Experimentally verified optimal bi-loop re-located IMC strategy for unstable and integrating systems with dead time

Internal model controllers (IMCs) are popular strategies for controlling stable systems with dead time. The relocated IMC (RIMC) design reportedly achieves the expected performance-robustness tradeoff for stable processes. Hence, an attempt has been made in this work to modify the RIMC (as a bi-loop RIMC proportional-derivative (RIMC-PD)) strategy to make it applicable to a class of unstable and integrating systems involving dead time. The secondary-loop stabilisation is achieved with a PD controller constructed by Routh stability constraints. The primary loop contains a RIMC controller for reference following. Both primary, as well as secondary-loop controller parameters, are optimally tuned in the search space using the equilibrium optimiser subjected to minimal integral square error. The RIMC-PD control strategy delivers reasonable enhancement in performance measures when compared with some of the recently reported strategies. A robust stability investigation is also carried out. Finally, experimental verification of the RIMC-PD strategy is carried out using a magnetic levitation laboratory setup.