Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers

Muhammad Rizwan S Khan,Robert N K Loh

doi:10.4236/ijmnta.2014.34017

Abstract

This paper addresses the analysis, design, and application of observer-based nonlinear controls by combining feedback linearization (FBL) and backstepping (BS) techniques with Luenberger observers. Complete development of observer-based controls is presented for a bioprocess. Controllers using input-output feedback linearization and backstepping techniques are designed first, assuming that all states are available for feedback. Next, the construction of observer in the transformed domain is presented based on input-output feedback linearization. This approach is then extended to observer design based on backstepping approach using the error equation resulted from the backstepping design procedure. Simulation results demonstrating the effectiveness of the techniques developed are presented and compared.

Highlights

In process control, a major difficulty is to provide direct real-time measurements of the state variables required to implement advanced monitoring and control methods on bioreactors [1]-[5]
Exponential and asymptotic observers and their variants to estimate unmeasured states in bioprocess systems have appeared in [1]-[5]
Observers are critical to control system analysis and designs that employ full-state feedback, where not all the state variables are accessible for on-line, real-time measurements, and/or where the measurements are corrupted by noise

Summary

Introduction

A major difficulty is to provide direct real-time measurements of the state variables required to implement advanced monitoring and control methods on bioreactors [1]-[5]. An alternative is to use state observers which, in conjunction with the process model and available measurements, How to cite this paper: Khan, M.R.S. and Loh, R.N.K. (2014) Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers. Exponential and asymptotic observers and their variants to estimate unmeasured states in bioprocess systems have appeared in [1]-[5]. Theoretical foundation of input-output feedback linearization (FBL) and controller design are outlined in Section 3 with simulation results.

Bioprocess Model

Comparison of FBL and BS Designs

Observer-Based FBL and BS Controls

Luenberger Observer for FBL Control

Luenberger Observer for BS Control

Conclusion