Nonlinear sliding mode control design: An LMI approach

A homogeneous extended state estimator-based super-twisting sliding mode compensator for matched and unmatched uncertainties

“…It is worth to mention that the lumped disturbances (equation 33) are generally very feeble as compared with the strong system dynamics and hence it is reasonable to assume that such disturbances can be compensated by the presented control method. Using equations (31) and (33), the complete dynamic model of the EMS vehicle is represented as…”

“…The second concern of handling unmatched uncertainty is justified because it has been observed that the major uncertainties present in many MCS such as rail track input in MAGLEVs, 28 load torque in PMSM, 29 external wind disturbances in flight control system, 30 and so on do not adhere to so-called matching condition and hence robust performance out of SMC may not be achieved. 31 Hence, due to the importance of nullifying mismatched uncertainties for getting precise and effective performance from MCS, many decent SMC strategies focusing the mismatched disturbance attenuation have been reported in the literature, for example, Riccati based approach, 32 LMI-based, 33 H ∞ control based, 34 adaptive approach, 35 and so on. However, these approaches are designed to handle mismatched uncertainties if they are vanishing type, that is, H 2 norm-bounded which may not be the case in real-time system, for example, in MAGLEV transportation system, the considered lumped uncertainties may not have zero steady-state and hence not H 2 norm-bounded.…”

Dynamic sliding mode control for nonlinear parameter‐varying systems

“…Specifically, the sliding mode observer synthesis for affine LPV systems was solved in Reference 23, where the output matrix is assumed to be common and the product between the output matrix and nonlinear coefficient matrix satisfies the full-column rank conditions. In addition, the literature 24 proposed a nonlinear SMC methodology for systems with matched constraint. More recently, a sliding mode controller design method based on the LPV model was proposed in Reference 25 to solve the engines control problem, where the common Lyapunov function was employed for the corresponding analysis and design.…”

Robust hierarchical sliding mode control with state-dependent switching gain for stabilization of rotary inverted pendulum

“…Utkin together with Yang continued their work and in 1978, they derived the term nonlinear switching from linear state space derivation which ensured the robustness of SMC [45]. Based on SMC, different new techniques are designed to address nonlinear control problems [36,41,48,53]. It is widely used to design controllers for robotics [33,37,54], under-actuated cranes [21,27,42,43], quadrotors for unmanned aerial vehicles (UAV) [1], and under-actuated vessels [22].…”