Technical report: PID design of second‐order non‐linear uncertain systems with fractional order operations

Abstract

Abstract This study considers a control problem related to the regulation of fractional‐order systems controlled by fractional order proportional‐integral‐derivative controllers (PIλDμ). The stability result of PIλDμ‐based control systems is provided, such that the closed‐loop systems can accomplish global stabilisation under some suitable conditions related to the system uncertainties. Finally, a simulation is demonstrated to verify the results.

Keywords

• stability
• three‐term control
• PI control
• closed loop systems
• uncertain systems
• control system synthesis