Nyquist diagram


In practice, only the frequencies lu = 0 to+oo are of interest and since in the frequency domain. v = jtu, a simplified Nyquist stability criterion, as shown in Figure 6.18 is A closed-loop system is stable if, and only if, the locus of the G(iLu)H(iuj) function does not enclose the (—l,j0) point as lu is varied from zero to infinity. Enclosing the (—1, jO) point may be interpreted as passing to the left of the point . The G(iLu)H(iLu) locus is referred to as the Nyquist Diagram.  [c.164]

Fig. 6.18 Nyquist diagram showing stable and unstable contours. Fig. 6.18 Nyquist diagram showing stable and unstable contours.
Construet the Nyquist diagram for the eontrol system shown in Figure 6.20 and find the eontroller gain K that  [c.166]

Table 6.3 Data for Nyquist diagram for system in Figure 6.20 Table 6.3 Data for Nyquist diagram for system in Figure 6.20
Fig. 6.21 Nyquist diagram for system in Figure 6.20. Fig. 6.21 Nyquist diagram for system in Figure 6.20.
Then n in equation (6.62) is the type number of the system and J([ denotes the product of the factors. The system type can be observed from the starting point uj 0) of the Nyquist diagram, and the system order from the finishing point bj oo), see Figure 6.22.  [c.168]

Fig. 6.22 Relationship between system type classification and the Nyquist diagram. For a step input, Fig. 6.22 Relationship between system type classification and the Nyquist diagram. For a step input,
In general, it is more eonvenient to use the Bode diagram in eontrol system design rather than the Nyquist diagram. This is beeause ehanges in open-loop gain do not affeet the Bode phase diagram at all, and result in the Bode gain diagram retaining its shape, but just being shifted in the y-direetion.  [c.170]

The M and N circles can be superimposed on a Nyquist diagram (called a Hall chart) to directly obtain closed-loop frequency response information.  [c.174]

Alternatively, the closed-loop frequency response can be obtained from a Nyquist diagram using the direct construction method shown in Figure 6.25. From equation (6.73)  [c.174]

Fig. 6.25 Closed-loop frequency response from Nyquist diagram using the direct construction method. Fig. 6.25 Closed-loop frequency response from Nyquist diagram using the direct construction method.
The Nyquist diagram for the same system is  [c.393]

Example 6.1(a) Nyquist Diagram  [c.393]

Example 6.4 Nyquist Diagram %Third-order type one system num=[1]  [c.394]

Data for Nyquist diagram for system in Figure 6.20 167  [c.453]

The ionization energies and impurity levels are shown in the flat-band figure next to the configuration diagram.  [c.2886]

The previous sections have dealt mainly with the representation of chemical structures as flat, two-dimensional, or topological objects resulting in a structure diagram. The next step is the introduction of stereochemistry (see Section 2.8), leading to the term "configuration of a molecule. The configuration of a molecule defines the positions, among all those that are possible, in which the atoms in the molecule are arranged relative to each other, unless the various arrangements lead to distinguishable and isolable stereoisomeric compounds of one and the same molecule. A major characteristic of stereoisomeric compounds is that they have the same constitution, but are only interconvertible by breaking and forming new bonds.  [c.91]

A schematic diagram of a six-vessel UOP Cyclesorb process is shown in Figure 15. The UOP Cyclesorb process has four external streams feed and desorbent enter the process, and extract and raffinate leave the process. In addition, the process has four internal recycles dilute raffinate, impure raffinate, impure extract, and dilute extract. Feed and desorbent are fed to the top of each column, and the extract and raffinate are withdrawn from the bottom of each column in a predeterrnined sequence estabUshed by a switching device, the UOP rotary valve. The flow of the internal recycle streams is from the bottom of a column to the top of the same column in the case of dilute extract and impure raffinate and to the top of the next column in the case of dilute raffinate and impure extract.  [c.302]

Liquid Crystal Displays. The workhorse of the LCD field is an electrooptic device called the twisted nematic display. A typical diagram of this device is shown ia Figure 16. A small amount of chiral dopant is added to a room temperature nematic Hquid crystal mixture with high dielectric anisotropy and low viscosity. This mixture is then iatroduced between two flat pieces of glass, the iaside surfaces of which have a transpareat metallic coatiag of indium—tin oxide covered by a surfactant which promotes alignment of the Hquid crystal director parallel to the surface. The direction of parallel alignment on one piece of glass is perpendicular to the direction of parallel alignment on the other piece of glass. The space between the pieces of glass is roughly p.m. Under these conditions, the Hquid crystal mixture spontaneously adopts a twisted stmcture, ia which the director rotates by 90° ia going from oae glass surface to the other. The two pieces of glass have polarizing films deposited oa their outside surfaces, with the polarizatioa directioa ideatical to the alignment directioa oa the iaside surface. Whea fabricated ia this way, light iacideat oa the ceU is polarized by the first polarizer, rotated by 90° by the twisted stmcture of the Hquid crystal, and passes through the analyzer. The ceU therefore appears bright or transparent. When a voltage is appHed, the anisotropy of the Hquid crystal molecules causes the director to align with the field, except for a very thin layer next to the glass surfaces. This untwisted stmcture no longer rotates the polarization direction of the light as it passes through the device, so the analyzer extinguishes it. The ceU appears dark.  [c.203]

