Multi-objective optimization of distributed-order fractional damping

• Proposed a novel hybrid method of generic algorithms and cell mapping techniques for optimal design of distributed order damping.
• Proposed the criteria of optimal damping with time domain specifications of step response and discussed its rationale for damping design.
• Studied effect of various distribution functions on the damping performance.

This paper investigates the multi-objective optimal design of distributed order fractional damper. A new hybrid method which takes advantages of both the evolutionary algorithms and the simple cell mapping method is used to obtain the Pareto solutions of the multi-objective optimal design. Three different cases of distributed damping coefficient c(α)c(α) are studied. The objective functions are taken from the time domain specifications of step response in the feedback control design, which include the overshoot, peak time and integrated tracking error. It is found that the multi-objective optimal designs of the damper can deliver much improved step responses in terms of the three objective functions, compared with the single-objective optimal design by minimizing the integrated tracking error alone. Numerical simulations of the three cases of c(α)c(α) demonstrate that better overall performance can be achieved with more design parameters in the multi-objective optimization setting.