Modes, process control, derivative proportional

PID control The modes of control used to control processes or part of a process. The three basic modes of control are proportional control, integral control, and derivative control. Derivative control is always used in combination with proportional control or both proportional and integral control. Integral control is generally used in combination with proportional or with both proportional and derivative control. PID control is also known as three-term control. 

Classical Feedback Control. The majority of controllers ia a continuous process plant is of the linear feedback controller type. These controllers utilize one or more of three basic modes of control proportional (P), iategral (I), and derivative (D) action (1,2,6,7). In the days of pneumatic or electrical analogue controllers, these modes were implemented ia the controller by hardware devices. These controllers implemented all or parts of the foUowiag control algorithm ... 

A capsule summary of the merits of the three kinds of corrective action can be made. The proportional action is rapid but has a permanent offset that increases as the action speeds up. The addition of integral action reduces or entirely eliminates the offset but has a more sluggish response. The further addition of derivative action speeds up the correction. The action of a three-mode PID controller can be made rapid and without offset. These effects are illustrated in Figure 3.3 for a process subjected to a unit step upset, in this case a change in the pressure of the control air. The ordinate is the ratio of the displacements of the response and upset from the set point. 

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. 

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 prevent an exaggerated response to step changes in the setpoint. 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. 

In process control only a few types of control action (control modes) are important, namely (1) on-off or two-position control (2) proportional control (3) integral control or automatic reset (4) derivative or rate action. 

In many process control applications, the control algorithm consists of three modes proportional (P), integral (I), and derivative (D). The ideal PID controller equation is... 

Proportional-plus-integral control is the most generally useful control mode and therefore the one usually applied to automated process-control. Its major limitation is in processes with large dead-time and capacitance if reset time is faster than process dead-time, the controller-response changes are faster than the process, and cycling results. In these cases, derivative control is beneficial. 

Although the primary functions of proportional, derivative, and reset have already been introduced, many of their features remain to be defined. The discussion will be restricted to the commonly available controllers, i.e.,. proportional-plus-derivative, proportional-plus-reset, and proportional plus reset-plus-derivative. (Reset controllers are rarely used in process work and are not available as standard items from most manufacturers. Derivative by itself is not recognized as a controlling mode.)... 

Now we consider the combination of the proportional, integral, and derivative control modes as a PID controller. PI and PID control have been the dominant control techniques for process control for many decades. For example, a survey has indicated that large-scale continuous processes typically have between 500 and 5,000 feedback controllers for individual process variables such as flow rate and liquid level (Desborough and Miller, 2001). Of these controllers, 97% utilize some form of PID control. 

Process-variable feedback for the controller is achieved by one of two methods. The process variable can (I) be measured and transmitted to the controller by using a separate measurement transmitter with a 0.2-I.0-bar (3-15-psi pneumatic output, or (2) be sensed directly by the controller, which contains the measurement sensor within its enclosure. Controllers with integral sensing elements are available that sense pressure, differential pressure, temperature, and level. Some controller designs have the set point adjustment knob in the controller, making set point adjustment a local and manual operation. Other types receive a set point from a remotely located pneumatic source, such as a manual air set regulator or another controller, to achieve set point adjustment. There are versions of the pneumatic controller that support the useful one-, two-, and three-mode combinations of proportional, integral, and derivative actions. Other options include auto/manual transfer stations, antireset windup circuitry, on/off control, and process-variable and set point indicators. 

However, there are some processes that cannot tolerate offset error, yet need good stability. The logical solution is to use a control mode that combines the advantages of proportional, reset, and rate action. This chapter describes the mode identified as proportional plus reset plus rate, commonly called Proportional-Integral-Derivative (PID). 

A controller compares its measurement (y) to its set point (r), and based on the difference (e = error) sends an output signal (m - manipulated variable) to the final control element (e.g., control valve) to eliminate the error. The control mode options include on-off, floating, proportional (P), integral (I), differential (D), and many others. The proportional mode considers the present state of the process error, the integral mode looks at the past history of the error, and the derivative mode anticipates the future values of the error... 

The derivative mode anticipates the future values of the error and acts on that prediction. This third control mode became necessary as the size of processing equipment increased and, correspondingly, the mass and the thermal inertia of such equipment also became greater. The purpose of the derivative mode is to predict the process errors before they have evolved and take corrective action in advance. The derivative action is not used by itself, but only in combination with the proportional mode. The output of a PD controller is as follows ... 

A special-purpose control action used on extremely fast processes is the so-called inverse derivative mode. The output of the inverse derivative mode is inversely proportional to the error s rate of change. It is used to reduce the gain of a controller at high frequencies and is therefore useful in stabilizing a flow loop. Inverse derivative can also be added to a proportional-plus-inte-gral controller to stabilize flow and other loops requiring very low proportional gain for stability. Because inverse derivative is available in a separate unit, it can be added to the loop when stability problems are encountered. 

To illustrate the influence of each control mode, consider the control system responses shown in Figure 9.4. These curves illustrate the typical response of a controlled process for different types of feedback control after the process experiences a sustained disturbance. Without control the process slowly reaches a new steady state that differs from the desired steady state. The effect of proportional control is to speed up the process response and reduce the offset. The addition of integral control eliminates offset but tends to make the response more oscillatory. Adding derivative action reduces the degree of oscillation and the response time, ... 

Controller modes—settings and functions that include proportional (P), proportional plus integral (PI), proportional plus derivative (PD), and proportbnal-integral-derivative (PID). Proportional control is primarily used to provide gain where little or no load change typically occurs in the process. Proportional plus integral is used to eliminate offset between the setpoint and process variables PI works best where... 

The question often arises whether proportional, reset, and derivative are really the best control modes for every application. For the easier-to-control processes, their use can be justified. A single-capacity process and some two-capacity processes need only narrow-band proportional action. Derivative is of great value in processes with two or three capacities. But for the more difficult processes, it has been found that reset action is essential. 

Reset, then, is necessary if offset is to be eliminated altogether. Whether proportional and derivative are useful modes depends on the nature of the process. If rapid load changes outside the forward loop may be encountered, proportional and derivative action could be advantageous. If the process Is fundamentally non-self-regulating, as in level control, proportional action Is essential. Finally, if the process is fairly easy to control because of the absence of dead time, derivative may be useful in Improving the dynamic load response-but this is unusual. 

Control algorithms We have discussed that in closed-loop control systems a corrective action is taken by the controller in response to feedback from a transducer. The exact corrective action depends on the algorithm which has been developed. The simplest control approach is a two position control which turns the control element on and off based on the monitored value of the output. With an on/off strategy, the process value will typically oscillate above and below the set point. The most common controller is the PID (proportional, integral, and derivative) loop controller which is able to detect an early trend, adjust quickly, and prevent an over-correction. A PID controller can maintain temperatures within 1°F. The controller provides the means to define the control algorithm by assigning a constant for each of the three control modes. Typically, most of the adjustment is accomplished with the proportional control element, with the control action, u be-... 

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