In a study of fiber crystal stmctures by diffraction, the dimensions of the unit cell are determined first. The unit cell is the smallest spatial unit (along with its atomic contents) that, through translational symmetry, can generate the entire crystal. The dimensions are indicated by the positions of the spots on the diffraction diagram. Next, the intensities of the spots on the diffraction pattern are measured. Model cellulose chains are placed at trial positions in the unit cell and the intensities are calculated. The model that gives the best agreement, ie, lowest R value, between the observed and calculated intensities corresponds to the final stmcture. Often the energies of the trial stmctures are calculated as well, and selection of the final stmcture takes into account both the extent of disagreement with the diffraction data and the energetic stabiUty of the model (48). Errors in the measured intensities may be important (49), but a more definitive approach is not available.  [c.240]

The general method of production for aqueous trivalent compounds involves dissolving a Cr(VI) source in an acid solution of the desired anion, eg, nitric acid, in a reactor constmcted of acid-resistant materials. Next, the reducing agent is added at a controUed rate until the Cr(VI) has been reduced to Cr(III). For some reducing agents it is necessary to complete the reduction at boiling or under reflux conditions. A simplified, general flow diagram for this process is given in Figure 3.  [c.138]

Light Mixing. Light or additive mixing applies to light beams. White results when any suitable set of three-color beams of the appropriate intensity are mixed. On the chromaticity diagram of Figures 8 and 9, the condition for equal intensity beams is that WHes at the center of gravity of the triangle formed by the three sources. A suitable set of primary light beams is red, blue, and green, each being near a corner of Figures 8 and 9. Red and green by themselves add to give yellow, red and blue give purple and magenta, and blue and green give blue-green and cyan, as can be estabUshed by tie lines on Figure 8. It is important to distinguish magenta from red and cyan from blue to avoid confusing the additive from the subtractive system described next.  [c.414]

Armed with this information, we are in a strong position to re-examine the mechanical properties, and explain the great differences in strength, or toughness, or corrosion resistance between alloys. But where does this information come from The eonstitution of an alloy is summarised by its phase diagram - the subject of the next chapter. The shape and size are more difficult, since they depend on the details of how the alloy was made. But, as we shall see from later chapters, a fascinating range of microscopic processes operates when metals are cast, or worked or heat-treated into finished products and by understanding these, shape and size can, to a large extent, be predicted.  [c.23]

The phase diagram for the copper-antimony system is shown on the next page. The phase diagram contains the intermetallic compound marked "X" on the diagram. Determine the chemical formula of this compound. The atomic weights of copper and antimony are 63.54 and 121.75 respectively.  [c.32]

Zone refining works like this. We start with a bar of silicon containing a small uniform concentration Cq of impurity (Fig. 4.4a). A small tubular electric furnace is put over the left-hand end of the bar, and this is used to melt a short length (Fig. 4.4b). Obviously, the concentration of impurity in this molten section must still be Cq as no impurity has either left it or come into it. But before we can go any further we must look at the phase diagram (Fig. 4.5). To have equilibrium between the new liquid of composition Cq and the existing solid in the bar, the solid must be of composition /cCq. And yet the solid already has a composition of Cq, (1//c) times too big. In fact, the situation is rescued because a loeal equilibrium forms between liquid and solid at the interface where they touch. The solid next to this interface loses a small amount of impurity into the liquid by diffusion, and this lowers the composition of the solid to /cCq. Naturally, a gradient is produced in the composition of the solid (Fig. 4.4b), but because solid-state diffusion is relatively sluggish we can neglect the atomic flux that the gradient causes in the present situation.  [c.39]

In 1962 a span of Kings Bridge (Melbourne, Australia) collapsed by brittle fracture. The fracture started from a crack in the heat-affected zone (HAZ) of a transverse fillet weld, which had been used to attach a reinforcing plate to the underside of a main structural I-beam (see the diagram on the next page). The concentrations of the alloying elements in the steel (in weight%) were C, 0.26 Mn, 1.80 Cr, 0.25. The welding was done by hand, without any special precautions. The welding electrodes had become damp before use.  [c.142]

