Robust indirect adaptive sliding model control for Wiener nonlinear systems

ABSTRACT

Wiener model structures have attracted considerable attentions due to their powerful modelling abilities to solve industrial problems. This paper considers a new class of Wiener model structure, which consists of a linear transfer function and a radial basis function (RBF) network. Based on this structure, the unstable zero-dynamics, the added disturbances and the approximation errors problems can be dealt with. Since the model parameters are assumed unknown, we develop a new indirect adaptive control scheme. It is a consensus that the certainty equivalence principle is the key that connects the adaptation algorithm with the control law. This paper explains that, for indirect adaptive control of Wiener model, this principle may not be applied directly. The main contribution of this paper is to address this issue by presenting a rigorous theoretical analysis. Representative examples including a simulated pH process control problem are studied to test the control performance. Comparison results indicate that the proposed controller has much wider applicability than some alternative methods, especially for its improved performance and smoother adaptation.

KEYWORDS:

• Wiener model
• adaptive control
• unstable zero-dynamics
• stability
• pH process

Acknowledgements

This paper was supported by the China Postdoctoral Science Foundation (No. 2019M661157), the Self-planned Project of the State Key Laboratory of Robotics (No. 2019-Z12), and also the Natural Science Foundation of Liaoning Province (No. 20180540131).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper was supported by the China Postdoctoral Science Foundation (No. 2019M661157), the Self-planned Project of the State Key Laboratory of Robotics (No. 2019-Z12), and also the Natural Science Foundation of Liaoning Province (No. 20180540131).

Notes on contributors

Bi Zhang

Bi Zhang is an associate Professor at the State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences. He received the Ph.D. degree in control theories and control applications from Northeastern University, Shenyang, China. His recent research interests are advanced control theories and their applications.

Xin-Gang Zhao

Xin-Gang Zhao is a Professor at the State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences. His main research interests include medical robots, rehabilitation robots, robot control, and pattern recognition.