On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design

Abstract

Abstract-This paper presents a new improved nonlinear tracking differentiator (INTD) with hyperbolic tangent function in the state-space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. The improved tracking differentiator (INTD) has the required filtering features and can cope with the nonlinearities caused by the noise. Through simulations, the INTD is implemented as a signal's derivative generator for the closedloop feedback control system with a nonlinear PID controller for the nonlinear Mass-Spring-Damper system and showed that it could achieve the signal tracking and differentiation faster with a minimum mean square error.

A New Nonlinear Dynamic Speed Controller for a Differential Drive Mobile Robot

“…This TD presents an enhanced dynamic performance relative to Han’s TD. An INTD for second-order systems has been designed using the hyperbolic tangent function [ 11 , 17 ], where , is the reference signal, and r 1 and r 2 are the tracking reference and its derivative, respectively. The coefficients and are tuning coefficients, with The configuration with the proposed INTD can effectively eliminate the chattering phenomenon and measurement noise and provide swift and smooth tracking of the desired reference signal.…”

“…The contribution of this paper lies in applying an improved version of Han’s classical ADRC to motion control of a DDMR, which is a nonlinear, multi-input–multi-output (MIMO) system, as an extension of our four previous published papers [ 11 , 12 , 13 , 14 ]. The proposed IADRC is constructed by combining three primary units.…”

Genetic Optimization-Based Consensus Control of Multi-Agent 6-DoF UAV System

“…The aim of the tracking formation is to keep the agents in a formation on the 3D space ( ) and the angle of rotation around -axis ( ) while tracking the leader. Therefore, the leader control is different from the followers, which can be represented by normal quadrotor control using a combination of NLPID for the outer loop control (OLC) and IADRC for the inner loop control (ILC) of the quadrotor system, which was designed in our previous works [ 26 , 27 , 28 ] and is shown in Figure 4 . The followers’ control is a mix of two controllers; the first is the local one and the second is the consensus controller, as shown in Figure 5 .…”

A High-Precision Control Scheme Based on Active Disturbance Rejection Control for a Three-Axis Inertially Stabilized Platform for Aerial Remote Sensing Applications

“…Kasim and Riyadh [20] have made some investigations on traditional structures and essential properties of the nonlinear TD. A kind of second-order nonlinear TD based on second-order bang-bang switch system has been proposed:…”

“…. The performance of the ESO is very important to the performance of the controller [18,20]. The state observer is used to determine the internal state of the system by observing the external state of the system in different situations.…”