Fase de planificación

Chapter Highlights

• Importance of performance specification

• Uses in existing product selection, design/development of new products

• Categories of performance specification: speed of performance, stability

• Types of performance parameters: (1) used in engineering practice (provided in manufacturer/

vendor’s data sheets) and (2) parameters defined using engineering theoretical considerations (model-based)

• Models used for performance specification: (1) differential-equation models (time domain) and (2) transfer-function models (frequency domain)

• Nonlinearties and effects

• Bandwidth considerations in instrumentation

• Sensitivity considerations in instrumentation

• Sensitivity considerations in error propagation and combination

3.1 Performance Specification

An engineering system consists of an integration of several components such as sensors, transducers, signal-conditioning and modification devices, controllers, and a variety of other electronic and digital hardware. The performance and realization of intended purpose of the system depends on the per-formance of the individual components and how the components are interconnected. All devices that assist in the intended functions of an engineering system can be interpreted as components of the sys-tem. Activities related to system instrumentation such as prescription of the components for the system, selection of available components for a particular application, design of new components, and analysis of the system performance should rely heavily on performance specifications. The performance require-ments have to be specified or established based on the functional needs of the overall system. These spec-ifications are established in terms of the rating parameters (performance parameters) of the components.

Some performance parameters are found in the product data sheet, which can be obtained from the manufacturer or vendor. For new developments of products, the required performance specifications have to be developed by the product development team (engineers, etc.) in consultation with the users, regulatory agencies, vendors, and so on.

3.1.1 Parameters for Performance Specification

In this chapter, we study ratings and parameters for performance specification of the components in an engineering system. Typically, the component performance is specified under three important types of performance measures:

1. Speed of performance 2. Stability

3. Accuracy

Performance parameters in all three types are discussed in this chapter. As expected, due to the dynamic interactions in an engineering system, there is some degree of interrelation among parameters of these three types.

Two categories of parameters are found in the performance specification of components in an engi-neering system:

1. Parameters used in engineering practice (e.g., parameters listed commercially in the component data sheets)

2. Parameters defined using engineering theoretical considerations and a reference model, either in the time domain or in the frequency domain

Instrument ratings for commercial products (category 1 in the list earlier) are often developed on the basis of the analytical engineering parameters (category 2 earlier). However, the nomenclature and the definitions used in category 1 may not be quite identical or consistent with the precise analytical defini-tions used in category 2, for reasons of convention and the history of engineering practice. Nevertheless, both categories of performance parameters are equally important in the instrumentation practice, and are addressed in this chapter. Specifically, the chapter addresses the basis (analytical basis, practical reasons, rationale, etc.) of performance specification of the components of an engineering system, and the parameters used for that purpose. Even though sensors and associated hardware are particularly emphasized in the chapter, the procedures are generally applicable to a variety of components in an engineering system since these components can be represented by similar dynamic models, which are used in the development of the parameters for performance specification.

A great majority of instrument ratings provided by manufacturers (or, parameters provided in com-mercial instrument data sheets, which come under category 1) are in the form of static parameters.

In engineering applications, however, dynamic performance specifications are also very important, and they primarily come under category 2. Both static and dynamic characteristics of instruments and rel-evant parameters are discussed in the chapter.

A sensor detects (feels) the quantity that is measured (measurand). The transducer converts the detected measurand into a convenient form for subsequent use (monitoring, diagnosis, control, actua-tion, predicactua-tion, recording, etc.). The transducer input signal may be filtered, amplified, and suitably modified as needed for its subsequent use. Components used for all these purposes may be addressed in this context of performance specification and rating parameters. Of course, the primary end goal of instrumentation is to achieve the desired performance from the overall integrated system. Performance of the individual components is critical in this regard because the overall performance of the system depends on the performance of the individual components and how the components are interconnected (and matched) in the system.

For performance specification in the analytical domain (i.e., category 2), two types of dynamic mod-els are used:

1. Differential-equation models in the time domain 2. Transfer-function models in the frequency domain

Specifically, the parameters for performance specification are commonly developed using these two types of dynamic models. Models are quite useful in representing, analyzing, designing, and evaluating

sensors, transducers, controllers, actuators, and interface devices (including signal-conditioning and modification devices). In the time domain, such performance parameters as rise time, peak time, set-tling time, and percent overshot may be specified. Alternatively, in the frequency domain, bandwidth, static gain, resonant frequency, magnitude at resonance, impedances, gain margin, and phase margin may be specified. These various parameters of performance specification will be discussed in this chap-ter. In particular, bandwidth plays an important role in specifying and characterizing many compo-nents of an engineering system. Notably, the useful frequency range, operating bandwidth, and control bandwidth are important considerations. In this chapter, we study several important issues related to system bandwidth in some detail.

