2. Introduction to the Principles of Feedback
To make progress on the control-system design problem as set out above, it is first necessary to gain an understanding of how the process operates. This understanding is typically expressed in the form of a mathematical model that describes the steady-state and the dynamic behavior of the process. To construct such a model, we first define relevant process variables. Thus, we introduce the following:
Physics suggests that the mould level will be proportional to the integral of the difference between in- and outflow:
where we have assumed a unit cross-section 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:
Hence, the process model becomes
The casting speed can be measured fairly accurately, but mould-level sensors are typically prone to high-frequency measurement noise, which we take into account by introducing an additive spurious signal n(t):
where hm(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.