The block diagram

It can be seen that the term control loop is appropriate as information passes around a closed loop of components. This form of control is called closed-loop or feedback (referring to the feedback of information from the controlled variable to the comparator). A simple loop of this kind can be represented in general terms as in Fig. 7.3. 

By comparing Figs 7.1, 7.2 and 7.3 it is obvious that Mv (the manipulated variable) represents the flowrate of the hot stream. The load U enters the loop at this point as changes in any of the load variables will affect the heat entering the system. Thus the total heat input to the process will be due to U and to Mv. The reasons when and why the net effect of U and Mv may be represented by a simple 

Apart from the controller itself, the major components of the control system are considered elsewhere. The reader is referred to Chapter 6 for the description of various measuring elements and their associated transmission systems. Final control elements in the form of control valves are discussed in Section 7.22.3, and a generalised approach to the representation of the processes themselves is described in Sections 7.5 and 7.6. 

It is useful now to examine some basic control mechanisms. 

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Fig. 1 shows the block diagram of the vibrometer, in which the most sensible to small phase variations interferometric scheme is employed. It consists of the microwave and the display units. The display unit consists of the power supply 1, controller 2 of the phase modulator 3, microprocessor unit 9 and low-frequency amplifier 10. The microwave unit contains the electromechanical phase modulator 3, a solid-state microwave oscillator 4, an attenuator 5, a bidirectional coupler 6, a horn antenna 7 and a microwave detector 11. The horn antenna is used for transmitting the microwave and receiving the reflected signal, which is mixed with the reference signal in the bidirectional coupler. In the reference channel the electromechanical phase modulator is used to provide automatic calibration of the instrument. To adjust the antenna beam to the object under test, the microwave unit is placed on the platform which can be shifted in vertical and horizontal planes. 

The programming language has mainly two parts the front panel and the block diagram. 

The block diagram accompanies each front panel and contains the graphical program. 

A reliability block diagram can be developed for the system from the definition of adequate performance. The block diagram represents the effect of subsystem or component failure on system performance. In this preliminary analysis, each subsystem is assumed to be either a success or failure. A rehabihty value is assigned to each subsystem where the appHcation and a specified time period are given. The reUabiUty values for each subsystem and the functional block diagram are the basis for the analysis. 

Other Considerations in Feedforward Control The tuning of feedforward and feedback control systems can be performed independently. In analyzing the block diagram in Fig. 8-32, note that Gy is chosen to cancel out the effects of the disturbance Us) as long as there are no model errors. For the feedback loop, therefore, the effects of L. s) can also be ignored, which for the sei vo case is ... 

Figure 8-41 includes two conventional feedback controllers G i controls Cl by manipulating Mi, and G o controls C9 by manipidating Mo. The output sign s from the feedback controllers serve as input signals to the two decouplers D o and D91. The block diagram is in a simplified form because the load variables and transfer functions for the final control elements and sensors have been omitted. 

The block diagram for the CNC machine tool control system is shown in Figure 1.11. 

The rudder provides a control moment on the hull to drive the actual heading towards the desired heading while the wind, waves and current produce moments that may help or hinder this action. The block diagram of the system is shown in Figure 1.13. 

Consider a second-order system whose steady-state gain is K, undamped natural frequency is Wn and whose damping ratio is (, where C < 1 For a unit step input, the block diagram is as shown in Figure 3.18. From Figure 3.18... 

The block diagram for the control system is shown in Figure 4.27. From the block diagram, the forward-path transfer function G(.v) is... 

The system element dynamic equations can now be combined in the block diagram shown in Figure 4.31. Using equation (4.4), the inner-loop transfer function is... 

Consider the block diagrams shown in Figure 7.8. In Figure 7.8(a) U s) is a sampled input to G(s) which gives a continuous output Xo(s), which when sampled by a... 

The angular positional control system shown by the block diagram in Figure 10.36 is to have the velocity feedback loop removed and controller K replaced by a fuzzy logic controller (FLC) as demonstrated by Barrett (1992). The inputs to the FLC... 

Case study Example 4.6.1 is a CNC machine-tool positional control system, whose block diagram representation is shown in Figure 4.31. When system parameter values are inserted, the block diagram is as shown in Figure A1.2. 

