I am working on a project, where I have a PID controlled Hotplate. I want to model the system in Simulink and for that I need to find the PID values which are unavailable due to some reasons. Is it possible that the transfer function I am getting from black box model, I use that and solve it to find the PID values. Is it a correct approach? Or I should create a whitebox model and tune the PID values and verify with the output of the heat plate. Will that give a correct values of PID parameters?
Hi.
One of the benefits of PID control is that you can tune the control gains even with a black box model (assuming the system is controllable and does no demonstrate any strong non-linear behavior). Simply start with increasing the P gain first to see a somewhat fast and stable transient response, then change the D gain to reduce overshoot and etc, and finally add the integral gain for eliminating steady-state errors. You can intuitively adjust the gains by running the simulation for the black-box model multiple times and fine tuning the gains. A very detailed and useful tutorial is in the following link
http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlPID#13
For model-based approaches, you can use root locus or other pole/zero placement techniques to design the control gains via the model and then implement them in the Simulink.
Hi.
One of the benefits of PID control is that you can tune the control gains even with a black box model (assuming the system is controllable and does no demonstrate any strong non-linear behavior). Simply start with increasing the P gain first to see a somewhat fast and stable transient response, then change the D gain to reduce overshoot and etc, and finally add the integral gain for eliminating steady-state errors. You can intuitively adjust the gains by running the simulation for the black-box model multiple times and fine tuning the gains. A very detailed and useful tutorial is in the following link
http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlPID#13
For model-based approaches, you can use root locus or other pole/zero placement techniques to design the control gains via the model and then implement them in the Simulink.
Is your system observable? if so, you can do a system identification to extract the transfer function from the input and output data, then you can tune your PID parameters on MATLAB and choose the preferred response.
It should be fairly easy to get a reasonable model for your plant. Observe the step response (i.e. the temperature output for a given voltage input), then fit a 1st or 2nd order model to it. For a hot-plate, real (i.e. non-oscillatory) poles should suffice. In the 2nd-order case, using repeated poles will make things easier, because there are fewer adjustable parameters to fit. If your PID controller is robust (i.e. if you are not too "aggressive" with your desired closed-loop response) then there is no need for your model to be perfect. To derive your (digital?) PID controller parameters, for this plant model, I would use the method in the link below. Using this method, the controller bandwidth is set (for the desired transient response) and a phase-margin constraint is applied (for robust stability).
Conference Paper Optimal Design of Digital Anticipatory Servomechanisms with ...
If your model does not present high nonlinearities the black box approach could be enough. In any case you could compare the white box and black box model and use the one that is giving the best predictions. You can tune the PID gains looking at the loop transfer function and using the Bode criterion. In this way you can choose cutoff frequency and phase margin of the closed loop. Or you can use a root locus to place the poles where you want. If your system has saturation be careful when using an integral action in the regulator since it could lead to instability, always better use it with an anti-windup configuration (look at the attachment).
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