The control system examples given above have been presented as physical or narrative descriptions of the application. In Section 1.3, the closed loop block diagram has been introduced as a common platform for describing control systems (Figure 1.4). Presentation of a control loop in this form develops a generalized view towards any physical variety of such system, and trains to think in terms of hardware blocks in the loop. Not only for that, this technique reduces the overlapping and abstractness in the physical description, and configures all the sub-systems in the loop, and the overall system in terms of input–output variables, and internal parameters. In fact, the
block diagram presentation is a step toward analysis and design of a given control problem.
To render a preliminary training of this exercise, a few of the given examples would be taken up to develop the descriptive figures in a way from which block diagram construction will be a natural step forward. That is, all the blocks with their labels as in Figure 1.4, will be attributed to the properly identified hardware in descriptive figures of the systems. Remember that at present we can attempt to address this task only in a qualitative way. This topic will be again taken up in Chapter 9 on Closed Loop Dynamics and there we shall workout a rigorous way to develop block diagrams containing quantitative information.
EXAMPLE 1.11 Let us begin with the Stirred Tank Liquid Heater of Example 1.5.
The development of the block diagram of this system should not be difficult because from Figure 1.9, the blocks, relevant variables and the feedback path are easily recognizable. In the following Figure 1.15, we have redrawn Figure 1.9, renaming the system parts and variables in terms of block diagram nomenclature.
Figure 1.15 Example 1.5 with block diagram nomenclature.
The reader should note that there is no separate module for the Comparator in Figure 1.15, as that unit is imbedded in a commercial Controller. Error e, and Controller Output, CO, are computed within the Controller module.
EXAMPLE 1.12 Next we consider Example 1.7, the Reflux Ratio Control of a
Distillation Column, depicted in Figure 1.11. Similar to the above example, Figure 1.16 is the version of Figure 1.11 with block diagram notations.
Figure 1.16 Example 1.7 with block diagram nomenclature.
A few things should be noted in the presentation of Figure 1.16:
1. The Feed Composition xF has been considered to be the only Load Variable, although in a practical distillation system, other recognized load variables are Flow rate and Total enthalpy of the feed stream.
2. The controller output CO is actually the ratio of the two exit stream flow rates from the three-way control valve.
3. The distillate composition xD depends also on the dynamics of the bottom part of the Column, although this influence is minor in comparison to the contribution of the top part.
The exercise of identifying the blocks and variables in terms of block diagram notation becomes harder for systems in which more than one block resides in one or more system hardware. There are instances where these blocks overlap in one or more system elements. Two such examples are shown as under.
EXAMPLE 1.13 Let us begin with the Governor of Example 1.2. The physical
description of the system in Figure 1.9 has been developed to the required form in the following Figure 1.17.
Figure 1.17 Example 1.2 with block diagram nomenclature.
Note the presence of set point and controller mechanism in the same system element.
EXAMPLE 1.14 In the next example, we shall consider Example 1.3, in which the
phenomenon of overlapping blocks also exists. The corresponding development has been shown in Figure 1.18.
Figure 1.18 Example 1.3 with block diagram nomenclature.
EXAMPLE 1.15 The last example in this discussion would be the Flashing System of
Example 1.8, described in Figure 1.19. The possibility of occurrence of more than one control loop in the same process has been demonstrated in this example.
Figure 1.19 Example 1.8 with block diagram nomenclature.
Physical description of control systems have been labelled by proper block diagram nomenclature in the above discussion. One can easily express this information in the standard form, by putting the identified parts of the system into the proper blocks of Figure 1.4.
However, in the last example system, existence of a pair of control loops has been identified. The Load affects both these loops simultaneously. We have drawn the relevant block diagram in Figure 1.20 with the information shown in Figure 1.19. Though, there is a possibility of interaction between the two loops, i.e. the manipulation of one loop may affect the other in such systems. However, for the sake of simplicity, the block diagram has been drawn considering them as separate loops.
Figure 1.20 Block diagram of two control loops in a flashing stage.
Block diagrams have been used in Process Dynamic Analysis by putting the process dynamic model as a mathematical function inside the block representing the process.
This function expresses how the process is going to convert any input variable to the corresponding response. This approach is more extensively used for the development of closed loop dynamic model of a control system. The exercise starts from the block diagram of the system. But such an analysis calls for the block diagram containing quantitative information about the signal and process streams, as well as the exact configuration of mathematical functions residing within the blocks. We will discuss this procedure in the chapter on closed loop dynamics.
The qualitative treatment on the subject that we have just described should be considered as a preliminary training to build up block diagrams from the physical description of a system. It is hoped that this exposure will support the reader as a conceptual help during the more rigorous treatment of the subject.
We have already presented a logical basis for the existence of control system around a process. This is probably the right place to demonstrate that the necessity of a control system also could be analytically established. Let us introduce the idea of
Degree of Freedom of a dynamic system.