In many practical applications it is not possible to measure all the states required to control the system. In such instances observer/filter is used to give a good estimate of the states of the system. The objective of the observer is to estimate the states such that the error between the actual and computed measurements goes to zero and obtain the “best” estimates of the states of a given system. In the current study a new nonlinear observer structure is proposed. The development of the observer is based on optimal control theory. A cost function is defined in terms of the measurement residual and the magnitude of correction term. The observer gains are obtained by minimizing the cost function with respect to the magnitude of corrections. The proposed observer is used to estimate the states of a one-dimensional electrostatic micro-actuator. The states of the actuator dynamics are, charge on the capacitor plates, the distance between the plates and the relative velocity between the plates. The regulation of the actuator states to desired trajectories is achieved through optimal control based state feedback. However in practice it is very difficult to measure the relative position and velocity of the plates. In this paper optimal feedback control based on the state estimates provided by the observer is used to regulate the actuator states to the desired location.
New Nonlinear Observer Design With Application to Electrostatic Micro-Actuators
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Durbha, V, & Balakrishnan, SN. "New Nonlinear Observer Design With Application to Electrostatic Micro-Actuators." Proceedings of the ASME 2005 International Mechanical Engineering Congress and Exposition. Dynamic Systems and Control, Parts A and B. Orlando, Florida, USA. November 5–11, 2005. pp. 101-107. ASME. https://doi.org/10.1115/IMECE2005-82163
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