As mentioned by @Sam Chak, The most proper way to design a PID controller is by modelling of plant and making its linear model. You can then use an input-output transfer of this model to decide the PID controller gains that satisfies the required time or frequency domain specifications. However, I was just searching across the MATLAB documentation and discovered that SIMULINK offers a convenient feature that might interest you.
The "PID Tuner App" in SIMULINK can automatically tune PID controller parameters to achieve your desired time or frequency domain response. It has an impressive graphical user interface, allowing the user to enter rise time, settling time, and other time domain specifications to be satisfied by the resultant closed loop system. When the "PID Tuner" launches, the software computes a linearized plant model seen by the controller. The software automatically identifies the plant input and output, and uses the current operating point for the linearization
For further information on the "PID Tuner App," you can refer to the following documentation:
I tried to reproduce the system, somewhat similiar to that demonstrated by you in the attached image. Below given figure demonstrates it. I have also attached the Simulink file along with this answer.
Properties of blocks:
System response with “on/off” relay:
I set a reference temperature of 305 kelvin, and the hysteresis of +-2 degrees. Below given is the response of temperature of the pipe with respect to time. You can see that it is between hysteresis band, but non-steady.
System response with PID controller:
Follow the following steps to use a PID controller:
- Add a “PID(s)” block (as shown in below image) to your model.
- Open the block parameters of "PID controller" by double clicking it. Go to the “main” tab, and click on “tune” button under the “Automated tuning” section.
- “PID tuner App” will open as shown below:
- Adjust the “rise time” and “transient behavior” from the sliding bars as per your requirements.
- To view the (“P”, “I”, and “D”) values computed by “PID tuner App, click on “show parameters” icon on the top menu bar.
- Click on ” Update Block” button on top menu bar to automatically set the parameters of PID controllers.
- Now close the “PID tuner App” and open the “block parameters” of “PID controller”. You will see the updated values of the controller gains.
- Run the model.
- The below given scope waveform shows the temperature of the pipe when PID controller is used.
Conclusions:
We can see that now temerature is controlled in very smooth way and steady state error is also zero.
This is the basic guidline to automatically tune the PID controller for your system. I have attached the simulink file. You can make changes to it according to your requirements, but repeat the above steps to tune your "PID" parameters again, as the plant is changed.
I hope this helps and is as per your expectation!
