An equivalent control based second order sliding mode observer using robust differentiators

Finite‐time sliding mode observer for uncertain nonlinear systems based on a tunable algebraic solver

“…In particular, condition (17) requires that there are enough algebraic equations to solve for the n state variables and the p unknown inputs, while Equation (18) represents a relative degree requirement that ensures that the employed output derivatives do not depend on the derivatives of the unknown inputs. Note that (18) characterizes the dependence of f .x; d/ on d in (14); for instance, in the case of a system with a single output and a single unknown input, this condition requires the relative degree to equal the order of the system. If conditions (17) and (18) [27], which has the following structure: where k is the order of differentiation, .t/ is a sufficiently smooth function to be differentiated, i is an estimate of .i / .t /, L is a Lipschitz constant for .k/ .t /, and 0 , 1 , : : :, k are positive parameters that must be properly chosen and whose recommended values for a fifth-order differentiator are given in [27].…”

“…For nonlinear systems, this inverse transformation is, in general, difficult to find explicitly. An alternative to finding an explicit inverse transformation is using the inverse of the observability matrix in the definition of the observer so that estimates for the original state variables are obtained during the integration ; however, this requires this matrix to be square, which does not allow for the use of more Lie derivatives than strictly necessary because then a non‐square observability matrix would be obtained. This restriction on the number of Lie derivatives to be used leads to the omission of useful information and the possible loss of observability when there are multiple outputs.…”

Comparación de desempeño de observadores de estado en sistemas lineales con aplicación a un motor de corriente continua

“…Además, los observadores de estado poseen importantes propiedades adicionales tales como la posibilidad de contar con una secuencia estructurada de diseño y la capacidad de utilizar dinámicas reducidas para la observación del proceso en cuestión [2]. En general, varios investigadores se han interesado por el diseño de observadores de estado y se encuentran varias soluciones reportadas en la literatura aplicadas a problemas de estimación, identificación de modelos y diseño de controladores, entre otros [3]- [11].…”