Frequency-Domain Performance Analysis for Multi-Rate Sampled-Data Sys- tern
Chapter 3 Chapter 3
Robust Control Structure Selection -
Secondary Measurement Selection in the Presence of Modellplant Mismatch
The purpose of this chapter is to present a unified methodology for measurement selection in the presence of model/plant mismatch. First, we outline an underlying philosophy on which we base our efforts to develop measurement selection tools.
The rest of the chapter presents various measurement selection tools that have been developed thus far within this philosophy. Some tools require only the system-intrinsic information ( i . e . , information that is independent of the controller) while other tools are developed assuming certain properties of the controller and are therefore tied to specific controller design methods. Even though we develop this chapter in the context of measurement selection only, all the proposed methods are applicable to the more general problem of control structure selection (which involves selection of actuators as well as measurements) without modification.
3.1 General Approach/Philosophy
The conventional approach to the problem of measurement selection has been to develop a criterion or a set of criteria based on which the comparative merits of measurement candidates are evaluated and the best candidate is chosen [5,31,35,29].
However, we believe there must be another layer to the measurement selection pro-
cedure. For most practical problems, the number of measurement candidates (that consist of all the possible combinations of the available sensors) is extremely large.
The criteria that accout for all the relevant characteristics of measurements with suf- ficient generality and precision are not only very difficult to develop, but also tend to be numerically complex. Reducing the number of candidates through simple criteria before applying detailed analysis should lessen the required efforts for measurement selection dramatically.
Hence, the approach we take to the problem of measurement selection is to elim- inate first systematically those candidates for which a controller meeting a given performance specification cannot be designed (as illustrated in Figure 3.1). This added layer resolves one difficult problem for the conventional approach: In practical applications, a nonconservative, rigorous uncertainty model is often unavailable. It is generally not desirable to make the ultimate measurement selection based on the uncertainty information that is either incomplete or conservative. When the objective is to eliminate undesirable candidates, however, "parsimonious" uncertainty models (that is, models that encompass only those mismatches that are highly probable to arise in practice and have strong influences on the closed-loop stability and perfor- mance) can be used. In other words, the elimination process can be carried out even with incomplete knowledge of system uncertainty. Once the number of candidates has been reduced to a sufficiently low level, detailed analysis (such as actual control system design and simulations) can be carried out to make the final decision.
The screening of the candidates can be accomplished in two steps as illustrated in Figure 3.1. The first proposed step is to eliminate the candidates for which a controller achieving a desired level of robust performance does not exist regardless of what controller design method is used. The criteria that can be used to accomplish this design-independent screening will be referred to as "general screening tools." This screening process leaves candidates for which a control system leading to satisfactory
performance may potentially exist. However, this alone may not reduce the number of candidates down to a sufficiently low level. In some cases, the control design methods available to the engineer may invariably lead to controllers with certain intrinsic properties. We may exploit these properties and carry out an additional screening in the context of a particular design method. That is, one may choose to further eliminate those candidates for which the particular design approach under consideration cannot yield a controller achieving a desired level of robust performance.
The criteria that can be used under a particular design approach will be referred to as "design-specific screening tools." If the second screening under a particular design approach does not leave any viable candidate, it is implied that a more complex, involved design approach is necessary. The screening process may be repeated in the context of another design approach.
In the subsequent parts of this chapter, we introduce a fiumber of numerically e 6 - cient screening tools, both general and design-specific, that can be used to reduce the number of measurement candidates. The whole approach will be based on the Struc- tured Singular Value theory, therefore, allowing a general norm-bounded uncertainty description.
Measurement Selection Problem Formulation
The general measurement selection problem we treat in this thesis is depicted in Fig- ure 3.2. y k represents the jth set of measurements (including the primary, secondary measured variables) excluding those variables that cannot be measured reliably. The reason for excluding the operationally unreliable measurements is because it is desir- able to choose a measurement set such that a required level of performance can be maintained even when some of the failure-prone measurements become unavailable.
In many practical applications, the primary variables that are sampled at a slow rate are also operationally unreliable. In this case, y, consists only of the secondary
Available Actuators/Measurements
I Control Structure Candidates:
All Possible Combinations of
Available Actuators 1 Measurements 1
General Screening Tools I
General-Screened Candidates:
Candidates That Can Potentially Yield A
Controller Satisfying Performance Specifications
I /1
I I