In any multicomponent system, the overall error depends on the component error. Component error degrades the performance of an engineering system. This is particularly true for sensors and transduc-ers as their error is directly manifested within the system as incorrectly known system variables and parameters. As error may be separated into a systematic (or deterministic) part and a random (or sto-chastic) part, statistical considerations are important in error analysis. The degree of seriousness of how a component error affects the overall system error concerns sensitivity. In particular, the sensitivity to desirable factors has to be maximized while the sensitivity to undesirable factors has to be minimized.

Since there may be vast number of factors that can affect the system performance, we need to find ways to select a reasonable factor of them that can be incorporated in the instrumentation task. This chapter also deals with such considerations of error and sensitivity analysis.

3.1.1.1 Performance Specification in Design and Control

As observed in the previous chapters, instrumentation is relevant in both design and control.

Instrumentation completes the design of a system. Control helps achieve performance requirements, and in some sense, control compensates for design shortcomings. In fact, in the context of Mechatronics, both instrumentation and control should be considered concurrently within the mechatronic design problem, which involves integrated multidomain optimal design. It is clear that, performance speci-fications are indeed design specispeci-fications. Both instrumentation and control help in achieving these specifications.

It will be clear in the sequel that control specifications are rather similar to the specifications for instrumentation and design. Specifically, a particular rating parameter such as sensitivity may be adapted to achieve some performance objective through control as well as design and instrumentation.

3.1.1.2 Perfect Measurement Device

Measuring devices, which include sensors and related hardware, are an important category of compo-nents in instrumentation of an engineering system. Their performance may be specified with reference to a perfect measuring device. A perfect measuring device can be defined as one that possesses the fol-lowing main characteristics:

1. Output of the measuring device instantly reaches the measured value (fast response).

2. Transducer output is sufficiently large (high gain, low output impedance, high sensitivity).

3. Device output remains at the measured value (without drifting or getting affected by environ-mental effects and other undesirable disturbances and noise) unless the measurand (i.e., what is measured) itself changes (stability and robustness).

4. The output signal level of the transducer varies in proportion to the signal level of the measurand (static linearity).

5. Connection of a measuring device does not distort the measurand itself (loading effects are absent and impedances are matched; see Chapter 2).

6. Power consumption is small (high input impedance; see Chapter 2).

All these properties are based on dynamic characteristics and, therefore, can be explained in terms of dynamic behavior of the measuring device. In particular, items 1 through 4 can be specified in

terms of the device response, either in the time domain or in the frequency domain. Items 2, 5, and 6 can be specified using the impedance characteristics of the device. First, we discuss the response charac-teristics that are important in the performance specification of a component of an engineering system.

3.1.2 Dynamic Reference Models

As noted earlier, in engineering applications, both static parameters and dynamic parameters are used in performance specification. Dynamic performance parameters for a device concern dynamics of the device. For example, the perfect requirements are never precisely realized for a sensor, perhaps in view of the sensor dynamics. For instance, the sensor will have a delay in providing its final reading due to the sensor dynamics (time constant).

Dynamic performance parameters are established with respect to a dynamic model, which represents the dynamics of the considered component (e.g., sensor). It may not be a complete and precise model of the device, but rather a model representing the performance specifications. Hence, it is a reference model. However, the dynamics of the reference model has to be related to the dynamics of the actual device (or a precise model of it). Two types of dynamic models are used:

1. Differential-equation models in the time domain 2. Transfer-function models in the frequency domain

Time-domain models can be converted into transfer-function (i.e., frequency-domain) models and vice versa by means of a simple operation (i.e., replacing the time-derivative operation d/dt by the Laplace variable s, and vice versa). However, for practical reasons of significance of the performance parameters in both domains, it is important to consider models in both domains.

The widely used reference models for a component are 1. First-order model

2. Second-order (simple oscillator) model

Both models have to be considered because a complete second-order model cannot be constructed by cascading two first-order models, since the cascading will always result in an overdamped model, which cannot represent oscillations that commonly and naturally occur in the device dynamics.

3.1.2.1 First-Order Model

A first-order linear dynamic system is given by (in time domain)

ty y ku+ = (3.1)

where

u is the input y is the output τ is the time constant k is the dc gain

The corresponding transfer-function model is Y s U s H s

s k ( )

( )= ( )=

t 1+ (3.2)

Suppose that the system starts from y(0) = y₀ and a step input of magnitude A is applied at that initial condition. The corresponding response is

ystep=y e₀ ^-t^/t+Ak(1-e^-t^/t) (3.3)