PID Controller Tuning Techniques

The process controllers are placed a tremendous role in plant control system and offered an efficient control of process parameters during steady state and transient conditions. But the tuning of process controller is the most important, least understood and difficult task in the controller design. The tuning procedure is the necessary step of selecting the proper P,PI,PID settings to control the process. Ultimately the performance of any controller depends of these settings only. It may possible to make some guess based on the experience in the plant control system for some processes even though extra care is needed for selecting the control parameters for efficient performance.

Finally it is concluded the trial and error method is only the solution to find better parameters but in aid this method, there are two methods which can reduce the number of trails to find the parameters. I.e by using these techniques trail steps can be reduced to 3 or 4 steps. The two methods are;

  • The first approach is the closed loop tuning which was developed by Ziegler and Nichols.

  • The second method is the guessing of best parameters by the knowledge of open loop parameters like gain, time constants and dead time of the process.

The objective controller tuning method is to find better parameters for good control and there are some trial and error methods which estimates the parameters based on some calculations. I.e the controller constants are changed to achieve some predetermined closed loop response. They are as follows.

1) In some methods the constants are changed in trial and error basis to achieve the one quarter decay ratio  for closed loop response. The decay ratio is the measure of the amount by which the controlled variable exceeds the set-point in successive peaks.

once the one quarter decay ratio is obtained in the closed loop response then the constants are taken as control parameters (P,I,D).

2) some methods tries to achieve a certain value of percentage overshoot also measures the degree of oscillation and one quarter decay ratio.

3) Other methods tries to achieve the combinations of settings that gives smallest area between the set-point and control variable during set-point or load change.

The above trial and error methods are depends on process dynamic behaviour, some process simply cannot stand for overshoot and and must settle more gradual with slow response. For example consider a level controller, the overshoot in level of the tank is not permitted because it may overflow. So extra care and knowledge of the process is needed for these methods to find better combination of parameters.

Closed loop tuning by Ziegler and Nichols:

The most often technique for closed loop technique was developed by  the Ziegler and Nichols technique in 1942. The following steps illustrate the procedure to find the ultimate gain and ultimate period.

  1. Set the integral and derivative constants to its maximum value i.e Ti is large and Td is ‘0’ by leaving the proportional value. Maintain the controller in auto mode with closed loop.

  2. Set the proportional constant to some arbitrary value and observe the response of the process by giving some upset to the process. The best way to provide upset to the process is to increase the set-point for small time and return back to the original value.

  3. If the response curve is does not damp out and gives a increasing decay ratio (as in curve A) , illustrates that the gain (Kp) is too high (Proportional Band (PB) is too low). The gain should be reduced (PB should be increased) and repeat the same step-2.

  4. If the response curve dams out (as shown in curve C) at steady state then the gain is too low (PB is too high), the gain should be increased (PB should be reduced) and repeat the step-2.

  5. The step-2 should be repeated by changing the proportional gain until the response of the closed loop is oscillatory (similar to curve B). i.e without damping and without increasing decay ratio. The values of the ultimate gain and ultimate period are noted if the response is similar as shown in curve B. The ultimate gain which results the closed loop response with sustained oscillation is the ultimate sensitivity Su and the ultimate period is Pu.

The ultimate gain and ultimate period are used to calculate the controller settings as per the tuning method. Ziegler and Nichols correlated in the case of proportional control that the value of proportional setting should be half of the ultimate sensitivity Su. This setting often provides a closed response with one quarter decay ratio in case of proportional controller.  Same way by following equations are found out as good rules of thumb for better combination of controller parameters.

Proportional controller 

Kc=  0.5 Su

Proportional- Integral (PI)controller

        Kc = 0.45 Su

        Ti = Pu / 1.2

Proportional – Derivative (PD) controller

        Kc = 0.6 Su

        Td  = Pu / 8

Proportional – Integral – Derivative (PID) controller

        Kc = 0.6 Su

       Ti = o.5 Pu

         Td = Pu / 8

Again it should be that the above equations are empirical and inherent and chosen to achieve a decay ratio of one quarter.

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