Analytical design of robust FO-PID controller for diffusion processes despite of uncertainty on all model parameters

Diffusion processes, as fundamental mechanisms for particle movement in systems with different concentrations, are used to describe many real-world physical, chemical, biological, engineering, economic and social phenomena. A diffusion process can be modelled via a fractional-order transfer function with time-delay, where its parameters may be affected by circumstance. Hereupon, this study proposes a pioneer robustness indicator to achieve the phase margin invariance regardless of concurrent uncertainty on different parameters of a diffusion process. Afterwards, an analytical procedure is suggested to tune a Fractional-Order Proportional-Integral-Derivative (FO-PID) controller for a diffusion process, to favourably regulate the values of gain crossover frequency and phase margin, such that the proposed robustness criterion is met. Moreover, the solvability of the problem is analytically investigated. Finally, a numerical simulation on robust temperature control during magnetic local hyperthermia, i.e. a common method to treat cancerous tumours, is presented to validate the efficiency of the paper achievements.