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In this paper, we describe the application of electrochemical impedance spectroscopy (EIS) to characterize process of formation and properties of solid-supported tethered bilayer membranes on solid conducting substrates. Along with the description of experimental procedures to prepare substrates and self-assembly of phospholipid bilayers onto gold-coated glass slides, we describe the detailed protocols of EIS measurements. We demonstrate the utility of EIS in the evaluation of the properties of both molecular anchor layers used to immobilize tBLMs as well as characterization of tBLMs. We show that the EIS methodology extends the applicability of this technique well beyond the mere evaluation of electric parameters. Specifically, we demonstrate how by using EIS one may evaluate both density and size of water-filled defects (ion-channels) in tBLMs, to determine the structural mode (homogeneous, heterogeneous, or clustered) of distribution of defects in tBLMs. Our methodology can be applied in both basic protein membrane interaction studies, as well as in the development of precision biosensoric systems with tBLMs as a sensing element.

In any negative feedback system the measured actual control variable xactual is compared with a given reference value xref. Ideally the actual instantaneous value of a control variable should follow the given reference value. However, this is not entirely possible and the quality of a control system depends to a large extent upon the type of controller used. In applications there are linear and nonlinear controllers. Here only the simplest linear controllers will be discussed: the proportional (P) controller and the proportional-integral (PI) controller.

In the first part of this chapter we will consider a graphical representation of the transfer function in terms of its frequency response \(H(j\omega ) = \left| {H(j\omega )} \right|e^{\angle H(j\omega )}\). Bode diagrams or plots consist of two separate plots, the amplitude \(\left| {H(j\omega )} \right|\) and the phase angle \(\angle H(j\omega )\), with respect to the frequency \(\omega\) on a logarithmic scale. These plots are named after Bode, in recognition of his pioneering work Bode (1945). Bode’s basic work was based upon approximate representation of amplitude and phase response plots of a communication system. Wide range of frequencies of interest in a communication system dictated the use of the logarithmic frequency scale. Bode plots use the asymptotic behavior of the amplitude and the phase responses of simple functions by straight-line segments and are then approximated by smooth plots with ease and accuracy. Bode plots can be created by using computer software, such as MATLAB. The topic is mature and can be found in most circuits, systems, and control books. For example, see Melsa and Schultz (1969), Lathi (1998), Close (1966), Nilsson and Riedel (1966), and many others.

As has been discussed in the previous chapter, the current steering topology is currently the preferred architecture for telecommunication applications requiring a high update rate and/or a high accuracy. Designing such a D/A converter requires a thorough understanding of both the static and the dynamic behaviour of this device.

Frequency response analysis is applied for the analysis of liquid chromatography output of protein separation. Reduced data from simple chromatograms suggest that various Bode plot parameters, magnitude ratios, phase shift, the steady state gain, break frequency, and system order in the frequency domain, can be used to gain phenomenological insights on the system. Such an approach is advantageous because the validity of the model can be checked for two plots, the magnitude ratio vs. frequency and the phase shift vs. frequency, as compared to a single plot in the time domain. This approach also provides a useful empirical tool which can be quantifiably used for process validation and scale-up, especially for immunoaffmity and immobilized metal affinity chromatographic systems used for protein C purification.

The classical methods known as frequency domain techniques have their origin with electrical engineers, who rely extensively on representations of signals as sums of sinusoids in their modelling and analysis. It has seemed natural for them to carry such ideas with them into control systems analysis and synthesis, often with considerable success. Less successful has been the direct use of the methods for sampled data control systems (although indirect use characterized by conversion of continuous system designs is possible). This has been for several reasons: the approximations that allow sketching do not always apply, the compensators of most common use are not so relevant for digital control systems, and well established relationships between step responses, pole locations, and frequency responses seem to hold only roughly for sampled data systems. Nevertheless having at least some knowledge of frequency domain methods is fundamental, and for that reason we review them here.

