Closed Loop Performance Metrics in Designing a Controller


A process engineer is in charge of controlling a process whose model is unknown. The engineer chooses to develop the model using an empirical approach and then design a controller using the direct synthesis technique.

1. In the first stage, the engineer generates the step response of the process by exciting the process with a step. The observations collected every T = 0.05 min. are provided in q3stepres.mat (variables ystepres and tvec). Use these data to build a suitable approximate continuous-time (i.e., FOPTD or SOPTD with or without zero) model.

2. Concerned about the quality of the approximation due to the extremely limited frequency content of a step input, the engineer decides to excite the process with an input rich in frequencies. The frequencies used for excitation and the response of the process are contained in q3freqres.mat (variables Gjw and wvec). Re-estimate the approximation in (1) using the frequency response data.

3. Use the models in parts (1) and (2) to design two separate controllers using the direct synthesis technique.

4. The engineer incidentally stumbles upon a first-principles model of the process in the records:


G(s) =                          0.04s2- 0.06s + 0.02


                     s4 + 1.8s3+ 0.97s2+ 0.18s + 0.01


Use this first-principles model and a closed-loop performance metric(s) of your choice to select the controller (and hence the model) that suits the process best. Justify your choice of controller and model with suitable arguments.

Please find the inputs in the zip file attached along with this document.



The question belongs to Chemical Engineering and the question is about closed loop performance metrics on designing a controller using direct synthesis technique. The data is given in the zip file attached and the solution contains the answers to the questions given.

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