Regulation by tables

Abstract

A computer-based regulator embodying a trivial background for regulation programmers is pursued. To start, logic is expanded until it incorporates rules and their obligations. Then, theory is withdrawn to rescue tables and interpolations. Finally, the regulator is implemented. It is a governor that follows (tolerant) ruling tables with (multi-) linear interpolations, requires minimal rationale and may govern even with few programmed table lines. For the time being, performance stands on the wisdom of programmers.

Introduction

Regulation tables such as Table 1 may be devised for human operators in charge of a plant.

These tables are very easy to understand. However, people with mathematical training avoid reading them and, when pushed to read, they utter something like: $\text{0.05(q}{}_{\mathrm{<mtext>o</mtext>}}\text{),}\text{115,000(p}{}_{\mathrm{<mtext>oref</mtext>}}\text{)…1.08(x),…0.05…125000…0.72(x)…}$and so on. Pushed much further, they may finally come up with complete sentences, such as: ifq_ois 0.05 andp_orefis 115,000, then x is 1.08; and ifq_ois 0.05 andp_orefis 125,000, then x is 0.72; and so on. Here, indicative verb moods provide propositions that reveal some binary logic studies. That explains the initial reluctance since words such as and are defined in binary logic courses by tables which may only be read by using the same (or equivalent) words. Another issue is that one may also read: q_ois 0.05,p_orefis 115,000 and x is 1.08; orq_ois 0.05,p_orefis 125,000 and x is 0.72; or so on. The problem is that, in the first case, the whole reading seems true when conditions are false (e.g. when q_o is 0.26) and, in the second case, it seems false for both the inclusive and the exclusive standard course versions of or. Puzzlement may be amusing and promote the chase of other words such as also to replace and in the first reading (Lee, 1990a). However it does not help much with the regulation of the plant. The key point is that the indicative mood misses the scenario. Regulation is the king's job. Its name comes from rex, the Latin name for kings. It deals with disturbances. Their name comes from turba, the Latin name for mobs. Not in vane, Watt called his fly-ball device a governor. Table 1 is not pictorial, but mandatory; i. e., it is meant to be read as: ifq_ois 0.05 andp_orefis 115,000, then let x be 1.08; ifq_ois 0.05 andp_orefis 125,000, then let x be 0.72; and so on. This imperative mood has been ignored in logic studies so far and, consequently, has produced elusive manoeuvres against basic grammar (e.g., within fuzzy logic). Let us foster a wider logic in Section 2. Then, let us abdicate and adhere to tables in Section 3. Let us explore applications in Section 4, and let us implement a regulator in Section 5. It will be a rather anthropomorphic governor: not a bright one, but a loyal delegate that will govern by following plain directions.