Page 267 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

256 STATE ESTIMATION IN PRACTICE

8.1 SYSTEM IDENTIFICATION

System identification is the act of formulating a mathematical model of a
given dynamic system based on input and output measurements of that
system, and on general knowledge of the physical process at hand. The
discipline of system identification not only finds application in estimator
design, but also monitoring, fault detection and diagnosis (e.g. for
maintenance of machines) and design of control systems.
A dichotomy of models exists between parametric models and non-
parametric models. The nonparametric models describe the system by
means of tabulated data of, for instance, the Fourier transfer function(s)
or the edge response(s). Various types of parametric models exist, e.g.
state space models, poles-zeros models and so on. In our case, state space
models are the most useful, but other parametric models can also be used
since most of these models can be converted to a state space.
The identification process can roughly be broken down into four parts:
structuring, experiment design, estimation, evaluation and selection.

8.1.1 Structuring

The first activity is structuring. The structure of the model is settled by
addressing the following questions. What is considered part of the system
and what is environment? What are the (controllable) input variables? What
are the possible disturbances (process noise)? What are the state variables?
What are the output variables? What are the physical laws that relate the
physical variables? Which parameters of these laws are known, and which
are unknown? Which of these parameters can be measured directly?
Usually, there is not a unique answer to all these questions. In fact, the
result of structuring is a set of candidate models.

Example 8.1 Candidate models describing a simple hydraulic system
The hydraulic system depicted in Figure 8.2 consists of two identical
tanks connected by a pipeline with flow q 1 (t). The input flow q 0 (t)is
acting on the first tank. q 2 (t) is the output flow from the second tank.
The relation between the level and the net input flow of a tank is
Cqh ¼ qqt. C is the capacity of the tank. If the horizontal cross-sections
of the tanks are constant, the capacity does not depend on h.Inthe
2
present example, the capacity of both tanks is C ¼ 420 (cm ). The order
of the system is at least two; the two states being the levels h 1 (t)and h 2 (t).