I am sure that Peter, Woody and others can help me with some simple question/interpretation of this equation. I can interpret this 20 years ago but not anymore now .

y=K[x(t) + 1/t1*integ x(t)dt+ t2* dx(t)/dt]

question:

1. If x is a current value(mA, A, etc), x(t) is just a value during a particular time?
2. The 2nd term has an integral value, would this mean that I just need to square the value of x and divide by 2(or 2!)?
3. The 3rd term is a derivative, meaning a change of current over change in time, if t2 is time, K is constant, and the value of y is current(mA, A, etc), this third term can result to a value of current, is this a minimum value? What is a differental value?

If I posted the question wrongly, you can change it. And if there are other basic logic that I did not specify, just please don't hesitate to correct it.

Some people might wonder why I post this topic here, but IMO, this is one equation that is very relevant to close loop control system.

Thanks and gudnite...

Maglub, you are going to lose your active clown status. Two serious questions on natural frequency and this one on closed loop control.

Your equation is posted correctly. There are problems with your question but that that's OK. It just makes the answer more challenging.

I know and will provide the answer if someone doesn't provide one in a few days. I should give others a chance to shine. Let's see if JA has the round ones to tackle this.

quote:

Some people might wonder why I post this topic here, but IMO, this is one equation that is very relevant to close loop control system.

It is the core of closed loop control. However, I never would have thought anybody would post a question like that here though.

I'll take a stab at it to keep the thread going.



My PID equation is a bit different, but the same.

quote:

1. If x is a current value(mA, A, etc), x(t) is just a value during a particular time?

Y = the control variable, or the 'new' control variable. This value will be the updated version of the latest value X(t). Then in the next cycle, X(t) will be Y from the previous.

quote:

The 2nd term has an integral value, would this mean that I just need to square the value of x and divide by 2(or 2!)?

If you were solving with respect to dX then yes, but an undefined integral will usually leave you with another integral. How can it be solved with repect to d(t)?

quote:

The 3rd term is a derivative, meaning a change of current over change in time, if t2 is time, K is constant, and the value of y is current(mA, A, etc), this third term can result to a value of current, is this a minimum value? What is a differental value?

T2 in this equation is not T*2 or T(2) it is the is the differential constant (KD) or Time differential (TD in my equation). (I got PD and PID mixed up), T2 or TV below, is the time it takes for the Proportional part, to reach the same level that the Derivitive jumped to immediatley. A differential equation or a derivitive is the amount or rate of change a function has, as it's input changes.

This message has been edited. Last edited by: Doug Hanson,

First, the equation that Maglub posted is valid but there are many different forms of PID equation. The PID equation that Maglub posted is commonly used in process control and is often called the standard or ISA form. The variables t1 and t2 are really τi and τd which are the integrator and derivative time constants. Normally the units for these is minutes which is way too long for motion control.

The K in Maglub's equation is the controller gain. Normally this is K or Kc not Kp. Kp is the plant gain. The controller gain normally has units of output units/error units which brings us to Maglubs first question. x(t) is not a current, it is an error. It is an error between where the set point and processes variable. In motion controller we call this the target and actual. The target is usually the position where you should be at each millisecond and the actual is from the feed back and tells you where you really are. The difference is the error

In motion control the parallel form of PID is used

error(t)=target(t)-actual(t)
CO(t)=Kp*error(t)
     +Ki*∫error(t)*dt
     +Kd*d error(t)/dt

If the error units are positions then the rate of change in error is the same as the error between the target and actual velocity.

CO(t) is the control output. Internally the controller may assume the control out has a range of -100 to 100%. At the last stage there is a scaling routine that converts the -100% to +100% to -10volts to +10volts or -40ma to +40ma or what ever is required to drive the valve.

Humnn, I'm learning...

I guess Doug and I have the same equation, probably we have the same book. I got it partially Peter, I know it is still hard to understand but as I read your post, then restudy back my book I have the idea now but still have some questions to ask. Actually your explanation is the same as from our book and have similar direction.

