Uncertainty in measurement and control

P. M. E. M. van der Grinten

Statistica Neerlandica, 1968, vol. 22, issue 1, 43-63

Abstract: Summary Controlling is intervening in a situation on the basis of measurements. The three elements occurring in this definition may each contain an uncertainty that sets a limit to the control efficiency: The measurements may be in error owing to both inaccuracies and sluggishness of the measurements. Proper and rapid data‐processing is essential therefore. The interventions may lose part of their effect through over‐determinancy or dynamically unfavourable (sluggish) responses. In either case statistical calculations disclose the average control errors that are liable to be made, and also the way in which these can be minimized. The situation may be unclear, i.e. the static and dynamic process characteristics are insufficiently known. In such cases regression and correlation techniques may aid in finding a solution. Following a general review, we shall discuss in more detail those aspects that are bound up with the dynamics of the phenomena. Arguments from information theory reveal that the dynamic efficiency of control actions depends on correlation functions of time series (disturbances) and response curves of the systems (processes). The effects of disturbance correlation time, disturbance variance, sampling time, sample treatment, measuring errors, measuring time, rapidity of the intervention, etc., on the efficiency are elucidated by means of some formulae, graphs and examples.

Date: 1968
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