The essential features of a modern liquid chromatograph are illustrated in the block diagram (Fig. 8.2) and comprise the following components ... 

The block diagram in Fig. 2-21 is subjected to a set of equal and opposite shearing forces (Q). The top view (a) represents a material with equal and opposite shearing forces and (b) is a schematic of infinitesimally thin layers subject to shear stress. If the material is imagined as an infinite number of infinitesimally thin layers, as shown at the bottom, then there is a tendency for one layer of the material to slide over another to produce a shear form of deformation or failure if the force is great enough. The shear stress will always be tangential to the area upon which it acts. The... 

Figure 10.5 The block diagram of the apparatus for the computer-assisted- irradiation method.

We will now discuss the individual components of a SIMS apparatus, as illustrated in the block diagram of Figure 4.2. 

The block diagram shows the main steps in the balanced process for the production of vinyl chloride from ethylene. Each block represents a reactor and several other processing units. The main reactions are ... 

Show on the block diagram the known flows (or quantities) and stream compositions. 

For the purposes of this example the high-pressure process has been selected. A typical process is shown in the block diagram. 

That is, if we move the break-in point from g out to the left of G, we need to divide the information by G] prior to breaking in. The block diagram after moving both the branch-off and break-in points are shown as Steps 1 and 2 in Fig. E2.15b. (We could have drawn such that the loops are flush with one another at R.)... 

Once the loops are no longer overlapping, the block diagram is easy to handle. We first close the two small loops as shown as Step 3 in Fig. E2.15c. 

Example 2.16. Derive the closed-loop transfer function X,/U for the block diagram in Fig. E2.16a. We will see this one again in Chapter 4 on state space models. With the integrator 1/s, X2 is the Laplace transform of the time derivative of x,(t), and X3 is the second order derivative of x,(t). 

Example 4.2 Draw the block diagram of the state space u ... 

Example 4.6. Derive the transfer function Y/U and the corresponding state space model of the block diagram in Fig. E4.6. 

To derive the state space representation, one visual approach is to identify locations in the block diagram where we can assign state variables and write out the individual transfer functions. In this example, we have chosen to use (Fig. E4.6)... 

In Fig. 5.1, we use the actual variables because they are what we measure. Regardless of the notations in a schematic diagram, the block diagram in Fig. 5.2 is based on deviation variables and their Laplace transform. 

For the rest of the control loop, Gc is obviously the controller transfer function. The measuring device (or transducer) function is Gm. While it is not shown in the block diagram, the steady state gain of Gm is Km. The key is that the summing point can only compare quantities with the same units. Hence we need to introduce Km on the reference signal, which should have the same units as C. The use of Km, in a way, performs unit conversion between what we dial in and what the controller actually uses in comparative tests. 2... 

A reminder is that a controller has a front panel with physical units such as °C. (Some also have relative scales of 0-100%.) So when we dial a change in the set point, the controller needs to convert the change into electrical signals. That s why Km is part of the controller in the block diagram (Fig. 5.5). 

Let s take another look at the algebra of evaluating the steady state error. The error that we have derived in the example is really the difference between the change in controlled variable and the change in set point in the block diagram (Fig. 5.6). Thus we can write ... 

This is a problem that we have to revisit many times in later chapters. For now, draw the block diagram of the dye control system and provide the necessaiy transfer functions. Identify units in the diagram and any possible disturbances to the system. In addition, we do not know where to put the photodetector at this point. Let s just presume that the photodetector is placed 290 cm downstream. 

The block diagram is shown in Fig. E5.7b, where the dye concentration is denoted by C and the set point by R. The flow rate is one probable source of disturbance. 

The Gsp function is obvious. To obtain the load function Gload, set R = 0, and try to visualize the block diagram such that it is unity in the forward path and all the functions are in the feedback loop. 

To make use of empirical tuning relations, one approach is to obtain the so-called process reaction curve. We disable the controller and introduce a step change to the actuator. We then measure the open-loop step response. This practice can simply be called an open-loop step test. Although we disconnect the controller in the schematic diagram (Fig. 6.1), we usually only need to turn the controller to the manual mode in reality. As shown in the block diagram, what we measure is a lumped response, representing the dynamics of the blocks Ga,... 

In the block diagram implementing IMC (Fig. 6.3a), our conventional controller Gc consists of... 

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