Equivalent block diagram

Figure 9 Lube Oil Cooler Temperature Control System and Equivalent Block Diagram...

Figure 20 illustrates a process using an integral controller to maintain a constant flow rate. Also included is the equivalent block diagram of the controller. 

The bond graph method defines the structure and constitutive equations of the system. Standard bond graph elements are used to build a model of the structure of the system. Suitable computer programs are available to generate the governing equations, and alternative methods have also been developed for deriving equivalent block diagrams, which can represent nonlinear systems. 

Figure 24.7 (a) A 2 x 2 process with one decoupler (b) with two decouplers (c) equivalent block diagram with complete decoupling. 

Figure 5.5 Example of a fault tree (A) with equivalent block diagram (B).

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... 

Figure 3 shows a block diagram of the spectrometer. The modules depicted inside the area surrounded by the bold lines have been built into the FPGA chip. By default, the spectrometer can equip with up to three equivalent and independent RF transmitters, while there is a single receiver. The observation channel is selected by manually plugging the cable from one of the three reference signals of the transmitters to the receiver (Figure IB). 

The result is the most useful of all the Laplace transformations. It says that the operation of differentiation in the time domain is replaced by multiplication by s in the Laplace domain, minus an initial condition. This is where perturbation variables become so useful. If the initial condition is the steadystate operating level, all the initial conditions like are equal to zero. Then simple multiplication by s is equivalent to differentiation. An ideal derivative unit or a perfect differentiator can be represented in block-diagram form as shown in Fig. 9.3. 

Thus differentiation twice is equivalent to multiplying twice by s, if all initial conditions are zero. The block diagram is shown in Fig. 9.3. 

The operation of integration is equivalent to division by s in the Laplace domain, using zero initial conditions. Thus, integration is the inverse of differentiation. Figure 9.4 gives a block-diagram representation. 

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. 

Thus, the equivalent completely decoupled control loops can be represented by the block diagram in Fig. 7.76. 

Fig. 7.86. Equivalent unity feedback block diagram of control system illustrated in Fig. 7.42 including non-linear element...

We can look at an equivalent hardware block diagram. Here we have a wavetable being addressed by what is essentially a counter whose rate is changed to vary the pitch. The term drop sample tuning refers to the fact that samples are either dropped (skipped) or repeated to change the frequency of the oscillator. The phase increment is added to the current value of the phase register every sample, and the integer part of the phase is used as an address to lookup a sample in waveform memory to output to aDAC. 

The series of blocks between the comparator and the controlled output (i.e., Gc, Gf, and Gp) constitutes the forward path, while the block Gm is on the feedback path between the controlled output and the comparator. If G = GcGfGp, then Figure 14.2a shows a simplified but equivalent version of the block diagram. 

Figure 20.4 (a) Block diagram of a cascade control system (b) simplified, but equivalent form. 

The last two equations demonstrate complete decoupling of the two loops since the controlled variable of each loop depends only on its own set point and not on the set point of the other loop. Figure 24.7c shows the net block diagram of the two noninteracting loops described by eqs. (24.25) and (24.26). It is completely equivalent to that of Figure 24.7b. 

Fig. 15 Mean-field phase diagram of supramolecular diblock copolymer model with equivalent block lengths. Labeled phases are Dis (hranogeneous disordered), Lam (lamellar), and 2 phase (coexisting A-rich and B-rich homogtaieons phases). The values of N indicate the diblock copolymer length. Solid dots denote Ltfshitz points (LS). The horizontal dashed line on the l denotes 1//N = 1/4, the macrophase separation transition for a binary blend of polymers. The horizontal dashed line on the right signifies 1//A1 = 0.095, the order-disorder transition for a symmetric diblock copolymer. Reprinted with permission from [97]. Copyright 2007 American Chemical Society...

Fault trees, which are equivalent to reliabihty block diagrams, are common in industry. Moreover, they provide an efficient tool for SIL calculations, under some quantification warnings (Signoret, 2007). A fault tree based approach is therefore chosen in the present paper. 

Mathematical Equivalence Between the Block Diagram Method and the Bond Graph Method... 

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