature is below the set-point and negative if it is above the set-point)

Proprotional
Proportional output = Error * Kp (Prop. output sign depend on error sign)

Integral
Integral output = Accumulated integral "strips" * Ki (where Ki is integral parameter entered by user)
where
Accumulated integral "strips" = Accumulated integral "strips" + Actual integral strip
Actual integral "strip" = ( (Measured current error - Previous error)/2 ) * T (T= sampling period = 2 seconds), (sign of one integral "strip" depend on Error sign)
Picture 3





Derivative
Derivative output = ( (Measured current error - Previous error) / T )* Kd (T= sampling period = 2 seconds)
The sign of the derivative output is:
1. tempereture bellow setpoint and falling toward setpoint (error decrease) - negative
2. tempereture above setpoint and raising from setpoint (error inrease)- positive
3. tempereture above setpoint and falling toward setpoint (error inrease)- negative
4. tempereture bellow setpoint and raising from setpoint (error inrease)- positive
Picture 4




Q2: Is this PID controller design correct?

Many thanks for help.

 

where you have long "dead times" and a single sensor, proportional only is the easiest to work with and doesn't over drive the system.

 

Dave, thanks for reply.

Yes, you are right Dave. This project is "school presentation project" where I will present different type of controls (P only, PI, PD, PID) and explain which control is best for my plant.

But my problem is that I am designing the PID controller as a program in the microprocessor PIC18F2550.
So I am not sure, whether that behavior (integral control is very high at set-point when system starts up from 20° to 80°C, so it cause that temperature raise up to 120°C) is normal and I have to apply Anti-windup system, or that behavior should not happen and I should to review my PID control equation (program) in micro-controller and check what is wrong there.
By othere words, I need to know whether to fix my program or introduce anti wind up algorithm for system start up.