Control schemes with outputs that can only be positive or negative

[Wayintenseone]

Hello. In the process of describing something to a colleague, I quickly realized that I have forgotten most of what I once knew about controls. I'm hoping somebody might point me in the right direction with some key-words or terms that relate to the following so I can search for and find comprehensive info on the subject. Here we go:

How do you, in technical terms, characterize a control system that can only output a positive or a negative output. For example: in a normal positioning application - we might be able to extend or retract an actuator or rotate a motor CW or CCW. (Move both ways.) On overshoots; no problem - the device just goes back the other way. But what about situations where the system can not move both ways. Let's take a car, for example, that we want to bring just to a brick wall as quickly as possible without actually making physical contact. We can only control our rate of braking; the ability to go in reverse is of no value to us.

Another example: say we have a vessel of liquid and we want to lower the liquid level to a specific point. We only have a level transducer and a proportional valve to control the rate of liquid that is drained. We have no ability to add liquid to teh vessel.

So I'm talking about systems that just can't recover from overshoots. The first overshoot is a permanent, uncorrectable error. What do we call this situation? Are there special modifcations to PID schemes or other control schemes/mechanisms that are used in these special cases?

I actually don't have a real application. This just popped into my mind and it's bugging me that I don't know the answer. Thanks for any education you might offer!

-Dave

 

[Compositepro]

You describe a couple of different situations. In cases where overshoot is not allowed the target must be approached asymptotically.

 

[ishvaaag]

Since what you are describing are situations like "on that and that then add as much" or "deduce as much" I would call them predictive controls, and in fact there are articles on them in google. Also look for adaptive, the step added adapts to some current situation. That the decision may be only positive is just one of the conditions for the predictive algorithm of control, there are others, such the "as much".

 

[MintJulep]

If you can't tolerate overshoot you need a "critically damped" system.

The Wikipedia article on PID control might be a good starting point for a refresher.

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

 

[zekeman]

Your car problem, without getting into fancy transfer functions, etc., is simply:
MX"=F=F(x,x0)
M= mass of car
meaning you need a control function that in general is a function of x and x0 where you want to move the car from any position x to x0 without overshoot.If you use linear proportional control, then F(x,x0)=k*(x0-x), and so
F=k*(x0-x)
and you end up with the control equation
Mx"+k*x =k*x0
which will overshoot. If you add damping, c*x', your control function is F(x,x0)=k*(x0-x)-c*x' and the control equation looks like
Mx"+c*x'+ k*x=k*x0
x'= velocity
c= damping coefficient
which will move the car from x to x0 and depending on the values of k and c, it will be "underdamped" or "overdamped", meaning that the car will either overshoot (unacceptable) or assymtotically approach the wall. In this particular case,it turns out that the roots of the quadratic equation
My^2+cy+k=0 determine this characteristic
If the roots are negative, you have the overdamped case you need; otherwise the roots are complex which is the underdamped case ( the case you don't want)
For your liquid level problem, since mass inertia is not involved, overshoot is not a problem; a simple on/off control should work, meaning you open the valve and let the level fall until you achieve the height you want and then instantly close the valve.

 

[sreid]

Perhaps the answer you are seeking is "How many quadrants can the control operate in?" For motion, four quadrant control allows you to accelerate or decelerate if the velocity is positive or negative.

 

[ishvaaag]

"Projective controls" also gives a number of articles in google.

 

[cntw1953]

If you remember "logic", it will help to smooth your thinking process.