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2. Introduction to the Principles of Feedback

2.3.3 Feedback and Feedforward

We will find later that the core idea in control is that of inversion. Moreover, inversion can be achieved conveniently by the use of two key mechanisms (namely, feedback and feedforward). These tools give an elegant and robust solution to many control design problems. In the context of mould-level control, the simplest feedback controller is a constant gain, K driving the valve proportionally to the error between the commanded mould level, h*, and the measurement of the actual mould level, hm(t):


\begin{displaymath}v(t)=K(h^{*}-h_m(t)) \end{displaymath} (2.3.6)

To anticipate how a controller of this form might perform, we observe that a deviation between set-point and measurement must first occur before the controller can react. We know, however, that a change in casting speed requires a modified operating point for the valve. Thus, rather than letting a change in casting speed occur, which then leads to an error in the mould level to which the feedback controller reacts, we can improve the strategy by changing the valve-position proactively. This is called feedforward. This leads to a final controller of the form:


\begin{displaymath}v(t)=K\left( \left[ h^{*}-h_m(t)\right] +\left[ \frac 1K\sigma(t)\right] \right) \end{displaymath} (2.3.7)

Note that this controller features joint feedback and a preemptive action (feedforward). In particular, the second term gives the predictable action necessary to compensate for the casting speed changes, while the first term reacts to the remaining error.

A block diagram for the final control system is shown in Figure 2.4.


Figure 2.4: Model of the simplified mould-level control with feedforward compensation for casting speed
Model of the simplified mould-level control with feedforward compensation for casting speed

Further discussion of this problem, together with the capability of the reader interacting with the design, is contained in the book's web page.