As explained, PID regulator is proportional, integral and differential regulator.

This boils down to an amplifier being controlled using resistors and capacitors. Depending on the type of regulator, be it PI, PD or PID, the output is being controlled a compound resistor and capacitor circuit to attain either a proportional, integral or differential kind of transfer elements. And it looked like a regulator/amplifier with an input x will produce an output y based on what is the transfer element.

With electrical feedback, there will be two sources of inputs(command and feedback) that gives an error signal(+-) until the error becomes zero, hence the position is reached.

Now with a differential regulator, what makes/affects the velocity of the input? Ramp?

For a PID, at what order does the transfer element function? Would it be P, then I,then D?

My statements/question can be rearranged/modified if necessary.

You know what Peter, you really made me think about controls. Although I have no applications or job that requires this, I guess I need to start learning this, even in theory for the meantime while waiting for some opportunity.

quote:

Originally posted by maglub:
Now with a differential regulator, what makes/affects the velocity of the input? Ramp?

I don't understand the question. The set point ramps are generate by a PLC, computer or motion controller.

quote:

For a PID, at what order does the transfer element function? Would it be P, then I,then D?

All are calculated at the same time. Actually they are calculated one after the other but it takes only a few microseconds to update the PID can update the control signal to the valve. The order of calculation is not that important since all the terms are added together.

Maglub,
You might find the Wiki definition helpfull.

http://en.wikipedia.org/wiki/PID_controller

Cheers Woody

Better yet a simulated position system to tune.
ftp://www.deltamotion.com/pete.../T1P1%20PID%20NG.xls
This is a position system where the target generator is generating a position sine wave with an amplitude of 5 inches. The goal is to tune the PID gains in $H$4:$H$6 so that the actual position in red follows the target position in blue. As you can see know the target and actual position are two separate lines. When properly tuned the two lines are on top of each other so you see only one except at the first 0.5 seconds. Nothing can be done about that because a real mass can't accelerate from 0 to 15.708 inches/sec instantly. The green line is the control signal to the valve and it has a range of -10 to +10 volts.

Here is the challenge. As your tuning gets better the integrate sum of squared errors, ISE, will decrease. You cannot get the to 0 but with some effort you should be able to get the ISE to below 1000. I can get below 500 but I cheat. The ISE number is in $D$40.

Enjoy.

Thanks Woody, I forgot to google it... The wiki explanation is better and simpler with example/tutorial.

Peter, I might need more days of study but gaining some knowledge/idea slowly. I can't log-in to that site to try. My e-mail is not being accepted since I have no log-in account.

I guess that the problem is manual fine tuning, which may require to adjust the constants. Adjusting the value of these constants may involve selecting/varrying resistor(for P)/capacitor(for I and D) values... just a guess.
I will try to restudy the principles and behavior of Xc(capacitance/delay) too... I am not sure if this is relevant to study the behavior of the circuit... One thing that I could simply understand is obtaining the set point by processing the error using a parallel R/C circuit so that the error can become almost zero(acceptable set point obtainable).

This is hard to understand/do but I will try my best...

Goodnight.

Maglub.

You just need to change ftp - http.
http://www.deltamotion.com/pet.../T1P1%20PID%20NG.xls

Peter.

The best I've managed is around 496 ...but I'm not sure if the numbers I've punched in are sensible....is there a limiting range to these input values?

Cheers Woody

This message has been edited. Last edited by: Woodygb,

There isn't any limit to the gains. There is a limit to the resulting control signal.

The ISE can be reduced to a little less than 500 and that is it. There will always be some error at the beginning.

Notice how the control output leads the actual position. This is necessary to make up for the lag in the system.

The system modeled is closer to an electric motor system than a hydraulic cylinder. Hydraulic systems are more 'springy' and harder to tune. I just happen to have the file around from about 7 years ago.

Also, the feed back resolution on an Excel spreadsheet is infinite. If the actual position was truncated to about 0.001 inches or even 10 microns you would find it much more difficult.