You are here : Control System Design  Index  Book Contents  Chapter 2  Section 2.3 2. Introduction to the Principles of Feedback

:  commanded level of steel in mould 
:  actual level of steel in mould 
:  valve position 
:  casting speed 
:  inflow of matter into the mould 
:  outflow of matter from the mould. 
Physics suggests that the mould level will be proportional to the integral of the difference between in and outflow:
(2.3.1) 
where we have assumed a unit crosssection of the mould for simplicity. We also assume, again for simplicity, that the measurements of valve position, v(t) and casting speed, , are calibrated such that they actually indicate the corresponding in and outflows:
(2.3.2) 
(2.3.3) 
Hence, the process model becomes
(2.3.4) 
The casting speed can be measured fairly accurately, but mouldlevel sensors are typically prone to highfrequency measurement noise, which we take into account by introducing an additive spurious signal n(t):
(2.3.5) 
where h_{m}(t) is the measurement of h(t) corrupted by noise. A block diagram of the overall process model and the measurements is shown in Figure 2.3.
This is a very simple model, but it captures the essence of the problem.