Implementation of servo systems for controlling a double purpose nonlinear plant: Inverted pendulum and crane

This paper develops design procedures of Proportional-Integral Servo Systems (SSs for short) for controlling a double purpose nonlinear plant: Inverted Pendulum and Crane (IP&C). Such a plant can be described by nonlinear differential equations, where the nonlinear terms complicate the analytical aspects of modeling and controller design. However, based on the linearized plant model, we can configurate discrete-time SSs by combining linear controllers with linear observers. Experimental results demonstrate that each SS is able to stabilize an IP (or a Crane) mounted on a servomotor-driven cart. Three SSs configurations are developed: A Steady-State Quadratic Optimal Controller (SSQOC) with a Quadratic Optimal State Observer (QOSO), a Pole Placement Controller (PPC) with a Full-Order State Observer (FOSO), and a PPC with a Minimum-Order State Observer (MOSO).