Introduction
Aim
In this task we are going to design the PI controller for the Process plant for which we have given the data and using the provided data, the first order transfer function for the plant we can find out the parameters by observing the pen loop response plot of the system. After finding the transfer function we have to design the Cohen-Coon and Haglund-Astrom tuning method and compare the both using the Ziegler-Nicholas tuning method. We can find out the performance of the response by computing the setting time, rise time and overshoot, we can also analyse the system response by adding disturbance to the system at time of 40 seconds and by adding the saturation block X in the model.
Methodology
PI Controller
Proportional plus integral controllers are another name for proportional integral controllers. It is a sort of controller made up of integral and proportional control actions. As a result, it is called a PI controller. Both proportional and integral controller control actions are used in the proportional-integral controller. When two different controllers are combined, a more effective controller is created, eliminating the drawbacks of each individual controller. It should be emphasised that integral controllers can be used independently of proportional controllers in this situation. To counteract the drawback of integral controllers, proportional and integral controllers are typically employed together. The fact that integrated controllers tend to be highly unstable is a significant drawback. This is due to the fact that integral controllers react to errors created fairly slowly.
Plant Model
A plant model represents the first order transfer function for which we have identify the parameters by observing the open loop response of the plot, first we have to plot the system response after that using the identified parameters, we have to overlay on the data so that we can verify that the computed results is correct. The first order transfer function is given as
We can see that the parameters we were used for the plant transfer function model is exactly matches with the response data so, we can use as the transfer function of the plant. We have to create the close loop system for the three controller and compare the performance of the controller with each other.We have designed the PI controller for the process plant, first we have conducted the system identification of the first order plant and identify the parameters of the plant response, by plotting the open loop response and first order transfer function of the plant we can verify the plant model, we have observed that we get exactly same response and we can use it as the transfer function model for the analysis of controller tuning method. We have conducted the analysis without and with disturbance in the system and using the saturation block, we have found that the Ziegler-Nicholas method gives us the best response in terms of settling time, rise time and overshoot. So, we have considered the Zeigler-Nicholas method is the best tuning method. We have concluded that we design the PI controller for the process plant and we get results as we desired.