Stabilité et précision de la régulation dynamique

Stability and accuracy of a dynamic control system

Ingénieur à la Société du Canal de Provence et d'Aménagement de la Région Provençale

Abstract

Main features of a dynamic control system a) Intermittent programmed control synchronized by the computer timer. b) The control system "anticipates" demand variation and other factors. c) Overall control of supply canal or duct sections and branch reservoirs. d) Optimization of canal duct flow conditions where necessary to reduce pumping cost or ensure maximal economic efficiency of run-of-the river turbine operation. Basic operating principle Consider a single canal section (a "reach" between two control works) : The system controls the volume of water in the reach at regular intervals, e.g. every 15 minutes, so that it delivers a given volume of water (Vd) for the following purposes : a) To correct the difference between the effective volume in the reach (Ve) (known from measurement data) and the required volume (Vn) determined from the computer's demand forecast for the time taken by the waves to travel the length of the reach (DT). b) To meet the demand during the following period : [H + DT] to [H + DT + 15'] Where H is the hour at which control is effected. The corresponding operating equation is determined by automatic system analysis methods. It expresses the proportional differential action of elementary dynamic control. Experimental verification A test with a simulated forecasting error of 100 % on the downstream reach of the Canal de Provence confirmed that the control error stabilised without oscillation at a value corresponding to the "residual error" of the control system and depending on the degree of inaccuracy of the forecast. Control stability Considering its method of application, dynamic control can be considered stable, since action of the control device is sufficiently "uncoupled" from the system under control. Control accuracy For offtakes operating "on demand", the forecasting principle is based on extrapolation of consumption data recorded when control takes place, using correlation laws with stastically-determined parameters. The maximum possible error downstream from the considered reach is estimated from the following : a) Relative forecasting error E for the time (in half-hours N) covered by the forecast. b) The representative daily peak consumption curve for an offtake supplying a mean daily discharge of 1 m³/sec. c) Reaction time of the considered reach, i.e. its length. The calculated data plot shows this error to be sufficiently small to be usually offset by normal canal freeboard, without any requirement for raised horizontal canal banks (i.e. civil engineering costs are lower than for conventional forms of control). Should this error unexpectedly exceed a given critical value, the general control arrangements for all canal sections discharge part of the surplus to reaches farther downstream or divert it to branch storage facilities, or they initiate other forms of appropriate action. Similar automatic action is also initiated in the event of a probable shortage, e.g. drawing of supplies from "over-stocked" reaches or spreading the shortage out over several reaches to make it barely noticeable for consumers during the time required for supply corrections to react along the system.