LQR approach to robust stabilization of state space systems with matched uncertainties.

This note shows an elegant relationship between the quadratic optimal control and robust stabilization for linear time-invariant (LTI) systems, where the former control can robustly stabilize the latter system, provided that the matched uncertainty is bounded. Through reviewing the relevant literature, some common mistakes in regard to this relationship are found. The correct results are obtained and proved in both frequency and time domains.

Active disturbance rejection control for non-minimum phase systems under plant reconstruction.

Active disturbance rejection control (ADRC) for non-minimum phase (NMP) systems is a challenging problem due to the conflict between stability and feedback tuning. The key point on this issue is to avoid heavy feedback tuning for robustness enhancement. We perform plant reconstruction to obtain an explicit expression of internal disturbance, such that it can be reduced by cascade compensation.

Design, analysis and application of a new disturbance rejection PID for uncertain systems.

In this paper, a new disturbance rejection proportional-integral-derivative (DR-PID) scheme is proposed for a class of minimum phase plants with low relative order. The essential active disturbance rejection (ADR) mechanism that is otherwise hidden in PID control structure has been illuminated and clarified in this paper for the first time.The proposed DR-PID scheme is derived on the basis of a modified disturbance observer to embed the active disturbance rejection mechanism seamlessly in the classical PID structure.

Combined gain and phase margins.

In this note, the limitations of conventional or separate gain or phase margin are shown. Then, the combined gain and phase margins are introduced to overcome the limitations and suit both stable and unstable systems. A simple method for their computation is presented and their applications in stabilization is demonstrated.