The Feedback Control Loop: Controller Characteristics (2)

Another, perhaps the most important, controller parameter is the control action, which is set as either ‘‘direct’’ or ‘‘reverse’’. If not set correctly, positive feedback in the control loop would result in unstable operation with the valve reaching a wide open or closed limit. By convention, if the valve position is to increase as the measurement increases, then the controller is considered ‘‘direct’’ acting.

By first determining the process action, then specifying the opposite controller action, the desired negative feedback loop is achieved. A typical flow loop is a good example as follows: the process action is ‘‘direct’’ because the flow increases as the valve position is increased, therefore the controller action should be specified as ‘‘reverse’’.

The actual output signal from the controller will further depend upon the specified failure mode of the valve. For example, a fail-closed valve will require an increase-to-open signal, whereas a fail-open valve will require an increase-to-close signal. Most industrial controllers will have a separate parameter to specify the required signal for the failure mode of the valve. In order to minimize confusion, rather than displaying actual output, most controllers display an ‘‘implied valve position’’, which indicates the desired position of the valve.

The response characteristics of a direct acting PID controller are shown in Figure 3.2. For illustrative purpose, a step change to the measurement is made and held constant without feedback. In response to this disturbance, the independent contributions of each controller mode are provided in Figures 3.2(A, B and C), and the combined PID response is presented in Figure 3.2(D). Note that the Proportional mode has an immediate effect on the output, as defined by its algebraic relationship. The Integral mode keeps changing the output at a constant rate as long as the constant error persists. The Derivative mode provides an initial exaggerated response, which decays rapidly since the measurement stops changing after the initial step disturbance.

Although there are many ways to implement PID modes into a controller, the ISA standard algorithm is an ideal, non-interacting combination of the modes. This algorithm is a relatively new standard, made feasible by digital implementation. Note that many previously published tuning guidelines have been developed based upon various analog implementations of an interacting, series combination of these modes.

The Feedback Control Loop: Controller Characteristics (1)

The design of the valve, process, and measurement should be made such as to minimize deadtime in the loop while providing a reliable, more linear response; then the controller can be tuned to provide the best performance, with an acceptable operating margin for robustness. The PID controller is the most widespread and applicable control algorithm, which can be tuned to provide near optimal responses to load disturbances. PID is an acronym for Proportional, Integral and Derivative modes of control.

Proportional mode establishes an algebraic relationship between input and output. The proportionality is set by a tunable gain parameter. This unitless parameter, controller gain (Kc), specifies percent change in output divided by percent change in input. On earlier versions of PID controllers, an alternate parameter, Proportional Band (PB), was defined as the percent change in input required to cause a 100 percent change in output. Thus by combining definitions, these two terms are related as follows: Kc = 100/PB.

The Integral mode is sometimes referred to as ‘‘reset’’ because it continues to take action over time until the error between measurement and set point is eliminated. The parameter to specify this action is Integral time, which can be thought of as the length of time for the controller to repeat the initial proportional response if the error remained constant. Note that as this parameter is made smaller, the reset increases as the control action is repeated in a shorter period of time. Some controllers use an alternate parameter, Reset, that is the reciprocal of Integral time and is referred to as repeats/unit time. This latter approach is perhaps more intuitive in that as the Reset parameter is increased, there is more reset action being applied.

The Derivative mode is sometimes referred to as ‘‘rate’’ because it applies control action proportional to the rate of change of its input. Most controllers use the process measurement, rather than the error, for this input in order to not have an exaggerated response to step changes in the set point. Also, noise in the process measurement is attenuated by an inherent filter on the Derivative term, which has a time constant 1/8 to 1/10 of the Derivative time. Even with these considerations, process noise is a major deterrent to the use of Derivative mode.

The Feedback Control Loop: Measurement Characteristics

Sensor type and location as well transmitter characteristics, noise, and sampled data issues also can affect loop performance. Most continuous measurement sensors and transmitters have relatively fast dynamics and a noise filter, which can be approximated by a first-order lag with a one or two second time constant. Temperature sensors are somewhat slower as the sensor is in a thermowell, and these measurements have a larger, 15–30 second time constant.

Noise is often a problem in flow, pressure, and level measurements. Because flow is a very fast loop, controller tuning can be set to ignore noise by using low gain and rely on a large amount of reset to take significant action only on sustained deviations. On slower, non self-regulating loops like level, noise in the measurement can degrade potential control performance by preventing the use of higher gains and/or derivative action in the controller.

