Synthesis of Optimal Static Gain Feedback Using a Fractional-Order Performance Index

This paper presents a methodology for synthesizing static state feedback controllers utilizing a Fractional-Order Performance Index. Linear Quadratic Regulators are designed using integer-order integral weighting functions. In the proposed approach, fractional-order calculus is utilized to introduce an additional degree of freedom in controller synthesis, enabling enhanced shaping of the plant’s dynamic properties. The controller gains are obtained by solving a fractional Riccati-like equation, through which the temporal weighting properties inherent to fractional integration are embedded into a static feedback matrix. This formulation is a minimalist control structure suitable for implementation on resource-constrained hardware. The proposed method is validated via rapid control prototyping on an industrial NI PXIe platform and an analog third-order plant. Performance evaluation using Integral Absolute Error and Integral Absolute Control metrics demonstrates that the fractional order serves as a flexible tuning parameter, providing an alternative trade-off between settling time and control effort. Furthermore, frequency domain sensitivity analysis demonstrates the absence of resonant peaks and inherent attenuation of high-frequency measurement noise. As a result, the presented framework bridges fractional-order optimization techniques with industrial control platforms.