The Feedback Control Loop

Feedback controllers have been used for many years, starting with speed control on windmills and then steam engines and now modern-day cruise control on automobiles. The concept is to increase the flow of energy when the speed falls below the desired value or reduce the flow of energy when the speed is too high. 

The controller output is determined by the three controller actions P, I, and D in response to the error and how it changes with time. 

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Imperfections in feed-forward control can often be overcome by the addition of suitable feedback action. A typical design is shown in Fig. 7.70 where any variations in xd which occur bring the feedback control loop into action. The reflux flow is shown on flow control in cascade with the boiling temperature of the liquid at an appropriate point within the column. The inner (or slave) flow controller maintains... 

The feedback control loop consists in measuring the height, comparing it with the set point, i.e., the height for the input flow rate of 2.3 to3/hour, and using the... 

A few comments about the method are warranted. The controlled (dominant) variables, Ycd, should be measured such that they belong to the set Yd for rapid control. Similarly, the manipulators in the feedback control loops should belong to the set, Ud. The feedback controllers should have integral action (PI controllers). These can be tuned with minimal information (e.g., ultimate gain and frequency from a relay test). The model Ms is usually quite simple and can be developed from operating data using statistical regressions. This works because the model includes all the dominant variables of the system, Y d, as independent variables by way of their setpoints, Y. The definition of domi-... 

In the feedback control loop of Figure 29.9 we have omitted the dynamics of the measuring sensor and final control element. Thus they are absent from the closed-loop response of eq. (29.21). Consider the loop of Figure 29.10, with the sensor and final control element included. Following the same procedure as above, it is easy to show that the sampled-value, closed-loop response of the loop is given by... 

EXAMPLE 4.1. Consider the two blending systems shown in Fig. 4.8. The flow rate or composition of stream 1 is the disturbance. The flow rate of stream 2 is the manipulated variable. In Fig. 4.8a the sensor is located after the tank, and therefore the dynamic lag of the tank is included in the feedback control loop. In Fig. 4.8h the sensor is located at the inlet of the tank. The process lag is now very small since the tank is not inside the loop. The control performance in part h, in terms of speed of response and load rejection, would be better than the performance in part a. In addition, the tank now acts as a filter to average out any fluctuations in composition. ... 

Actuate Apply the computed control voltages at the current time step of our simulation and advance the simulation to the next time step. This updates the droplet shape and particle positions. Then go back to step 2 and repeat the feedback control loop. 

The closed loop and open loop reactor dynamics are compared in Figs. 9 and 10, for a step decrease in the reactor pressure. A SISO controller was tuned to control the inlet temperature of the first bed, Toi, tl ugh the by-pass valve (see Fig. 1). When the reactor is operated without feedback control, the sudden reduction in the pressure leads to a decrease in Ae heat generation rate, the temperature Touti (and consequently Toi) decreases and the reactor moves to a lower (extinguished) steady state. This effect can be serai in Fig. 9, where the overall temperature rise drops from 230 C to 12 °C. Conversely, when the feedback control loop is included, the overall temperature rise shows a significantly lower decrease (from 230 to 199°C) as a consequence of the gradual reduction of the cold by-pass (Fig. 10). 

Identify all the feedback control loops in the process flow diagram for the production of DME, Figure B.l. and explain the control action of each. Note There are other control valves on the utility streams, but these are shown only on the PSdD and not considered here. 

General Guideline for Specifying the Controller Action (Direct or Reverse) The overall product of the gains for all of the components in the feedback control loop must be positive. 

For example, the blending control system in Fig. 8.1 has five components in the feedback control loop the process, the sensor, the controller, the I/P transducer, and the control valve. 

Having considered PID controllers in Chapter 8, we now consider the other components of the feedback control loop. As an illustrative example, consider the stirred-tank heating system in Fig. 9.1. A thermocouple measures the liquid temperature and converts it to a millivolt-level electrical signal. This signal is then amplified to a voltage level and transmitted to the electronic controller. The feedback controller performs the control calculations and sends the calculated value as an output signal to the final control element, an electrical heater that adjusts the rate of heat transfer to the liquid. This example illustrates the three important functions of a feedback control loop (1) measurement of the controlled variable (CV), (2) adjustment of the manipulated variable (MV), and (3) signal transmission between components. 

Components in parallel (redundant components) Improved system reliability can be achieved by using redundant components. For example, in Section 10.1, redundant sensors and control loops were used in SIS and BSD systems. Suppose that m independent sensors are available and only one needs to be operational in order for the feedback control loop to operate properly. The probability that all m sensors fail is ... 

Next, we develop a transfer function for each of the five elements in the feedback control loop. For the sake of simplicity, flow rate wi is assumed to be constant, and the system is initially operating at the nominal steady rate. Later, we extend this analysis to more general situations. 

The standard block diagram in Fig. 11.8 can be used to represent a wide variety of practical control problems. Other blocks can be added to the standard diagram to represent additional elements in the feedback control loop such as the current-to-pressure transducer in Fig. 11.7. In Fig. 11.8, the signal path from E to T through blocks Gc, Gv, and Gp is referred to as the forward path. The path from Y to the comparator through G is called the feedback path. 

In both the numerator and denominator of Eq. (11-26) the transfer functions have been rearranged to follow the order in which they are encountered in the feedback control loop. This convention makes it easy to determine which transfer functions are present or missing in analyzing subsequent problems. 

The filter time constant jp in (17-4) should be much smaller than the dominant time constant of the process Tdom to avoid introducing a significant dynamic lag in the feedback control loop. For example, choosing Tp < 0.1 Tdom generally satisfies this requirement. On the other hand, if the noise amplitude is high, then a larger value of may be required to smooth the noisy measurements. The frequency range of the noise is another important consideration. Suppose that the lowest noise frequency expected is denoted by (Ojv Then Tp should be selected so that (O/r < where (x)p = 1/t. For example, suppose we specify (Op = which corresponds to Tp = 10/(O/. Then... 

Next, we show that feedback reduces sensitivity by comparing the relative sensitivities for open-loop control and closed-loop control. By definition, open-loop control occurs when the feedback control loop in Fig. J.l is disconnected from the comparator. For this condition ... 

It is possible to adjust the feedback control loop to give any of the above responses. The form of the response desired depends on the process being controlled. For the most part, responses Ci to C3 would give desired behaviour, since each results in a return of... 

Proportional control is the simplest continuous control mode that can damp out oscillations in the feedback control loop. This control mode normally stops the process variable PV from cycling, but it does not necessarily return it to the set point. 

To understand cascade control better, we will examine a typical feedback control scheme and consider how it may be improved through the use of cascade control. Let us consider the feedback control loop for a heat exchanger shown in Figure 6.2. 

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