Robust feedback control of the underactuated Inertia Wheel Inverted Pendulum under parametric uncertainties and subject to external disturbances: LMI formulation

• Published in: Journal of the Franklin Institute Vol. 355; no. 18; pp. 9150 - 9191
• Main Authors: Gritli, Hassène, Belghith, Safya
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.12.2018; Elsevier Science Ltd
• Subjects: Computer simulation; Control systems; Controllers; Disturbances; Feedback control; Feedback control systems; Inertia; Linear matrix inequalities; Linear programming; Linearization; Matrix; Matrix methods; Mechanical engineering; Mechanical systems; Parameter uncertainty; Robust control; Robustness (mathematics); Stabilization; Theory of constraints
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2017.01.035

•A robust feedback stabilization of the Inertia Wheel Inverted Pendulum in its upright position is considered.•The underactuated mechanical system is under state constraints, norm-bounded parametric uncertainties and external disturbances.•We use the S-procedure to develop stability conditions and the problem is represented as a solving problem of BMIs.•We use the Schur complement and the matrix inversion lemma to transform these BMIs into LMIs.•An extensive portfolio of numerical studies and comparisons is presented and some simulation results are carried out. This paper proposes a robust feedback controller using Linear Matrix Inequalities (LMIs) formulation for the stabilization of an underactuated mechanical system, namely the Inertia Wheel Inverted Pendulum (IWIP), in its upright position. Such mechatronic system is subject to state constraints, external disturbances and norm-bounded parametric uncertainties. The main idea to solve the stabilization problem lies in the use of the S-procedure Lemma. Such problem is then transformed into a solving problem of Bilinear Matrix Inequalities (BMIs). Through the Schur complement Lemma and the Matrix Inversion Lemma, a linearization procedure is employed to transform the BMIs into LMIs. Some improvements and comparisons with other LMI-based design techniques without state constraints are developed and discussed. An extensive portfolio of numerical studies is presented. The effectiveness and robustness of the proposed feedback controller toward uncertainties in the friction parameters and external disturbances are illustrated through simulation results.