The Finite Element Method (FEM) has been used extensively in the analysis, of induction machines. This chapter describes the use of magneto-dynamic analysis to study the induction machine in the frequency domain. This information gives average torque, losses and flux density. The solutions can also be used to find equivalent circuit parameters. The magneto-dynamic solution has two other applications. By coupling the solution to external circuits we can obtain a Bode diagram from which a model can be synthesized. This is a simulation of the SSFR (stand still frequency response) test. A second application involves the time domain analysis of the induction motor described in the following chapter. While only the steady state solution may be of interest, it may take many cycles of computation before the starting transient disappears. This information may be of no interest. We can use the frequency domain solution to find initial conditions for the time domain analysis. It is found that when the transient solver is started from the frequency domain solution, the first cycle is close to the steady state solution.

Monolithic IC technology puts severe limitations on the options available for frequency compensation. A major restriction is the fact that inductors of any significant value cannot be integrated, while these components play an important role in the conventional compensation practice. This leaves capacitors as the only frequency dependent element to shape the frequency response. Unfortunately, even their use is limited to small values —much smaller than demanded by classical theory.

The possibility of using inspiratory, oscillating inert gas concentration forcing signals to measure the average lung ventilation-perfusion ratio was proposed by Zwart and colleagues (1976, 1978). These authors used halothane as the forcing gas, at sub-anaesthetic concentra­tions around 0.02% v/v, but this introduced severe measurement problems at these very low concentrations. Recently Hahn et al (1993) have described a similar but improved respiratory model which uses nitrous oxide (N2O) as the forcing gas. The advantages of nitrous oxide over halothane are that it is free from biological toxicity; it is easy to measure N2O with conventional gas analysis apparatus (especially at the concentrations used by Hahn et al (1993), around 2–10% v/v); and because nitrous oxide can be measured continuously in blood, the mathematical model can be extended to include shunt blood flow. In this technique, a three-compartment continuous ventilation mathematical model describes the imposition of a forced oscillating inspired inert gas concentration, Pi(t), which oscillates sinusoidally over a range of frequencies (0.6 to 6 min-1), and the subsequent measurement of the attenuation of the end-expired inert gas concentration, Pe(t), with changing forcing frequency (Figure 1). The plot of Pe/Piagainst forcing frequency (the Bode plot) is then used to derive alveolar volume, Va, and pulmonary blood flow, Qp. Dead space, Vds, is derived from the sinusoidal mixed expired indicator gas signal. We have further modified this technique by using a single forcing monosinusoid (forcing frequency 0.5 min-1) of two inert gases to measure cardio-respiratory lung function. This binary inert gas oscillation technique uses Argon, which is relatively insoluble in blood, to derive alveolar volume and dead space; and nitrous oxide, which is soluble in blood, to measure pulmonary blood flow.

A mathematical model must be constructed in order for either body fluid measurements of drug concentration or pharmacological response intensity data to be useful for computation of the time course of systemic drug bioavailability. For linear compartment models the time course of either drug concentration or pharmacological response is represented by a sum of exponentials. The usual method for establishing such models involves the use of some form of nonlinear least-squares estimation technique. For systems of order higher than first, such techniques are often cumbersome, time consuming, and in some cases inadequate. A general frequency response technique commonly used in systems engineering applications, pulse testing, has been successfully applied to pharmacological data for model identification. The method is general and can be applied equally well to blood or urine data. Theoretical descriptions of both the nonlinear least-squares estimation technique in the time domain and the frequency domain estimation technique are presented here. The frequency response data obtained by pulse testing are fitted with accurate model parameters by using a nonlinear least-squares estimation technique in the frequency domain. However, the number of parameters which must be determined, is decreased when modelling in the frequency domain. This results in decreased computation time. For example, the least-squares time domain technique required 25 and 190 seconds of computation time for second- and third-order models, respectively, while the frequency domain technique required 8 and 10 seconds for the same models.