-1 2 C ONTROLLER L OOP T UNING

1 5 -1 2 C ONTROLLER L OOP T UNING

For a process control system to work correctly, its control loop(s) must be tuned. Loop tuning involves selecting the constants [K P ,K I (or T I ), and K D (or T D )] that will be used with the proportional, integral, and derivative actions of a controller. With these constants at the proper levels, the controller can effectively and efficiently regulate the process variable to the set point.

A process often experiences disturbances caused by changes in the set point or the process load (see Figure 15-76). These disturbances cause an error in the system, thereby changing the controller output, which in turn, impacts

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IO N

A P p p L C P a lic ro Primary loop in manual. c Secondary loop transfer n tio e s ss After secondary is in auto, then

from manual to auto

In transfer from manual to auto. d

E Auto Auto

SP +

E Auto Auto

t.c Manual

Figure 15-75. Bumpless transfer in cascaded PID controllers.

S ECTION PLC Process Process Controllers C HAPTER 4 Applications

and Loop Tuning 15

Set Point

Change

Load Disturbance

Figure 15-76. Process disturbances.

the process variable. The process variable response to both system distur- bances and the controller action must be stable; that is, it must not oscillate or grow in value without limit. This process variable response can typically be categorized as either overdamped, critically damped, or underdamped (see Figure 15-77a). However, another type of process variable response is a quarter-amplitude response, also called a quarter-delay ratio response (see Figure 15-77b). This response, which is the desired response after closed-loop tuning, reduces the PV overshoot by one-quarter each cycle.

PV Critically damped

Each positive overshoot is 1/4 of the previous. t

(b)

Figure 15-77. Process variable reponses: (a) overdamped, critically damped,

underdamped, and (b) quarter-amplitude.

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S ECTION PLC Process Process Controllers C HAPTER 4 Applications

and Loop Tuning 15

Table 15-2 shows the characteristics of each type of process variable re- sponse. The tuning parameters of the system will have a decisive impact on the type of process response exhibited by the system.

Table 15-2. Process variable response characteristics.

There are several mathematical methods for determining the tuning constants of a PID controller and for analyzing the stability of a system. One method is

a Bode plot analysis, which analyzes amplitude (gain) and frequency re- sponse (phase shifts) to tune the system. This method is useful when the process transfer function is known. However, in continuous manufacturing processes, this is rarely the case. Therefore, we will present three other practical methods for determining the tuning constants that will produce a quality stable response. These methods are:

• the Ziegler-Nichols open-loop tuning method • the integral of time and absolute error (ITAE) open-loop tuning method • the Ziegler-Nichols closed-loop tuning method

The open-loop methods test the process response while the controller is in manual mode without any feedback connections (i.e., PV is not being fed back to the controller). Batch control processes are typical applications for open-loop tuning methods. The closed-loop technique tests the process response when the controller is in automatic mode. This tends to produce a better result, since the controller and the process are operating normally. Servo and positioning control processes are typical applications for closed- loop tuning methods. These processes cannot be tuned without feedback; therefore, they cannot use open-loop tuning techniques.

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S ECTION PLC Process Process Controllers C HAPTER 4 Applications

and Loop Tuning 15