Dual-loop fractional-order IMC structure for unstable systems to handle ramp input signals

One major concern in control engineering is the problem of introducing an unstable system. Such systems are even more sensitive to ramp input changes, either set-point or disturbance. We have proposed an extended fractional-order IMC (FOIMC) control for an unstable system exhibiting a time delay. The complete design involves only three adjustable parameters, such as PID tuning. In the proposed structure, the inner loop control stabilises the system, whereas the fractional IMC filter improves the overall performance, together to tackle the ramp inputs. A systematic approach is developed to tune the required design parameters to obtain the desired peak of the sensitivity function and stability margins. The proposed control is simple and can easily calculate the FOIMC parameters from the explicit formulae. The method works under practical considerations, such as process parameter perturbations and load disturbances. The developed scheme is also tested on the nonlinear continuous stirred tank reactor system. The proposed control method results in a percentage enhancement of 61.9% under the perfectly ideal condition (when the process model is equal to the actual plant) whereas 81.3% enhancement is obtained when the process parameter variations are considered for the CSTR system.