Excessive filtering of a signal to reduce noise would add effective deadtime to the loop, thus degrading the loop performance. One technique for reducing high amplitude, high frequency noise, without introducing an excessive lag, is to rate limit the signal to a rate comparable to the largest physically realizable upset. This approach chops off peak noise and allows a smaller time constant filter to effectively reduce the remaining lower amplitude, high frequency noise.

Non-continuous measurements, such as produced by the sample and hold circuitry of a chromatograph, can introduce significant deadtime into a loop. Also, the nature of the periodic step change in value prevents the use of derivative action in the controller.

Distributed Control Systems often sample the transmitted signal at a one second interval, sometimes faster or slower depending upon the characteristics of the process response. One concern related to sample data measurement is aliasing of the signal, which can shift the observed frequency. However at a one second sample interval, this has seldom been a problem for all but the fastest process responses. A general rule for good performance is to make the period between scans less than one-tenth of the deadtime, or one-twentieth of the lag in the process response.

The Feedback Control Loop: Process Characteristics

An agitated tank is often used as an example of a first-order lag process. However, mixing in real tanks falls far short of the ideal well-mixed tank. Real tanks have composition responses that are a combination of a first-order lag and deadtime. If the pumping rate of the agitator (Fa) is known, the deadtime (Td) of the real tank may be estimated by the following equation: Td = V/(F+Fa), where V is the volume of the tank and F is the flow through it.

Process responses often consist of multiple lags in series. When these lags are non-interacting, the resulting response is predominantly deadtime, varying linearly with the number of lags in series. However when these lags are interacting, such as the trays on a distillation column, the resulting response remains predominantly a first-order lag with a time constant proportional to the number of lags squared.

Other process characteristics that affect control performance are both steady-state and dynamic non-linear behavior. Steady-state non-linear behavior refers to the steady-state gain varying, dependent upon operating point or time. For example, the pH of a process stream is highly non-linear, dependent upon the operating point on the titration curve. Further, depending upon the stream component composition, the titration curve itself may vary over time.

Non-linear dynamic behavior can occur due to operating point, direction, or magnitude of process changes. For example, the time constant of the composition response for a tank will depend upon the operating point of liquid level in the tank. Some processes will respond in one direction faster than in the other direction, particularly
as the control valve closes. For example, liquid in a tank may drain quite rapidly, but once the drain valve closes the level can only rise as fast as the inlet stream flow allows. The magnitude of a change may cause different dynamic response whenever inherent response limits are reached. Process examples may include a transition
to critical flow, or a transition from a heat transfer to a mass transfer limiting mechanism in a drying processes.

These non-linearities are the main reason an operating margin must be considered when tuning the controller. If the loop is to be robust and operate in a stable manner over a wide range of conditions, conservative values of the tuning parameters must be chosen. Unfortunately, this results in poorer performance under most conditions. One technique to handle known non-linearities is to provide tuning parameters that vary based upon measured process conditions.

Rules Of Thumb : Filtration

1. Processes are classified by their rate of cake buildup in a laboratory vacuum leaf filter: rapid, 0.1–10.0 cm/sec; medium, 0.1–10.0 cm/min; slow, 0.1–10.0 cm/hr.
2. The selection of a filtration method depends partly on which phase is the valuable one. For liquid phase being the valuable one, filter presses, sand filters, and pressure filters are suitable. If the solid phase is desired, vacuum rotary vacuum filters are
   desirable.
3. Continuous filtration should not be attempted if 1/8 in. cake thickness cannot be formed in less than 5 min.
4. Rapid filtering is accomplished with belts, top feed drums, or pusher-type centrifuges.
5. Medium rate filtering is accomplished with vacuum drums or disks or peeler-type centrifuges.
6. Slow filtering slurries are handled in pressure filters or sedimenting centrifuges.
7. Clarification with negligible cake buildup is accomplished with cartridges, precoat drums, or sand filters.
8. Laboratory tests are advisable when the filtering surface is expected to be more than a few square meters, when cake washing is critical, when cake drying may be a problem, or
   when precoating may be needed.
9. For finely ground ores and minerals, rotary drum filtration rates may be 1500 lb/(day)(sqft), at 20 rev/hr and 18–25 in. Hg vacuum.
10. Coarse solids and crystals may be filtered by rotary drum filters at rates of 6000 lb/(day)(sqft) at 20 rev/hr, 2–6 in. Hg vacuum.
11. Cartridge filters are used as final units to clarify a low solid concentration stream. For slurries where excellent cake washing is required, horizontal filters are used. Rotary disk filters are for separations where efficient cake washing is not essential. Rotary drum filters are used in many liquid- solid separations and precoat units capable of producing
    clear effluent streams. In applications where flexibility of design and operation are required, plate-and-frame filters are used.