Riccati-Based Static Output-Feedback Optimization for PID Controller Tuning

Traditional proportional-integral-derivative (PID) tuning methods often struggle in nonlinear systems with limited measurement availability. This study investigates PID controller tuning within a Riccati-based static output-feedback (SOF) optimization framework. Two SOF-based approaches—a gradient-based method and a modified Newton-type method—are systematically evaluated and compared with optimization-based and linear quadratic regulator (LQR)-based benchmark strategies under identical simulation conditions. The proposed framework enables a unified and consistent evaluation of different tuning methods under identical modeling assumptions. It is applied to a three-state single-input single-output (SISO) Rössler chaotic system as a representative nonlinear benchmark. Simulation results demonstrate clear trade-offs among convergence speed, control smoothness, computational effort, and regulation accuracy. In particular, the Newton-based SOF method achieves smoother control actions and improved damping characteristics while maintaining acceptable computational cost.