Modes, process control, derivative

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 ... 

This is a mode of control that anticipates when a process variable will reach its desired control point by sensing its rate of change. This allows a control change to take place before the process variable overshoots the desired control point. You might say that derivative control gives you a little kick ahead. 

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. 

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. 

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. 

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. 

The stress—relaxation process is governed by a number of different molecular motions. To resolve them, the thermally stimulated creep (TSCr) method was developed, which consists of the following steps. (/) The specimen is subjected to a given stress at a temperature T for a time /, both chosen to allow complete orientation of the mobile units that one wishes to consider. (2) The temperature is then lowered to Tq T, where any molecular motion is completely hindered then the stress is removed. (3) The specimen is subsequendy heated at a controlled rate. The mobile units reorient according to the available relaxation modes. The strain, its time derivative, and the temperature are recorded versus time. By mnning a series of experiments at different orientation temperatures and plotting the time derivative of the strain rate observed on heating versus the temperature, various relaxational processes are revealed as peaks (243). 

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. 

The great majority of coloration processes demand some control over the treatment pH, which varies from strongly alkaline in the case of vat, sulphur or reactive dyes, to strongly acidic for levelling acid dyes. The concept of pH is a familiar one its theoretical derivation can be found in all standard physical chemistry textbooks and has been particularly well explained in relation to coloration processes [6,7] both in theory and in practice. We are concerned here essentially with the chemistry of the products used to control pH and their mode of action. It has been stated [7] that Unfortunately, pH control appears simple and easy to carry out. Add acid and the pH decreases add base (alkali) and the pH increases. However, pH is the most difficult control feature in any industry . 

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). 

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