Stabilization of General Linear Time-Invariant SISO Systems Using Two Stable Compensators to Produce All Left Half-Plane Zeros

Abstract

Abstract. Feedback stabilization of linear time-invariant (LTI) and single-input single-output (SISO) plants is considered within the framework of two-degree-of-freedom (2DOF) compensators, using only stable compensator components. In the classical 1DOF (or single feedback loop) setting, it is well known that a given plant can be stabilized by a stable controller if and only if it satisfies the parity interlacing property (PIP). With the 2DOF architecture proposed here, using stable components only, stabilization is possible for all plants with proper rational transfer functions. Our strategy is to create an effective plant that is biproper and has all its zeros in the left half-plane (LHP). Subsequently, a single large enough scalar gain (either positive or negative) is guaranteed to stabilize the system. We present several examples, including a cart with a double pendulum. While successful stabilization is mathematically achieved with stable compensator components in each case, some systems require high final gains.