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.

In this work, a proportional–integral (PI) controller with a set point filter is designed using the direct synthesis method for unstable plus time delay process. The Suggested method involves design parameters whose suitable values are recommended based on robust stability and robust performance constraints. The absence of derivative term makes PI controllers less sensitive to noise and, therefore, PI controllers are more preferable than PID in industrial applications. Despite a simple control architecture, the proposed method gives improved or comparable performance to previously presented approaches, which are comparatively complex. Four case studies are considered to evaluate the suitability and superiority of the suggested control technique. Proposed controller may be applied to the integrating plus time delay plants after some elementary transformations in the process model.

A double loop control structure is proposed based on the fractional order IMC for integrating plus time delay processes with inverse response characteristics. The inner loop having PD block is tuned based on the maximum sensitivity concept for stabilizing the plant and it also enhances disturbance rejection response. The fractional order IMC (FOIMC) in the outer loop is tuned and it results the satisfactory overall performance and robustness. Some integrating time delay processes are considered to show the superiority of the suggested scheme over other recently reported work. Method of choosing suitable values of design parameters is also explained through comprehensive study. The robustness is analyzed by applying the perturbation in the plant parameters through numerical simulations.

The proposed paper focuses on introducing a simple and practical PI control approach based on the direct synthesis method for unstable first-order or integrating processes with time delay. The control scheme highlights the enhancement on set-point tracking and disturbance rejection so that good performance can be analyzed. A PI controller is used for disturbance rejection, while a set-point filter is added to improve tracking response. The controller parameters are directly related to the process model and tuned using a single adjustment parameter selected through the maximum sensitivity to ensure robustness. By avoiding the derivative term, the proposed controller remains less sensitive to noise and is therefore more suitable for industrial use. Clear tuning guidelines are provided for different Ms values, making the method easy to apply even for processes with large time delays. Simulation results are compared with several unstable and integrating processes, which shows that the proposed approach delivers improved or comparable performance to existing methods, while maintaining the same level of robustness. The suggested approach is also verified for nonlinear continuous stirred tank reactor (CSTR) based on performance metrics like (ISE), (ITAE), (IAE), and (TV), are used to measure how well the controller works.