This paper proposes a method of robust optimal stabilization for balance systems such as rocket and missile systems, Segway human transportation systems, and inverted pendulum systems. Constant-gain controllers such as linear-quadratic regulators may not guarantee stability let alone optimality for balance systems affected by parametric variations. The robust stability and robust performance achieved through the proposed variable-gain controller are better than those of the linear-quadratic regulator. The proposed controller consists of two components, one of which is designed offline for nominal values of parametric variations and one of which is updated online for off-nominal values of parametric variations. A salient feature of the proposed method is a linear transformation that converts the vector control input of balance systems into scalar control input for application of the proposed method. A fourth-order linearized model of an inverted pendulum system is simulated to show the efficacy of the proposed method.
ZAFFAR, SALMAN and MEMON, ATTAULLAH
"Robust optimal stabilization of balance systems with parametric variations,"
Turkish Journal of Electrical Engineering and Computer Sciences: Vol. 25:
5, Article 48.
Available at: https://journals.tubitak.gov.tr/elektrik/vol25/iss5/48