Response Analysis

The initial response and stationary behavior are interesting in case of a step change in the inlet flow. For a unit change in the inlet flow = 1/s. The initial behavior then becomes  

When To T, the response is initially negative, since less heat is available for evaporation. Owing to the decreasing pressure, the boiling point temperature will decrease. On an increase in inlet flow, the outlet vapor flow will therefore initially decrease. 

For a step change in inlet flow, the outlet flow will eventually become equal to the inlet flow. 

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As discussed in Section 3.1, the transient response of a system is independent of the input. Thus for transient response analysis, the system input can be considered to be zero, and equation (3.41) can be written as... 

Cyclic voltammetry (adsorption, monolayers) Potentiodynamic polarisation (passivation, activation) Cathodic reduction (thickness) Frequency response analysis (electrical properties, heterogeneity) Chronopotentiometry (kinetics)... 

Electrical characteristics of surface films formed electrochemically can be analysed using frequency response analysis (FRA) (sometimes called electrochemical impedance spectroscopy, or This technique is... 

Bode Plot a graph of the frequency response see Frequency Response Analysis) of an electrode whereby the magnitude and the phase angle are separately plotted as a function of the frequency. 

Electrochemical Impedance Spectroscopy see Frequency Response Analysis. 

Frequency Response Analysis the response of an electrode to an imposed alternating voltage or current sign of small amplitude, measured as a function of the frequency of the perturbation. Also called Electrochemical Impedance Spectroscopy. 

Sodium dodecyl sulfate has been used to modify polypyrrole film electrodes. Electrodes synthesized in the presence of sodium dodecyl sulfate have improved redox processes which are faster and more reversible than those prepared without this surfactant. The electrochemical behavior of these electrodes was investigated by cyclic voltametry and frequence response analysis. The electrodes used in lithium/organic electrolyte batteries show improved performance [195]. 

Adsorption of rubber over the nanosilica particles alters the viscoelastic responses. Analysis of dynamic mechanical properties therefore provides a direct clue of the mbber-silica interaction. Figure 3.22 shows the variation in storage modulus (log scale) and tan 8 against temperature for ACM-silica, ENR-silica, and in situ acrylic copolymer and terpolymer-silica hybrid nanocomposites. 

FORNACE A J, AMUNDSON s A, BITTNER M, et ah, (1999) The Complexity of radiation stress responses analysis informatics and functional genomics approaches. Gene Expression 7 387-400. 

A complete dose-response analysis was generated for PCP for doses from 0.625 to 20 mg/kg IP (data not shown). PCP exhibited dose-related anticonvulsant action when day one minus day three differ ence scores were compared for all doses tested. When retested with saline only on day five, no reduction in convulsant sever it or super-sensitive response was observed (day one minus day five), indicating no carryover drug effect 48 hours after dosing. At behavioral ly equivalent doses, all compounds assayed were clearly anticonvulsant (table 3). TCP was most potent at the doses tested. PCA was the most efficacious, and reduced convulsant severity by 2.58 points. As with PCP, none of the other phencycli-noids had any carryover effects 48 hours after dosing (day one minus day five). 

We have given up the pretense that we can cover controller design and still have time to do all the plots manually. We rely on MATLAB to construct the plots. For example, we take a unique approach to root locus plots. We do not ignore it like some texts do, but we also do not go into the hand sketching details. The same can be said with frequency response analysis. On the whole, we use root locus and Bode plots as computational and pedagogical tools in ways that can help to understand the choice of different controller designs. Exercises that may help such thinking are in the MATLAB tutorials and homework problems. 

In effect, we are adding a very large real pole to the derivative transfer function. Later, after learning root locus and frequency response analysis, we can make more rational explanations, including why the function is called a lead-lag element. We ll see that this is a nice strategy which is preferable to using the ideal PD controller. 

The literature refers the term as a first order filter. It only makes sense if you recall your linear circuit analysis or if you wait until the chapter on frequency response analysis. 

