Compensation of Unmatched Disturbances via Sliding-Mode Control

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

“…where the states x = ½i, _ z, (z t À z) T represent the current variations, electromagnet vertical velocity, and air-gap, the input u = u c denotes the voltage, d(t) = _ z t is the disturbances generated due to vertical velocity of rail, the air gap variation y = z t À z is the controlled variable, DA is the uncertainty matrix and O(x, u, d) is the nonlinear function of high-order non-linearities. The matrices of system (31) are selected as…”

“…The high-order nonlinear expression O(x, u, d) in equation (31) is considered as a lumped disturbances consisting exogenous disturbances and parametric variation, denoted as…”

“…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.…”

Discrete‐time design and applications of uncertainty and disturbance estimator

“…While this characterizes real-world systems more accurately, compensating "unmatched" disturbances is a more complicated problem than compensating "matched" disturbances. Multiple studies propose methods such as higher-order sliding mode observation, [2][3][4] adaptive compensation 5,6 and the use of adaptive neural networks. 7 The focus of this study is on "matched" disturbances only, with compensation of "unmatched" disturbances being a promising avenue for future work.…”