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Mathematical Problems in Engineering
Volume 2016, Article ID 3796486, 9 pages
Research Article

ADRC Method for Noncascaded Integral System Based on the Total Derivative of Composite Functions of Several Variables

1Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China
2Institute of Power Plant and Automation, Shanghai Jiao Tong University, Shanghai 200030, China

Received 31 May 2016; Revised 13 October 2016; Accepted 30 October 2016

Academic Editor: Rafael Morales

Copyright © 2016 Zhijian Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The standard ADRC controller usually selects the canonical plant in the form of cascaded integrators. However, the condition variables of practical system do not necessarily have the cascaded integral relationship. Therefore, this paper proposes a method of total derivative of composite functions of several variables and a structure, which can convert the state space system of noncascaded integral form into the cascaded integral form. In this way, the converted system can be directly controlled with ADRC. Meanwhile, the control of Chen chaotic system is discussed in detail to show the conversion and the controller design. The control performances under different levels of complication and different strengths of disturbance are comparably researched. The converted system achieves significantly better control effects under ADRC than that of the PID. This converting method solves the control problem of some noncascaded integral systems in both theory and application and greatly expands the application scope of the standard ADRC method.