Confuse in PID concept need help

[ep.hobbyiest]

i am doing pid temperature controller. so now reading the PID theory. But i am confuse at proportional band. what is exactly proportional band.
Means if i have set 70 degree Celsius. then what will be proportional band.
Gain is reciprocal of proportional band. right??

 

[horace1]

the simplest control is ON/OFF where you apply power until the required temperture is reached when it is switched off. When the temperature falls below the required temperature power is switched on again. the Problem is that the power can be switched on/off rapidly so hysteresis is usually built in, e.g. power switches off at 72degC and on when it falls below 68degC. You still get the temperature oscillating but in many applications it is not critical.

Proportional control is where you measure the temperature and a proportion of the error is fed back to control the power input. e.g.
1. up to 60degC 100% power is applied
2. at 61degC 90% power is applied, e.g. using PWM
3. at 65 degC 50% is appplied
4. at 69decgC 10% is applied
5. at 70degC power is off

so the temperture approaches 70degC and flattens off
the problem is that if there is insufficent feedback the temperature never reaches 70degC if there is too much it can overshoot

to get it correct you need a mathematical model of the system

have a look at
https://control.com/thread/1026188392

 

[ep.hobbyiest]

Thank you sir
I read the link provided by you also.
Means as you given proportional band is 60-70 degree.
band is 10 degree. that is 14.28% right?
and gain is = 100/P. Band.

 

[FvM]

band is 10 degree. that is 14.28% right?

The relative (percent) PB is calculated based on the temperature range of the controller, which wasn't specified in your post. If it's e.g 0 - 200 °C, you get 5 % PB.

 

[D.A.(Tony)Stewart]

PID control needs specs to define , system step error response, overshoot under worst case gain and time lag and rate of change of disturbance response Impulse error response ( like opening door on ice cold day)

For stability , frequency / phase margin is used to determine correct feedback signal conditioning and gain to optimize speed, stability, overshoot, switch cycle rate, which are all tradeoffs to measurable specs.

The difference between desired temp and actual temp is used to control output power in fans for cooling in a proportional control system with the range specified over a limited range such as 5 to 10deg on a CPU. This is proportional control.

 

[ep.hobbyiest]

My set Temperature is 70 degree.
so if i given full on upto 60 degree and control temperature in 60-70 degree. Then this 60-70 degree is my proportional band. right??
That is 14.28 %.

 

[FvM]

10/70 = 14%. But that's only the proportional band, if the controller temperature (setpoint) range is 0 - 70 °C. See post #4.

 

[ep.hobbyiest]

yes sir this point is get cleared.
now integral term is to reset the error. the how to find the Ki term that is integral gain.

- - - Updated - - -

sorry for late reply.

 

[FvM]

You mean where to find Ki in your code or how to set Ki of a controller? In the latter case, I suggest to try with Ziegler-Nichols tuning method.

 

[ep.hobbyiest]

As we had calculate the PB term from set value, likewise how to calculate the Ki term? that is how set Ki of controller.?

 

[D.A.(Tony)Stewart]

In simple terms, PID control systems are ideal for any systems where you need zero steady state error for any setpoint, step input and ramp input response or minmal change due to a sensor disturbance. Thus assumptions to desired response to these inputs are essential.

However Proportional control only often gives acceptable results. Since power is limited, integrating to a higher error value achieves nothing as it may already be at full on or off power.

Thus integral gain is unnecessary under normal circumstances with a static heat load.

The reason for integral feedback is to accelerate the error due a Ramp change in setpoint or ambient. this results in a fixed proportional error. However if the change is only a few degrees and you have a proportional gain of 100/deg , it may already be at full on or off power past 1 deg difference. So ( I) feedback amplifies the error feedback over time to reduce the response error to these disturbances.

Too high a P gain is ok for solid state heat controllers but if using relays or blowers, the system would be cycling on and off too fast. Thus a deadzones or hysteresis is added to the control system.

When we analyse a control system, we ask is there a condition to cause a change in error by a ramp that is faster than the system can track, , then we know the proportional system will have a fixed error proportional to the gain and ramp rate. This is why we use integral (I) feedback to accelerate the error.

But I feedback can cause overshoot, so we need to know what the step input overshoot limit must be. This overshoot is a combination effect and P gain must be reduced if I gain is included.

To anticipate errors due to a ramp condition, the derivative (D) gain is used. This must be defined by the known requirements for disturbances for step and ramp input as well as impulse response.

Thus to design the ideal PID gain parameters , the user MUST know the requirements for step input overshoot or arbitrarily choose 10% and the acceptable error to a ramp input of known size. Further definitions of disturbance response, changes in thermal mass or heater power available add other test criteria to the stability error under each condition.

But or a simple temp controller of fixed mass and heat, even proportional gain can be increased to infinity with simple On/ off control using hysteresis to limit the acceptable error and toggle rate of the furnace.

 

[ep.hobbyiest]

sir i get the proportional action. but integral is not that much clear.