A novel double‐loop control configuration with two controllers is suggested for double integrating processes with dead‐time. The stabilizing range of the inner‐loop proportional‐derivative (PD) controller is obtained using the Routh stability criteria. From this range, the exact PD settings are obtained by following a graphical approach where the integration of absolute error (IAE) is plotted for different PD settings. The PD settings resulting in the minimum IAE are chosen. In addition to stabilizing the plant, the inner‐loop also rejects the disturbances. A fractional‐order internal model controller (FOIMC) is designed for satisfactory set‐point tracking response in the outer‐loop. The suggested strategy has four adjustable parameters (proportional and derivative time constants, outer closed‐loop adjustment parameter, and fractional‐order of the FOIMC low‐pass filter). Based on extensive simulations, the tuning ranges for the above‐mentioned adjustable parameters are specified. The simulation study is done with the help of benchmark double integrating plant models with large dead‐time. Quantitative performance measures are also computed for comparing the suggested and previously reported schemes. The suggested FOIMC‐PD control architecture yields enhanced control performance than some recently reported techniques.

A novel multi-loop control configuration with two controllers is suggested for integrating processes having large dead-time. The inner-loop consists of a Smith predictor having proportional (P)/proportional-derivative (PD) controller for first/second-order integrating processes, respectively. Once the dead-time is compensated by the inner-loop Smith predictor, a fractionalorder internal model controller (FOIMC) is designed in the outer-loop. The P/PD controllers are tuned using direct synthesis methodology. The proposed control architecture has three adjustable parameters (inner and outer closedloop adjustment parameters, fractional-order of the FOIMC low-pass filter).Based on extensive simulations, the tuning ranges for the above-mentioned adjustable parameters are specified. Suitable justification is also provided for the suggested range of tuning parameters. Several benchmark examples of plant models are used to study the set-point following and disturbance elimination capabilities of the proposed control architecture. Quantitative performance measures are also computed for comparing the suggested and previously reported schemes. It is evident that the suggested FOIMC based Smith predictor yields enhanced control performance than some recently reported techniques.

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The design of control methods for unstable plants is somewhat complex than that of stable plants. This is because unstable process models contain one or more poles lying on the right of the s-plane which yields unbounded closed-loop response. Further, the presence of the dead-time induces more complexity as it decreases the gain and phase margins which in turn deteriorates the closed-loop performance. The design of control strategies become more challenging for plants of unstable nature with positive zeros because they exhibit a phenomenon called inverse response. This paper suggests a method to design a double-loop scheme for unstable plants with/without inverse response. Accordingly, a proportional-derivative (PD)/proportional (P) controllers are used in the inner-loop for stabilizing the plant. A fractional order internal model controller (FOIMC) scheme is used to obtain the outer-loop controller using the stabilized plant model. The P/PD controller settings have been obtained by using the Routh-stability criteria and the maximum sensitivity approach. Procedure for selecting the outer-loop tuning parameter and fractional order is also given. Linear and nonlinear models of unstable plants including bioreactors and isothermal chemical reactors are used to demonstrate the merits of the suggested strategy. Robustness of the design and effect of measurement noise are also studied. Integrated absolute/squared error measures are also calculated. The suggested design is found to be more effective in controlling unstable processes than some reported works.