1. Structural analysis Supervisory control slides Control Engineering Department 2006

2. Structural analysis in FTC development

3. Structural analysis - background Analysis of the structural properties of the models, i.e., properties which are independent of the actual values of the parameters. Only links between the variables and relations, which are derived from the operating model, are represented in this analysis. The links are independent of the operating model and are thus independent of the form under which this operating model is expressed (qualitative or quantitative data, analytical or non-analytical relations).

4. Structural analysis approach

5. Structural graph representation Purpose: –To find the monitorable (over-determined) part of the system. Matching: –is a set of pairs (f j,x i ) such that any constraint f j  F X belongs to one pair. F X set of constraints which are applied at least on one unknown variable. Starting point: Hypothesis: An unknown variable x i is computed, using the constraint f j under the assumption that all other variables are known.

6. Structural model System considered as a set of components S = Each composing a set of relations f i between a set of variables z j, j=1,....,n.

7. Structured model - 1

8. Structured model - II Incidence matrix I A * is not necessarily the same as A T. It highlights the property of calculability. where

9. Example 1 Nonlinear diff. Eq.: Can be rewritten to the following diff.algebraic equations: Can then be represented by following relations:

10. Example II LTI system: Can be rewritten to diff. Alg. Eqs. Is represented by the following incidence matrix

11. An Example: P-control system Used information: variables with non-zero coefficients that are involved in equations/relations.

12. Incidence matrix of the P-control system

13. Matching and calculability property

14. Canonical decomposition Decomposition of the P-control system

15. Matching: P-control system

16. Sensor Fault representation Two different views are considered

17. Actuator fault representation Actuator malfunctions Completely Actuator functions but incorrectly (with bias)

18. Fault detection and isolation Any minimal over-determined subsystem results in an ARR expression: Residuals are obtained Fault isolation: look at how different faults affect different residuals

19. Software prototype A dedicated prototype software toolbox is been developed In the Cont. Eng. Dept. (AAU). The prototype can be downloaded from http://www.control.auc.dk/ftc/html/software_tools.html

20. Example (linear): LTI model of an wing dynamic of an aircraft: