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Extra resources for Applied control theory
A curve like that shown in Fig. 9 is typical for an existing plant whose performance is to be improved by the addition of a complex scheme. The plant is supposed to operate at performance level A originally and at level B with the control system working fully. The time scale will depend on the complexity of the scheme. It is clear that an economic justification based on an instantaneous step jump in performance is unlikely to be realised in practice. Clearly, monetary inflation makes matters worse and has to be taken into account.
Below we set up three categories of variables according to the ease with which continuous measurement can be made on-site. ) (A) Variables particularly suitable for continuous measurement Examples Position, velocity and acceleration (the servomechanism variables) Weight and density Mechanical stress Liquid level Gas or liquid pressure or flow rate Temperature Current and voltage (B) Variables for which universally accepted measurement techniques exist but where continuous on-line measurement is more difficult Examples Viscosity Chemical composition (C) Variables that, although economically important, do not have a fully scientific basis for their quantification Examples Product colour, taste and crispness (foods) Internal cracks, flatness and surface finish (metals) Although category (A) variables are the easiest to measure, they can still present some formidable problems in practice.
3(#). Of course, not every process can be modelled by this type of expression: (a) Processes containing integrators would be modelled equivalently by an expression of the form Ke~sT/s [Fig. 43(b)]. (b) Processes with oscillating step response would need at least a second-order model to represent them. (c) Processes with the step response as shown in Fig. 3(c) need at least a secondorder model and a numerator term if they are to be modelled at all accurately. Once the process model of form (Ke"$T2)/(l + sTt) is available, Ziegler and Nichols (1942) suggest the following settings for the three-term controller: Proportional gain only 1 T k = — —; A T2 Proportional + integral controller Three-term controller k = 1*2 T k = —~~, A T2 0-9 Tx , K T2 7> = 2T2, 7/ = 3*3T2; TD = 0-57^.