system pole and zero, zero ?!?!

Sometimes, system stabilization depends not only on pole points but on zero points. this can be easily prooved by transfer function.(preconditoin is that system tf is open loop)

system zero point depends not only one the postion of sensor, but its function. defferent function will result in different situation.

In many times, sensor position is fixed, but we can change different function (either feedback or feedforward parameters) to get suitable zero and poles to approch our goal.

Whether pole and zero change depend on our setting parameters.

you can find it from bode diagram.

In practice project, zero means to add a differntial action, and pole means integratial.

in other words, zero means change suddenly respond, but integratial means getal change respond.

for instance, from a rc circuit, you can find it. r and c is in different position , they will serve different. time constant ditermines their d or i value.

if system is too noise, you should reduce this d value.

Thank you very much !!

Let me ask you a question related above ^^;;

We assumed that the state space equation of one link inverted pendulum is xdot = ax +bu ( pin joint of inverted pendulum could be controlled by actuator )

then transfer function is b/(s-a).

In this case, system pole is a. there is no zero in this system.

Generally we hear that " add zero or add pole from the system "

If we add zero to the system, the transfer function could be bs/(s-a).

How can we add the zero in real system?

What I wonder is.. what is the real, practical meaning of adding zero to the system.

What should I do to add the zero in the inverted pendulum ??

you are welcome,

Dear friend, I think you may make a nistake. you list out a space state equation. its matrix formal and cannt divid directly.

matrix operation dont meet simple algibaric algorithm. you can refer to some material. and lets left the question to doctor or professor to answer it ( as matter fact, its out of my depth)

can we back to classical control theory to solve it?

I only remember a little about the ivert pendulum. I was told its very hot studied by scholar.

no matter how many sticks add upright together, the principle is same. if we hope it stand stability. we have to supply suitable force at its low terminal.

lets talk about one stick.

suppose it stands already, and then has a incline angle

if you hope it up right again, you have to add a force, how to add the force?

at first, you suddenly add the force. we can call it a differential procedure. now its a zero point.

it makes th e stick back to stable positon repidly.

( I hve to left a moment) next...

you may understand now.

Thank you very much again, ^^ !!

Almost done. Yet, what I wonder is..

Ok, add the force, you said how add the force is related to the zero.

but.. how can I think that it's related to the sensor or sensor function ?

adding a fast force is related to the control. in open loop control, there is no zero then??

Acturally, this is very simple and basic thing..but I am struggling to understand but not easy. I couldn't match this concept with real control system.

Adding zero means.. adding a fast force to the inverted pendulum by feedback control ?

in my understanding, feedback makes the system change into stable situation something like that.. and it also change the eigenvalues.. anyway... I am not sure..

U know what i mean ??

anyway I appreciate that you try to talk with me..

Thanks..

Feedback is a total loop system.

you can add the zero(differential) either at feedback channel or at forward channel which depend on power, effective etc.

generally we speak, zero increase damp. the force can be from current to motor and depend on how many value you get from sensor.

I can arrange an equation for instruction.

lets speaking a tf(transfer function)at first;

[you give the tf above is wrong. becasue its not tf. if you hope to get tf, you have to give output equation which you lost, i.e. Y/U=tf, not X/U]

suppose output y = G(t) which is impulse response and u is a input step.

we get, H(s)=L[G(t)]

this is our familiar laplace form. now we study it.

lets discuss the simple form of unit feedback

we get

Y=1/s[H/(1+H])

if we have a feenback efficience of k, we get

Y=1/s[H/(1+kH)]; more complex, if there a tf of B at forward channel, which is our discussion situation. we get

Y=1/s[BH/(1+kBH)]

if youi make system stable, we can add adjustor either at B or at k.

if you add at B, you neednet too much power, whereas at k, you should have larger power. thisis their distinct.

B use to be this net

aTs+1/Ts+1, where a >1 (if a<1 is anothe situatio}

now you see. you add a zero. this net can be active or passive.

thats ok.

this illustration will do the trick.

Are you stilll vague? or cannt understand what I said ?

many people was stuck by autocontrol. dont think so much zero or pole, just think how to make your system work well.

are you student?