| Repeat at each kth instant (sampling period, ): |
| Step 1. Update the current premise vector. Measurement of |
| all the necessary variables for the determination of |
| the current premise or antecedent vector, : |
| |
| Step 2. Update the state matrices. The TS fuzzy model was |
| formalized in the form of linear time-varying state space |
| equations, and the state matrices depend on the current |
| premise vector. Therefore, at each instant, the following |
| parameters must be updated, using (14): |
| and |
| Step 3. Calculate the predicted model outputs. The use of a |
| model to predict future behaviour is essential in MPC. |
| By means of the appropriate mathematical treatment, |
| the outputs predicted by the model can be calculated. In |
| our case, using (18), we will get: |
| |
| Step 4. Compute the current control action. By establishing |
| the desired behaviour of our system through the previous |
| definition of certain reference trajectories, which must |
| be followed by the outputs of the plant, and applying |
| principles of PFC, we can determine the expression of |
| the necessary control action to achieve such behaviour. |
| Thus, using (36), we will obtain: |
| |
| Step 5. Apply the calculated control action to WWTP. |
