Block-Diagram Manipulations

There are oeeasions when there is interaetion between the eontrol loops and, for the purpose of analysis, it beeomes neeessary to re-arrange the bloek diagram eonfigur-ation. This ean be undertaken using Bloek Diagram Transformation Theorems. 

A complete set of Block Diagram Transformation Theorems is given in Table 4.1. 

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The Smith predictor is a model-based control strategy that involves a more complicated block diagram than that for a conventional feedback controller, although a PID controller is still central to the control strategy (see Fig. 8-37). The key concept is based on better coordination of the timing of manipulated variable action. The loop configuration takes into account the facd that the current controlled variable measurement is not a result of the current manipulated variable action, but the value taken 0 time units earlier. Time-delay compensation can yield excellent performance however, if the process model parameters change (especially the time delay), the Smith predictor performance will deteriorate and is not recommended unless other precautions are taken. 

As an illustrative example, consider the simplified block diagram for a representative decoupling control system shown in Fig. 8-41. The two controlled variables Ci and Co and two manipulated variables Mi and Mo are related by four process transfer functions, Gpn, Gpi9, and pie, Gpii denotes the transfer function between Mi... 

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 components of the basic feedback control loop, combining the process and the controller can be best understood using a generalised block diagram (Fig. 2.29). The information on the measured variable, temperature, taken from the system is used to manipulate the flow rate of the cooling water in order to keep the temperature at the desired constant value, or setpoint. This is illustrated by the simulation example TEMPCONT, Sec. 5.7.1. 

The use of block diagrams to illustrate cause and effect relationship is prevalent in control. We use operational blocks to represent transfer functions and lines for unidirectional information transmission. It is a nice way to visualize the interrelationships of various components. Later, they are crucial to help us identify manipulated and controlled variables, and input(s) and output(s) of a system. 

Of all manipulations, the most important one is the reduction of a feedback loop. Here is the so-called block diagram reduction and corresponding algebra. 

Here, we use L to denote the major load variable and its corresponding transfer function is GL. We measure the load variable with a sensor, Gnu., which transmits its signal to the feedforward controller GFF. The feedforward controller then sends its decision to manipulate the actuating element, or valve, Gv. In the block diagram, the actuator transfer function is denoted by G v. The idea is that cascade control may be implemented with the actuator, Gv, as we have derived in Eq. (10-1). We simply use G v to reduce clutter in the diagram. 

Figure 10.12. Block diagram of a 2 x 2 servo system. The pairing of the manipulated and controlled variables is not necessarily the same as shown in Fig. 10.11.

A block diagram of a simple openloop process is sketched in Fig. 11.4o. The load disturbance L, and the manipulated variable affect the controlled variable... 

In practice, many feedforward control systems are implemented by using ratio control systems, as discussed in Chap. 8. Most feedforward control systems are installed as combined feedforward-feedback systems. The feedforward controller takes care of the large and frequent measurable disturbances. The feedback controller takes care of any errors that come through the process because of inaccuracies in the feedforward controller or other unmeasured disturbances. Figure 11.4d shows the block diagram of a simple linear combined fe forward-/ feedback system. The manipulated variable is changed by both the feedforward controller and the feedback controller. 

Draw a block diagram of a process that has two manipulated variable inputs (Mi and M]) that each affect the output (2T). A feedback controller Si is used to control X by manipulating Mi since the transfer function between Mj and X has a small time constant and smaU deadtime. 

Similarly, if the behaviour of the components of the block diagram illustrated in Fig. 7.3 can be assumed to be linear, then the effects of load and manipulated variable on the process can be added using the principle of superposition. 

Figure 4.29 shows a block diagram of a reactor with manipulated inputs U. other measured inputs W, and unknowm or unmeasured inputs N. We may assume that this reactor is more complicated than a simple plug-flow reactor or a CSTR. It may be more along the lines of the fluidized catalytic cracker that we showed in Fig. 4.4. The reactor can be described by a set of nonlinear differential equations as we have previously demonstrated. This results in a set of dynamic state variables X The state vector is often of high dimension and we normally only measure a subset of all the states. Y is the vector of all measurements made on the system.

FIGURE 9.1. Block diagram of laser and microcapillary manipulation, absorption/fluorescence microspectroscopy and microelectrochemistry system. 

Block Diagram Analysis One shortcoming of this feedforward design procedure is that it is based on the steady-state characteristics of the process and, as such, neglects process (Ramies (i.e., how fast the controlled variable responds to changes in the load and manipulated variables). Thus, it is often necessary to include dynamic compensation in the feedforward controller. The most direct method of designing the FF dynamic compensator is to use a block dir rram of a general process, as shown in Fig. 8-34, where G, represents the disturbance transmitter, (iis the feedforward controller, Cj relates the disturbance to the controlled variable, G is the valve, Gp is the process, G is the output transmitter, and G is the feedback controller. All blocks correspond to transfer fimetions (via Laplace transforms). 

FIGURE 15.3 Block diagram of a generalized feedback system e is the error from setpoint, c is the controller output, and u is the manipulated variahle. 

Figure 15.3 shows a block diagram of a generalized feedback control system for the system shown in Figure 15.2. That is, this example has a controller, a final control element, a process, and a sensor, in that order, along with feedback of the measured value of the controlled variable to the controller. In addition, the example process is affected by disturbances. Note that the sensor reading, y, is compared with the setpoint, and the controller chooses control action based on this difference. The final control element is responsible for implementing changes in the level of the manipulated variable. The process for a control loop is only the part of the system that determines the value of the controlled variable from the inputs. The overall process can be based on a number of processing units.

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