Closed block diagram

Figure 6.6 Typical block diagram of a W/control scheme with open- or closed-loop control scheme...

The elements of a closed-loop control system are represented in block diagram form using the transfer function approach. The general form of such a system is shown in Figure 4.1. 

Fig. 4.1 Block diagram of a closed-loop control system. R s) = Laplace transform of reference input r(t) C(s) = Laplace transform of controlled output c(t) B s) = Primary feedback signal, of value H(s)C(s) E s) = Actuating or error signal, of value R s) - B s), G s) = Product of all transfer functions along the forward path H s) = Product of all transfer functions along the feedback path G s)H s) = Open-loop transfer function = summing point symbol, used to denote algebraic summation = Signal take-off point Direction of information flow.

Fig. 4.39 Block diagrams for closed-loop systems. Amplifier...

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). 

We can check with MATLAB that the model matrix A has eigenvalues -0.29, -0.69, and -10.02. They are identical with the closed-loop poles. Given a block diagram, MATLAB can put the state space model together for us easily. To do that, we need to learn some closed-loop MATLAB functions, and we will defer this illustration to MATLAB Session 5. 

Figure 5.4. Block diagram of a simple SISO closed-loop system.

We first need to derive the closed-loop functions for the system. Based on the block diagram, the error is... 

We now reduce the block diagram. The first step is to close the inner loop so the system becomes a standard feedback loop (Fig. 10.2b). With hindsight, the result should be intuitively obvious. For now, we take the slow route. Using the lower case letter locations in Fig. 10.2a, we write down the algebraic equations... 

The time delay effect is canceled out, and this equation at the summing point is equivalent to a system without dead time (where the forward path is C = GCGE). With simple block diagram algebra, we can also show that the closed-loop characteristic polynomial with the Smith predictor... 

In this section, we add the so-called decoupler functions to a 2 x 2 system. Our starting point is Fig. 10.12. The closed-loop system equations can be written in matrix form, virtually by visual observation of the block diagram, as... 

Below are several terms associated with the closed-loop block diagram. 

Fig. 2. Block diagram for the complete closed-loop behavior. Here, the block corresponding to the refrigeration system is neglected.

Figure 13.2 Block diagram of a closed feedback control system.

Consider a simple feedback loop (Fig. 7.3a) in which the feedback path consists of elements which approximate to a steady-state gain K (Fig. 7.37). In this instance, the equivalent unity feedback loop is determined by placing 1 IK in the set point input to the main loop and compensating for this by adding an additional factor K in the forward part of the loop prior to the entry of the load disturbance, as in Fig. 7.38. It is easy to confirm that the standard closed loop transfer functions and are the same for the block diagrams in Figs 7.37 and 7.38. 

The evolution of Raman spectroscopy from a spectroscopic novelty, to a complementary technique in niche applications, to an analytical powerhouse, has closely paralleled the advancement of enabling technologies. While a simple block diagram of the components of a Raman spectrometer shown in Figure 1.1 would still be comparable to the very early instruments built by C.V. Raman [1], the improvement in functionality of each component has dramatically increased the impact of Raman spectroscopy in areas where it was... 

If the optimum region is close by, the research by this model ends and we switch to constructing the design of experiments for the second-order model. Fig. 2.38 shows the block diagram of searching for an optimum for an inadequate linear model. 

Basic block diagram of a closed-loop motion control system. 

Figure 4-33. Block diagram of capillary electro- carried out close to the cathode in a region phoresis equipment. Capillary electrophoresis where the capillary is transparent, allowing equipment consists of a thermostatted capillary photometric or fluorimetric analysis of the whose ends are placed in the electrode buffer eluate. The detector system is linked either to a chambers these contain the electrodes attached recorder/integrator or to a PC. to a high-voltage power supply. Detection is...

Draw the block diagram for the above closed-loop process. Make sure that each block and the value of each block is labeled clearly. Use the following additional transfer functions to complete the diagram ... 

Figure 14.3b shows the block diagram for the closed-loop system with the transfer functions for each component of the loop. The closed-loop response of the liquid level will be given by eq. (14.5), where the transfer functions Gp, Gd, Gm, Gc, and Gf are shown in Figure 14.3b. The servo problem arises when the inlet flow rate F, remains constant and we change the desired set point. In this case the controller acts in such a way as to keep the liquid level h close to the changing desired value Asp. On the other hand, for the regulator problem the set point Asp remains the...

Figure 14.4b shows the block diagram for the closed-loop system with the transfer functions for each component of the loop. The closed-loop response is easily found to be... 

The closed-loop block diagram is shown in Figure 14.6b and gives... 

Figure 15.3 shows the block diagram of the closed-loop system. 

Let us now turn our attention to the closed-loop behavior of cascade control systems. Consider the block diagram of a general cascade system shown in Figure 20.4a. To simplify the presentation we have assumed that the transfer functions of the measuring devices are both equal to 1. 

From the block diagram of Figure 24.7b it is easy to develop the following two closed-loop input-output relationships ... 

Consider the process of Figure 24.1a. Couple y 1 with m2 and y2 with m, to form the two loops. Draw the corresponding block diagram. Develop the resulting closed-loop input-output relationships, similar to those given by eqs. (24.9) and (24.10). Has the closed-loop characteristic equation changed or not ... 

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