Bode's Amplitude/Phase relation for discrete time systems
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From: Tim Wescott on 22 May 2010 21:08 On 05/22/2010 05:26 PM, Jerry Avins wrote: > On 5/22/2010 5:23 PM, HardySpicer wrote: > > ... > >> Indeed and I cannot understand why people still toute root-locus and >> Nyquist. They are excellent teaching tools but practically Bode has >> it. > > The more ways you have to look at a problem or procedure, the better > able to understand it. Root-locus plots illuminate the effect of gain > changes on many systems. Nyquist plots can be constructed from the > information in a Bode plot, and if the Nyquist plot has frequency ticks > along the curve, vice versa. The choice between the two is a matter of > preference. When I'm doing design from frequency-domain measurements, I find it helpful to plot both at the same time -- the Nyquist plot gives me stability margins and disturbance rejection at a glance, the Bode plot gives me loop closure frequencies. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Jerry Avins on 22 May 2010 21:46 On 5/22/2010 9:08 PM, Tim Wescott wrote: > On 05/22/2010 05:26 PM, Jerry Avins wrote: >> On 5/22/2010 5:23 PM, HardySpicer wrote: >> >> ... >> >>> Indeed and I cannot understand why people still toute root-locus and >>> Nyquist. They are excellent teaching tools but practically Bode has >>> it. >> >> The more ways you have to look at a problem or procedure, the better >> able to understand it. Root-locus plots illuminate the effect of gain >> changes on many systems. Nyquist plots can be constructed from the >> information in a Bode plot, and if the Nyquist plot has frequency ticks >> along the curve, vice versa. The choice between the two is a matter of >> preference. > > When I'm doing design from frequency-domain measurements, I find it > helpful to plot both at the same time -- the Nyquist plot gives me > stability margins and disturbance rejection at a glance, the Bode plot > gives me loop closure frequencies. If not making my point, you are at least amplifying it. The two plots contain the same data and indeed are interconvertable, yet they elucidate different aspects of the system. Just as a graph is often more illustrative than a table of numbers, different graphs illustrate different features. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Tim Wescott on 23 May 2010 01:16 On 05/22/2010 06:46 PM, Jerry Avins wrote: > On 5/22/2010 9:08 PM, Tim Wescott wrote: >> On 05/22/2010 05:26 PM, Jerry Avins wrote: >>> On 5/22/2010 5:23 PM, HardySpicer wrote: >>> >>> ... >>> >>>> Indeed and I cannot understand why people still toute root-locus and >>>> Nyquist. They are excellent teaching tools but practically Bode has >>>> it. >>> >>> The more ways you have to look at a problem or procedure, the better >>> able to understand it. Root-locus plots illuminate the effect of gain >>> changes on many systems. Nyquist plots can be constructed from the >>> information in a Bode plot, and if the Nyquist plot has frequency ticks >>> along the curve, vice versa. The choice between the two is a matter of >>> preference. >> >> When I'm doing design from frequency-domain measurements, I find it >> helpful to plot both at the same time -- the Nyquist plot gives me >> stability margins and disturbance rejection at a glance, the Bode plot >> gives me loop closure frequencies. > > If not making my point, you are at least amplifying it. That was my intent. > The two plots > contain the same data and indeed are interconvertable, yet they > elucidate different aspects of the system. Just as a graph is often more > illustrative than a table of numbers, different graphs illustrate > different features. Which is why I use both at once -- each coughs up information at a glance that would be tedious or impossible to extract from the other; looking at both while I cut and try tunings against measured data helps immensely. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Rune Allnor on 23 May 2010 06:50 On 23 Mai, 00:06, Tim Wescott <t...(a)seemywebsite.now> wrote: > The book is "Digital Control Systems: Theory, Hardware, Software", > Constantine H. Houpis & Gary B. Lamont, McGraw-Hill, 1985. Their > discussion starts on page 216 under the heading "Bilinear > Transformations", and they just call it the 'w plane'. > > z = (w + 1) / (-w + 1), from which one derives that w = (z - 1)/(z + 1). > > There's no prewarping -- in fact there's significant warping after the > fact. Pre-warping has to do with countering that 'after the fact' warping of the BLT. The end target of the BLT-based techniques is a discrete-time (DT) domain filter, and the continuous time (CT) is only a convenient domain to do the computations. Now, since the end target is DT the up front spec is also DT. But one does need a CT spec to do the core computations of the CT filter. Because of all this, one accounts for the BLT warps already at the spec stage, so that the CT filter is designed from an already warped - pre warped - spec. Done correctly, the end DT filter woks out exactly right. Rune
From: Jerry Avins on 23 May 2010 11:42
On 5/23/2010 6:50 AM, Rune Allnor wrote: ... > Done correctly, the end DT filter woks out exactly right. For any _one_ frequency. Also, a high band edge is sharpened. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. ����������������������������������������������������������������������� |