A temperature-time diagram is shown on Figure 2.1.3 on the next page.  [c.31]

In addition to the previously mentioned shortcut equations, plotting a McCabe-Thiele diagram is also a very useful tool. The equation for the equilibrium X-Y diagram and plotting of the operating lines are described next.  [c.54]

Fig. 6.19 Gain margin (GM) and phase margin (PM) on the Nyguist diagram. Fig. 6.19 Gain margin (GM) and phase margin (PM) on the Nyguist diagram.
The Nyquist diagram is constructed, for A" = 1, at frequencies either side of the 180° point, which, from equation (6.59) can be seen to be tu = 2rad/s. Using equations (6.58) and (6.59), Table 6.3 may be evaluated.  [c.167]

Set K = 1 and plot the Nyquist diagram by calculating values of open-loop modulus and phase for angular frequency values from 0.8 to 3.0rad/s in increments of 0.2rad/s. Hence find the value of K to give a gain margin of 2 (6dB). What is the phase margin at this value of A  [c.194]

The Nyquist diagram uj varying from —oo to +oo) is produced by examp64.m where  [c.394]

The material presented in this book is as a result of four deeades of experienee in the field of eontrol engineering. During the 1960s, following an engineering apprentiee-ship in the aireraft industry, I worked as a development engineer on flight eontrol systems for high-speed military aireraft. It was during this period that I first observed an unstable eontrol system, was shown how to frequeney-response test a system and its elements, and how to plot a Bode and Nyquist diagram. All ealeulations were undertaken on a slide-rule, whieh I still have. Also during this period I worked in the proeess industry where I soon diseovered that the ineorreet tuning for a PID eontroller on a 100 m long drying oven eould eause eatastrophie results.  [c.454]

Another feature arising from field-density considerations concerns the coexistence curves. For one-component fluids, they are usually shown as temperature T versus density p, and for two-component systems, as temperature versus composition (e.g. the mole fraction x) in both cases one field is plotted against one density. However in tluee-component systems, the usual phase diagram is a triangular one at constant temperature this involves two densities as independent variables. In such situations exponents may be renonualized to higher values thus the coexistence curve exponent may rise to (3/(1 - a). (This renonualization has nothing to do with the renonualization group to be discussed in the next section.)  [c.649]

It is instmctive to view this sequence of transfonnations in tenns of a bifurcation diagram. We use the procedure described earlier to examine the chaotic orbit the intersections of the periodic trajectories with the Poincare surface are recorded for each value of the rate constant k 2- hi figure C3.6.6 we plot the concentration < 2 on the Poincare plane versus k 2- One can clearly see the sequence of period-doubling bifurcations leading eventually to the chaotic attractor. One can understand the origin of this sequence of bifurcations by considering the next-amplitude map discussed earlier. We remarked in section C3.6.3.2 that this map has the nearly parabolic functional fonn shown in figure C3.6.2(fc) so that, after suitable scaling, we can write the next-amplitude map in the standard quadratic fonn C2(n-l-l) = Xc2(n)(l - C2( )), thereby preserving the local and global features of the bifurcation diagram C3.6.6. We know what happens  [c.3062]

The flow diagram illustrating the commercial implementation of this fixed-bed continuous adsorption process by UOP is shown in Figure 8. The feed, desorbent, and product ports are continuously changed, using a patented rotary valve. In the particular example shown in Figure 8, 12 lines are coimected to the rotary valve. Only four lines are active at any one instant. Desorbent is injected into one line, feed is injected into another, extract is withdrawn from another, and raffinate is withdrawn from stiU another. By rotating the valve by one position, a different set of four ports is activated. Thus a condition is simulated whereby the soHd appears to be moving past fixed portions of fluid feed, product, and withdrawal. The operating conditions are 250—400°C and moderate pressures. Earlier versions of Parex used a light desorbent, toluene. More recent versions have used a heavier desorbent, usually Adiethylbenzene, which has resulted in lower energy costs associated with separating the PX from the desorbent. The newest adsorbent, ADS-27 was  [c.419]

Initial Sketch. Figure 2 shows a process flow diagram for a petrochemical plant (1,2). This drawiag shows the feed and products so the designer knows what to allow for these lines ia the iatemnit pipeway routing. The process engineer has iadicated with notes which pieces of equipment will be located ia elevated stmctures, such as the overhead condensers, and has also shown which equipment should be located close by other equipment, such as the reboiler next to its column. Primary iastmmentation is shown to iadicate that room is required for instmment drops to these control valves. AH this  [c.70]

