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Additional info for Advanced regulatory control : system design and application
Hence, its temperature is indirectly determined by the position of the valve. From this stable condition, let us make a step increase in the valve position. This will increase the steam flow, causing the pressure in the coil to rise. The steam within the coil represents a point of (thermal) energy storage. The steam pressure, and hence the temperature in the coil, will not rise instantaneously. It will rise only as the mass of steam within the coil increases. This will be similar to the response of a first-order lag, with a very short time constant.
This is redrawn as Figure 3-1 here, but in this case the independent and dependent variables are identified. Let us assume that we have a liquid phase process that must be heated to a specified temperature. We also assume that we have a liquid phase heating medium, such as hot water or hot oil. 7KLQ )K 7FRXW ',6785%$1&(6 7FLQ )F 7FLQ 7FRXW 2WKHU )F 7KRXW Figure 3-1. Disturbances to a Control Loop From a process control viewpoint, the independent variable is the valve position, or equivalently, the controller output.
Both of these situations represent two first-order lags, but in Figure 3-12a the lags are said to be uncoupled, whereas in Figure 3-12b, the lags are said to be coupled. In both cases, the response to a step change in input will be an “S-shaped curve” rather than the idealized first-order lag response of Figure 2-4. A more detailed discussion of the shape of the S-shaped curve follows later in this section. We note, however, that coupled lags are representative of many physical processes. For example, heat transfer from the hot to the cold side of a heat exchanger is dependent upon the differential temperature between the two sides.