Optimal design of discrete-time fractional-order PID controller for idle speed control of an IC engine

This paper aims at proposing a discrete-time fractional-order PID (FOPID) controller, which can stabilise the variation of the idle speed of an internal combustion engine due to the occurrence of the external load disturbance. The nonlinear idle speed dynamics is linearised to be approximated by a first order plus dead time (FOPDT) model so that the FOPID controller can be initialised by a Ziegler-Nichols type tuning rule. The initialised FOPID controller can stabilise the linearised model, but it may lose its control capability in nonlinear idle speed dynamics. Therefore, an optimisation problem is solved through genetic algorithm (GA) to minimise a cost function within a small region around the FOPID's initial parameters. The optimal discrete-time FOPID controller are compared to a conventional discrete-time PID controller. The simulation study reveals that the optimal discrete-time FOPID controller secures an excellent control performance to the nonlinear idle speed model.