PID controller

PID controller is a flexible, effective, and rehable controller for the process industries. A considerable range of controller actions is possible by selecting tuning parameters to provide different weights to the present (proportional), the past (integral), and the projected future (derivative). References related to the tuning of PID controllers are available (20—24). 

Dead-Time Compensation. Dead time within a control loop can greatiy iacrease the difficulty of close control usiag a PID controller. Consider a classical feedback control loop (Fig. 18a) where the process has a dead time of If the setpoiat is suddenly iacreased at time t, the controller immediately senses the deviation and adjusts its output. However, because of the dead time ia the loop, the coatroUer does aot begia to see the impact of that change ia its feedback sigaal, that is, a reductioa ia the deviatioa from setpoiat, uatil the time t +. Because the deviatioa does aot change uatil... 

K. J. Astrom and T. Automatic Tuning of PID Controllers, Instmment Society of America, Research Triangle Park, N.C., 1987. 

Proportional-plus-Integral-plus-Derivative (PID) Control. 8-12... 

Proportional-plus-Integral-plus-Derivative (PID) Control The derivative mode moves the controller output as a function of the rate-of-change of the controlled variable, which adds phase lead to the controller, increasing its speed of response. It is normally combined... 

In some analog PID controllers, the integral and derivative terms are combined serially rather than in parallel as done in the last equation. This results in interaction between these modes, such that the effective values of the controller parameters differ from their set values as follows ... 

The performance of the interacting controller is almost as good as the noninterac ting controller on most processes, but the tuning rules differ because of the above relationships. With digital PID controllers, the noninteracting version is commonly used. 

For a PI or PID controller, the integrated deviation—better known as the integrated error IE—is related to the controller settings ... 

FIG. 8 26 Resp onse for a step change in disturbance with tuned P, PI, and PID controllers and with no control. 

A recent addition to the model-based tuning correlations is Internal Model Control (Rivera, Morari, and Skogestad, Internal Model Control 4 PID Controller Design, lEC Proc. Des. Dev., 25, 252, 1986), which offers some advantages over the other methods described here. However, the correlations are similar to the ones discussed above. Other plant testing and controller design approaches such as frequency response can be used for more complicated models. 

While the single-loop PID controller is satisfactoiy in many process apphcations, it does not perform well for processes with slow dynamics, time delays, frequent disturbances, or multivariable interactions. We discuss several advanced control methods hereafter that can be implemented via computer control, namely feedforward control, cascade control, time-delay compensation, selective and override control, adaptive control, fuzzy logic control, and statistical process control. 

Time-Delay Compensation Time delays are a common occurrence in the process industries because of the presence of recycle loops, fluid-flow distance lags, and dead time in composition measurements resulting from use of chromatographic analysis. The presence of a time delay in a process severely hmits the performance of a conventional PID control system, reducing the stability margin of the closed-loop control system. Consequently, the controller gain must be reduced below that which could be used for a process without delay. Thus, the response of the closed-loop system will be sluggish compared to that of the system with no time delay. 

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. 

During the 1980s, several adaptive controllers were field-tested and commerciahzed in the U.S. and abroad, including products by ASEA (Sweden), Leeds and Northrup, Foxboro, and Sattcontrol. At the present time, some form of adaptive tuning is available on almost all PID controllers. The ASEA adaptive controller, Novatune, was... 

Foxboro developed a self-tuning PID controller that is based on a so-called expert system approach for adjustment of the controller parameters. The on-line tuning of K, Xi, and Xo is based on the closed-loop transient response to a step change in set point. By evaluating the salient characteristics of the response (e.g., the decay ratio, overshoot, and closed-loop period), the controller parameters can be updated without actually finding a new process model. The details of the algorithm, however, are proprietary... 

The subject of adaptive control is one of current interest. New algorithms are presently under development, but these need to be field-tested before industrial acceptance can be expected. It is clear, however, that digital computers will be required for implementation of self-adaptive controllers due to their complexity. An adaptive controller is inherently nonlinear and therefore more complicated than the conventional PID controller. 

Strong process interacHons can cause serious problems if a conventional multiloop feedback control scheme (e g., PI or PID controllers) is employed. The process interacHons canproduce undesirable control loop interac tions where the controllers fight each other. Also, it may be difficult to determine the best pairing of controlled and manipulated variables. For example, in the in-hne blending process in Fig. 8-40(<7), should w be controlled with and x with tt>g, or vice versa ... 

With the exception of pneumatic controllers for special applications, commercial single-loop controllers are almost entirely microprocessor-based. The most basic products provide only the PID control algo-... 

Programmable Logic Controllers The programmable logic controller (PLC) originated as a solid-state replacement for the hardwired relay control panel and was first used in the automotive indus-tiy for discrete manufacturing control. Today, PLCs are used to implement Boolean logic functions, timers, counters, and some math functions and PID control. PLCs are often used with on/off process control valves. 

Presently, fieldbus controllers are single-loop controllers with 8- and 16-bit microprocessors and are options to digital field-control devices. These controllers support the basic PID control algorithm... 

Digital Field Communications An increasing number of valve-mounted devices are available that support digital communications in addition to, or in place of, the traditional 4—20 mA current signal. These control-valve devices have increased functionality, resulting in reduced setup time, improved control, combined functionality of traditionally separate devices, and control-valve diagnostic capabihty. Digital communications also allow the control system to become completely distributed where, for example, the process PID controller could reside in the valve positioner or in the process transmitter. 

This is the speed controller block that consists of both a PID (proportional integral derivative, a type of programming) controller and an acceleration compensator. The required speed reference signal is compared with the actual speed signal obtained from the motor model (section 2). The error signal is then fed to both the PID controller... 

The selection of the PID controller parameters K, T[ and can be obtained using the classical control system design techniques described in Chapters 5 and 6. In the 1940s, when such tools were just being developed, Ziegler and Nichols (1942) devised two empirical methods for obtaining the controller parameters. These methods are still in use. 

From the R and D values obtained from the process reaction curve, using the Zeigler-Nichols PID controller settings given in Table 4.2... 

Fig. 4.35 Closed-loop step response of temperature control system using PID controller tuned using Zeigler-Nichols process reaction method.

In section 4.5, controllers, particularly PID controllers for closed-loop systems were discussed. In Chapter 5 it was demonstrated how compensators could be designed... 

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