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Robust control for time‐fractional diffusion processes: application in temperature control of an alpha silicon carbide cutting tool

Different real-world processes can be described by a linear model parameterised with respect to the process operating point, as an uncertain parameter. The family of transport processes with long memory is a kind of these processes which are characterised by the parameterised time-fractional diffusion equations. This study proposes a generalised iso-damping feature for achieving the phase margin invariance regardless of the uncertain parameter variations in control of time-fractional diffusion processes. Also, the study suggests an analytical method to tune stabilising fractional-order proportional–integral/proportional–derivative controllers for adjusting a desired value for the phase margin at a desired gain crossover frequency, while the proposed robustness criterion is satisfied in control of time-fractional diffusion processes. Furthermore, conditions for solvability of the problem and stability of the obtained control system are analytically derived. Finally, an example on robust temperature control of the cutting edge in alpha silicon carbide cutting tools is presented to confirm the effectiveness of the obtained achievements.