One may question whether direct substitution is a better method. There is no clear-cut winner here. By and large, we are less prone to making algebraic errors when we apply the Routh-Hurwitz recipe, and the interpretation of the results is more straightforward. With direct substitution, we do not have to remember ary formulas, and we can find the ultimate frequency, which however, can be obtained with a root locus plot or frequency response analysis—techniques that we will cover later. 

Note 1 This result is consistent with the use of frequency response analysis later in Chapter 8. 

In this computer age, one may question why nobody would write a program that can solve for the roots with dead time accurately Someone did. There are even refined hand sketching techniques to account for the lag due to dead time. However, these tools are not as easy to apply and are rarely used. Few people use them because frequency response analysis in Chapter 8 can handle dead time accurately and extremely easily. 

On the other hand, frequency response analysis cannot reveal information on dynamic response easily—something root locus does very well. Hence controller design is always an iterative procedure. There is no one-stop-shopping. There is never a unique answer. 

Frequency response analysis allows us to derive a general relative stability criterion that can easily handle systems with time delay. This property is used in controller design. 

This is a crucial result. It constitutes the basis of frequency response analysis, where in general, all we need are the magnitude and the argument of the transfer function G(s) after the substitution s = jco. 

We need to appreciate some basic properties of transfer functions when viewed as complex variables. They are important in performing frequency response analysis. Consider that any given... 

We do not need to expand the entire function into partial fractions. The functions Gb G2, etc., are better viewed as simply first and at the most second order functions. In frequency response analysis, we make the s = jto substitution and further write the function in terms of magnitude and phase angle as ... 

With these results, we are ready to construct plots used in frequency response analysis. The important message is that we can add up the contributions of individual terms to construct the final curve. The magnitude, of course, would be on the logarithmic scale. 

Another advantage of frequency response analysis is that one can identify the process transfer function with experimental data. With either a frequency response experiment or a pulse experiment with proper Fourier transform, one can construct the Bode plot using the open-loop transfer functions and use the plot as the basis for controller design.1... 

The pulse experiment is not crucial for our understanding of frequency response analysis and is provided on our Web Support, but we will do the design calculations in Section 8.3. 

This example shows us the very important reason why and how frequency response analysis can... 

With frequency response analysis, we can derive a general relative stability criterion. The result is apphcable to systems with dead time. The analysis of the closed-loop system can be reduced to using only the open-loop transfer functions in the computation. 

The gain and phase margins are used in the next section for controller design. Before that, let s plot different controller transfer functions and infer their properties in frequency response analysis. Generally speaking, any function that introduces additional phase lag or magnitude tends to be destabilizing, and the effect is frequency dependent. 

We know from frequency response analysis that time lag introduces extra phase lag, reduces the gain margin and is a significant source of instability. This is mainly because the feedback information is outdated. 

When we use pade () without the left-hand argument [q, p], the function automatically plots the step and phase responses and compares them with the exact responses of the time delay. Pade approximation has unit gain at all frequencies. These points will not make sense until we get to frequency response analysis in Chapter 8. So for now, keep the [q, p] on the left hand side of the command. 

After that, we can use the result to do frequency response analysis. If you are interested in the details, they are provided in the Session 7 Supplement on our Web Support. 

Kleemann, M., Elsener, M., Koebel, M., et al. (2000) Investigation of the Ammonia Adsorption on Monolithic SCR Catalysts by Transient Response Analysis, Appl. Catal. B, 27, 231. 

Waalkes, M.P., S. Rehm, C.W. Riggs, R.M. Bare, D.E. Devor, L.A. Poirier, M.L. Wenk, and J.R. Henneman. 1989. Cadmium carcinogenesis in male Wistar [Crl (Wl)BR] rats dose-response analysis of effects of zinc on tumor induction in the prostate, in the testes, and at the injection site. Cancer Res. 42 4282-4288. 

Ando, K., Ikeda, H., Yamamoto, K., and Sagami, F., Dose (concentration)-response analysis of drug-induced QT interval prolongation in conscious monkeys (JPMA QT prodact), /. Pharmacol. Toxicol. Methods, 49, 220, 2004. 

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