Extended state observer-based robust non-linear integral dynamic surface control for triaxial MEMS gyroscope

Abstract

SUMMARYThis paper reports an extended state observer (ESO)-based robust dynamic surface control (DSC) method for triaxial MEMS gyroscope applications. An ESO with non-linear gain function is designed to estimate both velocity and disturbance vectors of the gyroscope dynamics via measured position signals. Using the sector-bounded property of the non-linear gain function, the design of an $\mathcal{L}_2$-robust ESO is phrased as a convex optimization problem in terms of linear matrix inequalities (LMIs). Next, by using the estimated velocity and disturbance, a certainty equivalence tracking controller is designed based on DSC. To achieve an improved robustness and to remove static steady-state tracking errors, new non-linear integral error surfaces are incorporated into the DSC. Based on the energy-to-peak ($\mathcal{L}_2$-$\mathcal{L}_\infty$) performance criterion, a finite number of LMIs are derived to obtain the DSC gains. In order to prevent amplification of the measurement noise in the DSC error dynamics, a multi-objective convex optimization problem, which guarantees a prescribed $\mathcal{L}_2$-$\mathcal{L}_\infty$ performance bound, is considered. Finally, the efficacy of the proposed control method is illustrated by detailed software simulations.

Immersion and invariance‐based extended state observer design for a class of nonlinear systems

“…Hence, ESOs, as effective tools for disturbance estimation, lie at the core of active disturbance rejection control (ADRC) methods 1‐4 . ESOs can be also used to robustify the existing control methods against wider classes of disturbances while removing the need for full‐state measurement 5,6 …”

“…A convex optimization‐based method has been proposed to establish the convergence of an ESO with dead‐zone‐type nonlinear gain functions 5 . A more involved model of the total disturbance dynamics, instead of the commonly used integral action, has been applied to improve the disturbance estimation quality of a nonlinear ESO 6 …”

“…[1][2][3][4] ESOs can be also used to robustify the existing control methods against wider classes of disturbances while removing the need for full-state measurement. 5,6 The core idea of ESOs is to augment an approximate dynamical model of the total disturbance (usually an integral action) to the underlying system's dynamics and subsequently design an observer for the resultant extended system. Following the seminal works of Han, 1,2 the problems of design and convergence analysis of ESOs, for effective disturbance estimation, have been studied intensively.…”

On performance recovery of robust dynamic surface control

“…Nevertheless, the classical RDSC in Reference and its variations are conservative in the following aspects: (a) on the control synthesis, due to the need of a small damping factor, the nonlinear damping terms applied may cause high control gains and substantial energy costs resulting in an impractical control law; and (b) on the control analysis, the closed‐loop stability relies on both large control gain parameters and a small filter parameter. DSC has been extensively studied in recent years, for example, see References for adaptive DSC and References for (adaptive) RDSC. However, the conservative nature of the classical RDSC has not been investigated, and thus, the technical connection between RDSC and MSSC is still unclear.…”

Adaptive control of micro-electro-mechanical system gyroscope using neural network compensator

“…In recent years, some researchers have proposed many advanced adaptive control methods to control MEMS gyroscopes. Some advanced sliding mode control methods were discussed in previous studies [1][2][3][4][5][6][7] to improve the control accuracy of the gyroscopes. Hu and Gallacher 8 presented a high-precision mode tuning method for the MEMS gyroscope.…”