The next tool is a cause and effect diagram (44), illustrated by Figure 4. This diagram is used by teams to relate an effect to its potential causes. Diagram constmction often begins with the four main branches shown. These diagrams resemble the skeleton of a fish and thus are sometimes called fishbone diagrams. All possible primary causes and their associated subcauses and their next-level associated causes should be shown. When the lowest level causes are identified, the team can use the chart for ranking the most likely origin of an effect. Once this is accompHshed, other TOQ can be used for the collection of data to confirm the cause lea ding to the effect in question.  [c.370]

Fig. 14-6 Circuit diagram for a dc decoupling device with nickel-cadmium cell. (KE) insulated cable end sealing, (E) grounding installation, (1) grounding side bar (2) NiCd cell, 1.2 V (3) breakdown fuse (4,5) isolating links. Fig. 14-6 Circuit diagram for a dc decoupling device with nickel-cadmium cell. (KE) insulated cable end sealing, (E) grounding installation, (1) grounding side bar (2) NiCd cell, 1.2 V (3) breakdown fuse (4,5) isolating links.
The next step in the testing proeedure is to reeord aeeelerometer readings at various dise, blade, and shroud loeations at lower eritieal frequeneies. The objeetive of this test is to quantitatively identify the high and low exeitation regions. For this test, a six- or five-blade region is eonsidered suffieiently large to be representative of the entire impeller. The results of these tests are plotted on a Campbell diagram, as shown for one sueh impeller in Figure 5-28. Lines of exeitation frequeneies are then drawn vertieally on the Campbell diagram, and a line eorresponding to the design speed is drawn horizontally. Where the lines of exeitation frequeneies and multiples of running speed interseet near the line of design rpm, a problem area may exist. If, for instanee, an impeller has 20 blades, a design speed of 3000 rpm (50 Hz), and a eritieal frequeney of 1000 Hz, the impeller is very likely to be severely exeited, sinee the eritieal is exaetly 2QN. On a Campbell diagram the previous  [c.214]

Figure S.7 The subunit structure of the neuraminidase headpiece (residues 84-469) from influenza virus is built up from six similar, consecutive motifs of four up-and-down antiparallel fi strands (Figure 5.6). Each such motif has been called a propeller blade and the whole subunit stmcture a six-blade propeller. The motifs are connected by loop regions from p strand 4 in one motif to p strand 1 in the next motif. The schematic diagram (a) is viewed down an approximate sixfold axis that relates the centers of the motifs. Four such six-blade propeller subunits are present in each complete neuraminidase molecule (see Figure 5.8). In the topological diagram (b) the yellow loop that connects the N-terminal P strand to the first P strand of motif 1 is not to scale. In the folded structure it is about the same length as the other loops that connect the motifs. (Adapted from J. Varghese et al.. Nature 303 35-40, 1983.) Figure S.7 The subunit structure of the neuraminidase headpiece (residues 84-469) from influenza virus is built up from six similar, consecutive motifs of four up-and-down antiparallel fi strands (Figure 5.6). Each such motif has been called a propeller blade and the whole subunit stmcture a six-blade propeller. The motifs are connected by loop regions from p strand 4 in one motif to p strand 1 in the next motif. The schematic diagram (a) is viewed down an approximate sixfold axis that relates the centers of the motifs. Four such six-blade propeller subunits are present in each complete neuraminidase molecule (see Figure 5.8). In the topological diagram (b) the yellow loop that connects the N-terminal P strand to the first P strand of motif 1 is not to scale. In the folded structure it is about the same length as the other loops that connect the motifs. (Adapted from J. Varghese et al.. Nature 303 35-40, 1983.)
We can immediately discern from Figure 5.11 that the molecule is divided into two clearly separated domains that seem to be of similar size. For the next step we would need a stereopicture of the model or, much better, a graphics display where we could manipulate the model and look at it from different viewpoints. Here instead we have made a schematic diagram of one domain (Figure 5.12), which is normally not done until the analysis is completed and the structural principles are clear.  [c.74]

Conditions CDCI3, 25°C, 200 MHz (H), 50 MHz ( C). (a) H NMR spectrum with expansion (b) and NOE difference spectra (c,d), with decoupling at Sh = 2.56 (c) and 2.87 (d) (e-g) C NMR spectra (e) H broadband decoupled spectrum (f) NOE enhanced coupled spectrum (gated decoupling) with expansions (g) (8c = 23.6, 113.3, 113.8, 127.0, 147.8, 164.6 and 197.8) (h, next page) section of the CH COSY diagram.  [c.99]


See pages that mention the term Nyquist diagram : [c.165]    [c.348]    [c.634]    [c.308]    [c.167]    [c.169]    [c.31]   
Advanced control engineering (2001) -- [ c.164 , c.165 , c.166 , c.167 , c.170 , c.174 , c.194 ]