In industrial unstable processes, disturbance rejection is more challenging task than setpoint tracking. So, cascade control structure is widely used in many chemical processes to reject disturbances. In this work, an advanced dead-time compensatorbased series cascade control structure (SCCS) is suggested for unstable processes. The suggested SCCS has three controllers (named as primary, secondary and stabilizing controllers). Both primary and secondary controllers are designed using fractional order-based internal model control (IMC) approach. The stabilizing proportional-derivative controller is designed using maximum sensitivity considerations and Routh-Hurwitz stability criteria. Optimal values of the closed-loop time constants and fractional orders of IMC filters are obtained using constrained artificial bee colony (ABC) algorithm. This ABC algorithm uses a multi-objective function involving minimization of integral of absolute error, integral of time weighted absolute error and integral of squared error. Simulation studies are conducted using some benchmark plant models used in literature for illustrating the advantages of the proposed strategy compared to the state of the art. Moreover, robust stability of the proposed design is analysed and quantitative performance measures are also computed. Keywords Fractional calculus • IMC • ABC algorithm • Series cascade control • Dead-time compensator • Unstable processes B Deep Mukherjee

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Controlling concentration and temperature of continuously stirred tank reactor (CSTR) is an extremely challenging task in chemical process industries. This is because conventional unity feedback schemes do not guarantee stable operating conditions for the CSTR process. Therefore, fractional calculus is augmented with multi‐loop control to achieve enhanced stability and closed‐loop performance than unity feedback structure in this work. Accordingly, three different fractional‐order‐based novel multi‐loop control structures are proposed based on time domain analysis. In two of the proposed strategies, fractional‐order PID controller (FOPID) and internal model control (IMC)‐based FOPID controller with fractional filter are used in the inner‐loop. Moreover, fractional‐order‐based Lyapunov stability rule of model reference adaptive control (MRAC) is used in outer‐loops for both of the above mentioned methods. Finally, an advanced multi‐loop predictor with FOPD controller in the inner‐loop and FOIMC controller in the outer‐loop is also proposed. In this work, fractional‐order, filter parameters, and FOPID settings are obtained by minimizing multi‐objective functions using modified particle swarm optimization (PSO) algorithm. Closed‐loop responses and control efforts of the proposed control strategies are compared with that of FO‐Lyapunov‐based MRAC scheme. Quantitative performance analysis is also carried out on all proposed methods based on error metrics and total variation of the control signal.

This paper presents a new way to design MIT rule as an advanced technique of MARC (Model Adaptive Reference Controller) for an integer order inverted pendulum system. Here, our work aims to study the performance characteristics of fractional order MIT rule of MARC controller followed by optimal fractional order PID controller in MATLAB SIMULINK environment with respect to time domain specifications. Here, to design fractional order MIT rule Grunwald-Letnikov fractional derivative calculus method has been considered and based on Grunwald-Letnikov fractional calculus rule fractional MIT rule has been designed in SIMULINK. The proposed method aims finally to analyze overall desired closed loop dynamic performance on inverted pendulum with different performance criteria and to show the desired nature of an unstable system over optimal fractional order PID controller.

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In this article, a stability analysis on an inverted pendulum system has been approached using a fractional order PID controller and a fractional order-based model reference adaptive controller. A modified MIT rule provides an extra degree of freedom, unlike an MIT rule of MRAC controllers to stablize the pendulum angle of the inverted pendulum system which is highly unstable in nature. Here, to analyze better stability performance of the inverted pendulum over the fractional order MIT rule of MRAC controller optimal fractional order, a PID controller has been approached and FMINCON numerical optimization algorithm has been chosen to optimize the fractional order PID controller using ITSE as a scaler objective function. Next, the behaviourial characteristics of the pendulum have been compared between the FMINCON-based FOPID controllers and the fractional order MIT rule of the MRAC controller to show robust performance using an optimal FOPID controller with respect to performance indices increases time, settling time, followed by errors ISE, IAE, ITSE.