  The Proportional-Integral-Derivative Controller is widely used in industries
for process control applications. Fractional-order PID controllers are known to
outperform their integer-order counterparts. In this paper, we propose a new
technique of fractional-order PID controller synthesis based on peak overshoot
and rise-time specifications. Our approach is to construct an objective
function, the optimization of which yields a possible solution to the design
problem. This objective function is optimized using two popular bio-inspired
stochastic search algorithms, namely Particle Swarm Optimization and
Differential Evolution. With the help of a suitable example, the superiority of
the designed fractional-order PID controller to an integer-order PID controller
is affirmed and a comparative study of the efficacy of the two above algorithms
in solving the optimization problem is also presented.
