Ind. Eng. Chem. Res. 1987,26, 179-180
179
Cascade Temperature Control System for the Berty Reactor A cascade control system is described that enables precise control of the gas temperature in a Berty reactor. The “Berty” reactor (Berty, 1974) is a popular commercially available “gradientless” laboratory reactor that is useful for studies of solid-catalyzed reaction kinetics. Of THERMOWELLS
CATALYST
BASKET DRAFT TUBE
IMPELLER
INLET OUTLET
SKIN: LOWER SIDE INITIALTEMPERATURES INSIDE: 329’C SKIN 210’C TOP 196’C
0
r
I
I
I
20
40
60
80
I
100
120
TIYE(MIN)
Figure 1. Schematic diagram of “Berty” gradientless reactor.
Figure 4. Response of gas and skin temperatures to sustained 30% decrease in power to bottom furnace element.
i PRIMARY IT& CONTmLLER
SECONDARY I T s d CONTROLLER
Figure 2. Block diagram of cascade control system.
AT(’C) 6
TGAS
4
TSKIN
2
0 50
60
TIME(MIM
Figure 3. Response of gas and top skin temperatures to 5.75 “C gas temperature set-point change. 0888-5885/87/2626-0179$01.50/0
particular importance in such studies is the precise control of the gas temperature inside the reactor. However, owing to the large thermal mass of the reactor and the low heat-transfer rate from the electric furnace, conventional single-loop controllers are unable to provide the required precision of gas temperature control. In contrast, a simple cascade control system, described below, yields excellent temperature control with respect to both gas temperature set-point changes and load disturbances. As shown in Figure 1,the Berty reactor employs a fixed bed of catalyst supported inside a draft tube. A magnetically driven impeller provides an internal gas recycle. The reactor is sheathed with a removable three-zone electrical furnace. The reactor’s outside-wall (skin) temperature is measured at three points (top, middle side, lower side) with spring-loaded thermocouples. The slow heat-transfer rate achievable with this furnace, combined with the 50-kg mass of the vessel and internals, results in a dominant time constant of 2.4 h for the response of the gas temperature to a change in furnace power input. In all control systems tested, the bottom furnace heating element was maintained at a constant power level by an independent VARIAC. The top and middle furnace elements were treated as a single manipulated variable. The power applied to the top element was a fixed fraction of the power applied to the middle element. These two furnace elements will hereafter be referred to as “the furnace”.
0 1987 American Chemical Society
Ind. Eng. Chem. Res. 1987,26, 180-181
180
As shown in Figure 2, the cascade control system comprises two loops. The primary loop measures gas temperature and manipulates the set point of the secondary top-skin-temperature controller. The top-skin-temperature controller manipulates the furnace power in order to track its set point. The cascade controller performance is shown in Figure 3 for a 5.75 “C increase in gas temperature set point. The gas temperature settled at the desired set point after only 40 min. The top skin temperature is seen to follow a complex trajectory; a simple step change in furnace power would have resulted in a much slower gas temperature response. The controller also performs well in the face of load disturbances. Figure 4 shows the gas temperature response to a 30% decrease in power to the bottom furnace zone.
Acknowledgment I gratefully acknowledge the General Electric Company for permission to publish this work. Literature Cited Berty, J. M. Chem. Eng. h o g . 1974, 70(5), 78.
James M. Silva General Electric Company Corporate Research and Development Center Schenectady, New York 12301 Received for review June 20, 1985 Accepted June 10, 1986
CORRESPONDENCE Comments on “Shortcut Operability Analysis. 1. The Relative Disturbance Gain” Sir: In a recent article, Stanley et al. (1985) proposed a new steady-state control loop interaction index, the Relative Disturbance Gain (RDG). The present correspondence addresses two problems associated with the concept of the RDG in relation to its development and its use in assessing the benefits of loop decouplers. 1. “Perfect Control” and the Transfer Function or Gain Matrix
Stanley et al. (1985) and other recent workers in the area of interaction analysis (Friedly, 1984; McAvoy, 1983;Tung and Edgar, 1981) use a transfer function matrix or the corresponding steady-state gain matrix as the basis of their analysis. This is despite the fact that such a representation may hide valuable information about the interactive properties of the system (Johnston and Barton, 1985). This is particularly true when the concept of “perfect control” enters the interaction index definition, as it does with the RDG. An example used by Stanley et al. is a case in point. The model considered had the form x = A x + Bm + D d (1) with A =
R = [:‘5
-2.0 - 5 7
:,J D
=
[:1
where x1 was paired in a control loop with m, (loop 1)and with m2 (loop 2 ) . The RDG is based on a steady-state gain matrix which for the example above is given by x2
From eq 2, it is possible to calculate the RDG elements for the two loops pi = -4.0 p2
= 0.926
0888-5885/87/2626-0180$01,50/0
Stanley et al. claim that the large value of PI indicates unfavorable interaction from loop 2 to loop 1. However, consider the state-space model, eq 1,which is shown as a cause and effect graph in Figure 1. If x 2 is held exactly at its set point at all times through perfect control action, then m2 will have no effect whatsoever on xl. This is because m2 can only influence x1 via changes in x 2 ; the perfect control action blocks this influence and effectively decouples loop 2 from loop 1. Similarly, when x l is under perfect control, loop 1is decoupled from loop 2. If perfect control were possible at all times, the loops would be completely decoupled and there would be no interaction. Any interaction index, such as RDG, based on perfect control behavior should reveal the increased decoupling effect as control quality improves (in the limit approaching perfect control). However, this is only possible if the analysis is based on the state-space model rather than on a steady-state gain or transfer function matrix. No interaction index is perfect, and as McAvoy (1985) has pointed out, different workers define their measures of interaction in different ways and for different purposes. However, it is important to note that significant interaction information may be hidden in steady-state gain or transfer function matrices, whereas this information is revealed explicitly by a state-space model. It is appreciated that in many cases, a state-space model will not be available. However, in cases where such a model is available (as in the examples given by Stanley et al.), methods such as the steady-state and dynamic “direct gain” interaction analysis of Johnston and Barton (1985) can be used to a great advantage. 2. RDG as a Guide to the Need for Decouplers Stanley et al. claim that the RDG may be interpreted as giving a comparison of multiloop control to ideal decoupled control. They base this claim on the statement (Stanley et al., 1985, p 1184) that “if the two loops in the system under consideration were decoupled by using an ideal decoupler, then their response would be the same as the SISO response”. This is only true of the response of the controlled variables, not the response of the m a n i p 0‘ 1987 American Chemical Societv
