Stabilization of open-loop unstable systems by the combine use of state-variable and transfer-function techniques

The inverted pendulum system, expressed mathematically by a third order transfer function with a zero at the origin, has many practical applications. Because of the complexity of the third order transfer function with zero at the origin, optimization is difficult. In this paper a combination of the classical and state variable approach is used to analyze, compensate, and design a working model of an inverted pendulum system. The state variable feedback technique is used to provide system stability. Performance criteria optimization of the above third order transfer function is investigated in classical methods for application to practical models.