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1. INTRODUCTION A feedback control system is utilized to manipulate the output of the plant so that it follows a reference signal. In a digital implementation, the controller collects samples through the sensor, compares it to the reference and computes the corresponding input to the plant based on the control law. The state feedback control laws require access to all state variables. For those states that are not directly measured, their estimates, obtained from a state observer, are used. Consequently, observer design has become a key factor in control design. Luenberger introduced the state observer for linear systems, known as the Luenberger Observer. For nonlinear system, several methods have been proposed. Misawa et al surveyed some of these methods. The performance of these observers and the resulting control system largely depend on the accuracy of the mathematical model of the plant, which poses a practical concern. To address this issue, an ingenious observer, known as Extended State Observer (ESO), was proposed by Han, where the states as well as the uncertainties in the plant are estimated. This allows the controller to actively compensate for the uncertainties, and it led to the Active Disturbance Rejection Control (ADRC) . By using a linear feedback instead of a nonlinear one, Gao proposed the Linear Active Disturbance Rejection Control (LADRC) for the Single-Input Single-Output (SISO) nonlinear uncertain system. LADRC is easy to use and to tune because it has only two tuning parameters, namely, the closed loop bandwidth and the observer bandwidth. However it requires that the ESO converges quickly. The objective of this paper is to find the LADRC¡¯s observer design condition in discrete time to make the estimate converge to the real signal quickly. |
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