Block-Oriented Continuous-Time Modelling For Nonlinear Systems Under Sinusoidal Inputs

Abstract

Discrete-time modelling (DTM) dominates the systems engineering literature in the applications of block-oriented modelling. The discrete environment of computer-based process control systems and discrete sampling are two major reasons [1]. Also, a DTM is easier to obtain because all input changes are approximated by piecewise step input sequences. Nonetheless, DTM has (potentially) two critical drawbacks relative to continuous-time modelling (CTM). DTM requires constant and frequent sampling and can only predict at those points. DTM is not potentially as accurate as CTM because, at best, it can only approximate continuous-time processes. For Hammerstein and Wiener CTM, this article proposes compact CTM algorithms under sinusoidal input sequences for Hammerstein and Wiener modelling. The proposed method depends only on the most previous input changes and provides exact solutions that are applicable to multiple-input, multiple-output systems as demonstrated.

Key Words:

• Nonlinear systems
• continuous-time modelling
• sinusoidal input sequence
• Hammerstein and Wiener models

Additional information

Notes on contributors

D. Zhai

Dongmei Zhai is a graduate Student in the Department of Chemical Engineering and Department of Statistics at Iowa State University. Zhai worked at the Lanzhou Institute of Chemical Physics, the Chinese Academy of Sciences for more than one year. Zhai holds her B.S. and M.E. in Chemical Engineering from Zhejiang University, China. She has an M.S. in Chemical Engineering and an M.S. in Statistics from Iowa State University also. She is now working on her Ph.D. co-major degree in Statistics and Chemical Engineering at Iowa State University.

D.K. Rollins

Derrick K. Rollins, Sr. is an Associate Professor with a joint appointment in the Chemical and Biological Engineering and StatisticsDepartmentsatthe IowaState University, Ames, IA. He has been in his current position since 1990. Prior to graduate school, Rollins worked for 7 years for Du Pont in process engineering at three different sites. He has worked as a consultant for several industrial companies, including Dow, 3M, and Shell, and has taught short courses in statistics for Amoco and IMC Agrico. Rollins holds a B.S. in chemical engineering and an M.S. and Ph.D. in chemical engineering and an M.S. in statistics from the Ohio State University.

N. Bhandari

Derrick K. Rollins, Sr. is an Associate Professor with a joint appointment in the Chemical and Biological Engineering and Statistics Departments at the Iowa State University, Ames, IA. He has been in his current position since 1990. Prior to graduate school, Rollins worked for 7 years for Du Pont in process engineering at three different sites. He has worked as a consultant for several industrial companies, including Dow, 3M, and Shell, and has taught short courses in statistics for Amoco and IMC Agrico. Rollins holds a B.S. in chemical engineering and an M.S. and Ph.D. in chemical engineering and an M.S. in statistics from the Ohio State University.

Nidhi Bhandari was a post-doc research associate in the Department of Chemical Engineering at Iowa State University when this research was completed. She is now an Assistant Professor in the Department of Chemical Engineering at Indian Institute of Technology, Roorkee, India. Her research is in the area of predictive modelling and model predictive control. She has a bachelor degree in Chemical Engineering from University of Roorkee, Roorkee, India. Bhandari worked briefly at Reliance Industries Limited, India before joining graduate school at Iowa State University. She holds a Ph.D. in Chemical Engineering from Iowa State University.