Optimal design of sequential excitation for identification of multi-variable systems

While designing excitation signals for identification of industrial processes, it is important to obtain desired model accuracies, reduce the experimental time and limit the output amplitudes within the specified bounds to avoid serious disruptions of the nominal process operation. In this work, we design a multi-frequency multi-amplitude square wave (multi-square) input based on a nominal model by minimizing the experiment length and placing constraints on the model accuracy (in the frequency domain) and the output amplitudes. A separate design is carried out for each input where the resulting optimization problem has the same structure as a semi-definite program but with the decision variables restricted to integers corresponding to the number of half-periods of each square-wave. For processes with multiple inputs, the corresponding designs are carried out sequentially. The violations in the output constraints either due to model-plant mismatch or unmeasured disturbances should be mitigated by appropriate closed loop control actions. The efficacy of the proposed design is shown by means of a simulation case study.