# Z-Transform

Started by April 21, 2011
What is the role of "zeros" in deciding the stability of the system?
why only "poles" are being used to decide the stability of the system?

Dhaval
On 04/21/2011 11:35 AM, dhaval_shah wrote:
> What is the role of "zeros" in deciding the stability of the system? > why only "poles" are being used to decide the stability of the system?
See http://www.wescottdesign.com/articles/zTransform/z-transforms.html. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
On Apr 21, 2:35&#2013266080;pm, "dhaval_shah"
<shah.dhavalshah@n_o_s_p_a_m.gmail.com> wrote:
> What is the role of "zeros" in deciding the stability of the system? > why only "poles" are being used to decide the stability of the system? > > Dhaval
Dhaval, If N(z) goes to zero, can that ever cause N(z)/D(z) to "blow up"? --Randy
On Apr 22, 6:35&#2013266080;am, "dhaval_shah"
<shah.dhavalshah@n_o_s_p_a_m.gmail.com> wrote:
> What is the role of "zeros" in deciding the stability of the system? > why only "poles" are being used to decide the stability of the system? > > Dhaval
Nothing, except if you use negative feedback around your system. Zeros act like a magnet for the locus eminating from the poles, so if the zeros are outside the unit circle (open loop) then there is a very good chance that at some value of gain the closed-loop poles will find there way there. Hardy
On Apr 22, 6:56&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote:
> On 04/21/2011 11:35 AM, dhaval_shah wrote: > > > What is the role of "zeros" in deciding the stability of the system? > > why only "poles" are being used to decide the stability of the system? > > Seehttp://www.wescottdesign.com/articles/zTransform/z-transforms.html. > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html
That part on PID in your article uses "pure" differentiation. Not so good if you have a structural resonance to deal with (which you always do). You don't discuss filtering this with a pole? Hardy
On 04/21/2011 01:26 PM, HardySpicer wrote:
> On Apr 22, 6:56 am, Tim Wescott<t...@seemywebsite.com> wrote: >> On 04/21/2011 11:35 AM, dhaval_shah wrote: >> >>> What is the role of "zeros" in deciding the stability of the system? >>> why only "poles" are being used to decide the stability of the system? >> >> Seehttp://www.wescottdesign.com/articles/zTransform/z-transforms.html. >> >> -- >> >> Tim Wescott >> Wescott Design Serviceshttp://www.wescottdesign.com >> >> Do you need to implement control loops in software? >> "Applied Control Theory for Embedded Systems" was written for you. >> See details athttp://www.wescottdesign.com/actfes/actfes.html > > That part on PID in your article uses "pure" differentiation. Not so > good if you have a structural resonance > to deal with (which you always do). You don't discuss filtering this > with a pole?
I originally wrote that intending to submit it to Embedded Systems Programming magazine, and was adhering to a 5000 word limit. Were I to re-write it (which it needs), I would include that tidbit -- particularly given that frequency domain design really makes it clear why you want to band limit your differentiator. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
On Apr 22, 9:22&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote:
> On 04/21/2011 01:26 PM, HardySpicer wrote: > > > > > On Apr 22, 6:56 am, Tim Wescott<t...@seemywebsite.com> &#2013266080;wrote: > >> On 04/21/2011 11:35 AM, dhaval_shah wrote: > > >>> What is the role of "zeros" in deciding the stability of the system? > >>> why only "poles" are being used to decide the stability of the system? > > >> Seehttp://www.wescottdesign.com/articles/zTransform/z-transforms.html. > > >> -- > > >> Tim Wescott > >> Wescott Design Serviceshttp://www.wescottdesign.com > > >> Do you need to implement control loops in software? > >> "Applied Control Theory for Embedded Systems" was written for you. > >> See details athttp://www.wescottdesign.com/actfes/actfes.html > > > That part on PID in your article uses "pure" differentiation. Not so > > good if you have a structural resonance > > to deal with (which you always do). You don't discuss filtering this > > with a pole? > > I originally wrote that intending to submit it to Embedded Systems > Programming magazine, and was adhering to a 5000 word limit. > > Were I to re-write it (which it needs), I would include that tidbit -- > particularly given that frequency domain design really makes it clear > why you want to band limit your differentiator. > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html
I woudn't differentiate from dc either as this knocks out an integrator (or part of it). Better to have a differentiator from freuqency f1 to f2 spanning unity gain crossover. Hardy
