Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers
Affiliation(s)
1 Department of Electrical and Computer Engineering, Oakland University, Rochester, Michigan, USA.
1 Department of Electrical and Computer Engineering, Oakland University, Rochester, Michigan, USA.
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.
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.
KEYWORDS
Bioprocess, Feedback Linearization, Backstepping, Luenberger Observers, Observer-Based Control
Bioprocess, Feedback Linearization, Backstepping, Luenberger Observers, Observer-Based Control
Cite this paper
Khan, M. and Loh, R. (2014) Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers. International Journal of Modern Nonlinear Theory and Application, 3, 150-162. doi: 10.4236/ijmnta.2014.34017.
Khan, M. and Loh, R. (2014) Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers. International Journal of Modern Nonlinear Theory and Application, 3, 150-162. doi: 10.4236/ijmnta.2014.34017.
References
[1] Bastin, G. and Dochain, D. (1990) On-line Estimation and Adaptive Control of Bioreactors. Elsevier, Amsterdam. [2] Dochain, D. (2003) State and Parameter Estimation in Chemical and Biochemical Processes: A Tutorial. Journal of Process Control, 13, 801-818. http://dx.doi.org/10.1016/S0959-1524(03)00026-X [3] Dochain, D. and Rapaport, A. (2005) Internal Observers for Biochemical Processes with Uncertain Kinetics and Inputs. Mathematical Biosciences, 193, 235-253. http://dx.doi.org/10.1016/j.mbs.2004.07.004 [4] Dochain, D. (2000) State Observers for Tubular Reactors with Unknown Kinetics. Journal of Process Control, 10, 259-268. http://dx.doi.org/10.1016/S0959-1524(99)00020-7 [5] Hulhoven, X., Vande Wouwer, A. and Bogaerts, Ph. (2006) Hybrid Extended Luenberger-Asymptotic Observer for Bioprocess State Estimation. Chemical Engineering Science, 61, 7151-7160.
http://dx.doi.org/10.1016/j.ces.2006.06.018 [6] Dochain, D. and Perrier, M. (2003) Adaptive Backstepping Nonlinear Control of Bioprocesses. International Federation of Automatic Control Proceedings, ADCHEM, 77-82. [7] Khalil, H.K. (2002) Nonlinear Systems. 3rd Edition, Prentice Hall, Upper Saddle River. [8] Marquez, H.J. (2003) Nonlinear Control Systems: Analysis and Design. John Wiley & Sons, Hoboken. [9] Krstic, M., Kanellakopoulos, I. and Kokotovic, P. (1995) Nonlinear and Adaptive Control Design. John Wiley, New York. [10] Isidori, A. (1995) Nonlinear Control Systems. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-1-84628-615-5 [11] Krener, A.J. (1999) Feedback Linearization. In: Baillieul, J. and Willems, J.C., Eds. Mathematical Control Theory, Chapter 3, Springer-Verlag, New York, 66-98. [12] Luenberger, D.G. (1964) Observing the State of a Linear System. IEEE Transactions on Military Electronics, 8, 74-80.
http://dx.doi.org/10.1109/TME.1964.4323124 [13] Kalman, R.E. and Bucy, R.S. (1961) New Results in Linear Filtering and Prediction Theory. Transactions of the ASME, 83D, 429-438. [14] Ogata, K. (2010) Modern Control Systems. 5th Edition, Prentice Hall, Upper Saddle River. [15] Dorf, R. and Bishop, R. (2008) Modern Control Systems. 11th Edition, Pearson Education, Upper Saddle River.
[1] Bastin, G. and Dochain, D. (1990) On-line Estimation and Adaptive Control of Bioreactors. Elsevier, Amsterdam. [2] Dochain, D. (2003) State and Parameter Estimation in Chemical and Biochemical Processes: A Tutorial. Journal of Process Control, 13, 801-818. http://dx.doi.org/10.1016/S0959-1524(03)00026-X [3] Dochain, D. and Rapaport, A. (2005) Internal Observers for Biochemical Processes with Uncertain Kinetics and Inputs. Mathematical Biosciences, 193, 235-253. http://dx.doi.org/10.1016/j.mbs.2004.07.004 [4] Dochain, D. (2000) State Observers for Tubular Reactors with Unknown Kinetics. Journal of Process Control, 10, 259-268. http://dx.doi.org/10.1016/S0959-1524(99)00020-7 [5] Hulhoven, X., Vande Wouwer, A. and Bogaerts, Ph. (2006) Hybrid Extended Luenberger-Asymptotic Observer for Bioprocess State Estimation. Chemical Engineering Science, 61, 7151-7160.
http://dx.doi.org/10.1016/j.ces.2006.06.018 [6] Dochain, D. and Perrier, M. (2003) Adaptive Backstepping Nonlinear Control of Bioprocesses. International Federation of Automatic Control Proceedings, ADCHEM, 77-82. [7] Khalil, H.K. (2002) Nonlinear Systems. 3rd Edition, Prentice Hall, Upper Saddle River. [8] Marquez, H.J. (2003) Nonlinear Control Systems: Analysis and Design. John Wiley & Sons, Hoboken. [9] Krstic, M., Kanellakopoulos, I. and Kokotovic, P. (1995) Nonlinear and Adaptive Control Design. John Wiley, New York. [10] Isidori, A. (1995) Nonlinear Control Systems. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-1-84628-615-5 [11] Krener, A.J. (1999) Feedback Linearization. In: Baillieul, J. and Willems, J.C., Eds. Mathematical Control Theory, Chapter 3, Springer-Verlag, New York, 66-98. [12] Luenberger, D.G. (1964) Observing the State of a Linear System. IEEE Transactions on Military Electronics, 8, 74-80.
http://dx.doi.org/10.1109/TME.1964.4323124 [13] Kalman, R.E. and Bucy, R.S. (1961) New Results in Linear Filtering and Prediction Theory. Transactions of the ASME, 83D, 429-438. [14] Ogata, K. (2010) Modern Control Systems. 5th Edition, Prentice Hall, Upper Saddle River. [15] Dorf, R. and Bishop, R. (2008) Modern Control Systems. 11th Edition, Pearson Education, Upper Saddle River.