A gain‐tuning method for almost disturbance decoupling problems of nonlinear systems with zero dynamics

• Published in: International journal of robust and nonlinear control Vol. 32; no. 7; pp. 4459 - 4476
• Main Authors: Liu, Xiaoping, Wang, Zhengqi, Wang, Wilson
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.05.2022
• Subjects: almost disturbance decoupling; Control systems; Decoupling; Dynamical systems; Feedback control; Linear matrix inequalities; Linear systems; Mathematical analysis; Nonlinear control; Nonlinear systems; robust control; Tuning
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6031

In this paper, a gain‐tuning method for almost disturbance decoupling problems of nonlinear systems with zero dynamics is developed. Firstly, a linear subsystem is formed by linearizing the nonlinear system. Then, a linear matrix inequality can be formed for the linear subsystem. After that, a linear state‐feedback controller can be obtained by solving the linear matrix inequality. A nonlinear state‐feedback controller can be obtained for the original nonlinear system by using backstepping design method. Another linear state‐feedback controller can be derived by linearizing the nonlinear state‐feedback controller. Finally, the backstepping gains can be solved by equating the two linear controllers. The detailed derivations of the method are provided. Some comparisons with the existing techniques are discussed. Moreover, the designed method is verified by simulations and some comparisons are made accordingly.