This study presents a simulation-based investigation into the application of a Cascade Proportional-Integral-Derivative (PID) combined with Linear Quadratic Regulator (LQR) control scheme for managing the complexities of a Nonlinear Flexible Inverted Pendulum System (NFIPS). The NFIPS. characterized by nonlinear dynamics and structural flexibility. demands a sophisticated control stra... https://allfixelectricales.shop/product-category/spst-24volt-relay/