On 04/22/2011 08:36 PM, HardySpicer wrote:
> On Apr 22, 9:22 am, Tim Wescott<t...@seemywebsite.com> wrote: >> On 04/21/2011 01:26 PM, HardySpicer wrote: >> >> >> >>> On Apr 22, 6:56 am, Tim Wescott<t...@seemywebsite.com> wrote: >>>> On 04/21/2011 11:35 AM, dhaval_shah wrote: >> >>>>> What is the role of "zeros" in deciding the stability of the system? >>>>> why only "poles" are being used to decide the stability of the system? >> >>>> Seehttp://www.wescottdesign.com/articles/zTransform/z-transforms.html. >> >>>> -- >> >>>> Tim Wescott >>>> Wescott Design Serviceshttp://www.wescottdesign.com >> >>>> Do you need to implement control loops in software? >>>> "Applied Control Theory for Embedded Systems" was written for you. >>>> See details athttp://www.wescottdesign.com/actfes/actfes.html >> >>> That part on PID in your article uses "pure" differentiation. Not so >>> good if you have a structural resonance >>> to deal with (which you always do). You don't discuss filtering this >>> with a pole? >> >> I originally wrote that intending to submit it to Embedded Systems >> Programming magazine, and was adhering to a 5000 word limit. >> >> Were I to re-write it (which it needs), I would include that tidbit -- >> particularly given that frequency domain design really makes it clear >> why you want to band limit your differentiator. >> >> -- >> >> Tim Wescott >> Wescott Design Serviceshttp://www.wescottdesign.com >> >> Do you need to implement control loops in software? >> "Applied Control Theory for Embedded Systems" was written for you. >> See details athttp://www.wescottdesign.com/actfes/actfes.html > > I woudn't differentiate from dc either as this knocks out an > integrator (or part of it).
Only if you cascade the differentiator with the integrator. If you run it in parallel with the integrator and sum the results then that does not happen.
> Better to have a differentiator from freuqency f1 to f2 spanning unity > gain crossover.
-- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
On Apr 23, 5:50&#2013266080;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On 04/22/2011 08:36 PM, HardySpicer wrote: > > > > > On Apr 22, 9:22 am, Tim Wescott<t...@seemywebsite.com> &#2013266080;wrote: > >> On 04/21/2011 01:26 PM, HardySpicer wrote: > > >>> On Apr 22, 6:56 am, Tim Wescott<t...@seemywebsite.com> &#2013266080; &#2013266080;wrote: > >>>> On 04/21/2011 11:35 AM, dhaval_shah wrote: > > >>>>> What is the role of "zeros" in deciding the stability of the system? > >>>>> why only "poles" are being used to decide the stability of the system? > > >>>> Seehttp://www.wescottdesign.com/articles/zTransform/z-transforms.html. > > >>>> -- > > >>>> Tim Wescott > >>>> Wescott Design Serviceshttp://www.wescottdesign.com > > >>>> Do you need to implement control loops in software? > >>>> "Applied Control Theory for Embedded Systems" was written for you. > >>>> See details athttp://www.wescottdesign.com/actfes/actfes.html > > >>> That part on PID in your article uses "pure" differentiation. Not so > >>> good if you have a structural resonance > >>> to deal with (which you always do). You don't discuss filtering this > >>> with a pole? > > >> I originally wrote that intending to submit it to Embedded Systems > >> Programming magazine, and was adhering to a 5000 word limit. > > >> Were I to re-write it (which it needs), I would include that tidbit -- > >> particularly given that frequency domain design really makes it clear > >> why you want to band limit your differentiator. > > >> -- > > >> Tim Wescott > >> Wescott Design Serviceshttp://www.wescottdesign.com > > >> Do you need to implement control loops in software? > >> "Applied Control Theory for Embedded Systems" was written for you. > >> See details athttp://www.wescottdesign.com/actfes/actfes.html > > > I woudn't differentiate from dc either as this knocks out an > > integrator (or part of it). > > Only if you cascade the differentiator with the integrator. &#2013266080;If you run > it in parallel with the integrator and sum the results then that does > not happen. > > > Better to have a differentiator from freuqency f1 to f2 spanning unity > > gain crossover. > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html
Yes of course, that's how I do it. The PID stuff tends to come from process control whereas the lag-lead compensation is your traditional motor servo stuff - historically. I am guessing that in proces control it is more guesswork as you don't have a good model of the plant. Hence the fiddling with three-term controllers. Whereas for motors, PLLs etc we can draw a fairly accurate Bode Plot. Hardy
I got some idea, poles are considered bcoz real part of the poses are
placed as a damping factor when u perform inverse Z-Transform.

Is this correct?

Dhaval