Sliding mode control design based on the state-dependent Riccati equation: theoretical and experimental implementation

• Published in: International journal of control Vol. 92; no. 9; pp. 2136 - 2149
• Main Authors: Korayem, A. H., Nekoo, S. R., Korayem, M. H.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.09.2019; Taylor & Francis Ltd
• Subjects: Differential equations; Feedback control; integral sliding surface; Integrals; Nonlinear systems; Riccati equation; Robot arms; Robust control; SDDRE; SDRE; Sliding mode control; Suboptimal sliding mode controller; Uncertainty
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2018.1428769

In this paper, a suboptimal sliding mode control method is derived from combination of the sliding mode control (SMC) and the state-dependent Riccati equation (SDRE) technique, applied for a class of nonlinear closed-loop systems. One of the distinguished features of this control method is its robustness towards uncertainty. Due to lack of optimality in SMC method, in this paper, a robust and suboptimal method is presented by considering the SDRE in design of the sliding surface in two types of: algebraic and integral sliding surfaces. In addition, due to the use of the state-dependent differential Riccati equation in the integral form of sliding surface, proposed method is able to provide a robust attitude with desired finite-time control option. The sensitivity of various percentage of uncertainty in the physical structure of the system is studied and control strategies for general manipulators are provided. The proposed control structure was implemented on Scout robot theoretically and practically by the LabVIEW software; and the results were compared by considering the uncertainty in its structure. In comparison with conventional SMC, the proposed method reduced the required time to reach the sliding surface almost 50%.