“Discrete LQ optimal control with integral action: A simple controller on incremental form for MIMO systems”
Authors: David Di Ruscio,Affiliation: Telemark University College
Reference: 2012, Vol 33, No 2, pp. 35-44.
Keywords: Control Theory, Closed loop, Linear Systems, Modeling
Abstract: A simple Linear Quadratic (LQ) optimal controller of velocity (incremental) form with approximately the same properties as a conventional PID controller of velocity form is presented, i.e. integral action. The proposed optimal controller is insensitive to slowly varying system and measurement trends and has the ability of stabilizing any linear dynamic system under weak assumptions such as the stabilizability of the system and the detectability of the system seen from the performance index.
PDF (656 Kb)
DOI: 10.4173/mic.2012.2.1DOI forward links to this article:
| [1] David Di Ruscio (2013), doi:10.4173/mic.2013.3.2 |
| [2] Christer Dalen, David Di Ruscio and Roar Nilsen (2015), doi:10.4173/mic.2015.3.5 |
| [3] J.K. Woodacre, R.J. Bauer and Rishad Irani (2018), doi:10.1016/j.oceaneng.2018.01.030 |
| [4] Vinayambika S Bhat, I. Thirunavukkarasu, S. Shanmuga Priya, C Shreesha, P. Tandon, W. Wisnoe and M.Z. bin Abdullah (2018), doi:10.1051/matecconf/201815306010 |
| [5] Nicolás Cervantes-Escorcia, Omar-Jacobo Santos-Sánchez, Liliam Rodríguez-Guerrero, Hugo Romero-Trejo and Alberto González-Facundo (2018), doi:10.1007/s13369-018-3199-x |
| [6] Leonel Palacios, Anthony Harness, N. Jeremy Kasdin and Stuart B. Shaklan (2019), doi:10.1117/12.2528437 |
| [7] Leonel M. Palacios, Anthony Harness and N. Jeremy Kasdin (2020), doi:10.1016/j.actaastro.2020.02.011 |
| [8] Jacopo Mocci, Martino Quintavalla, Alessandro Chiuso, Stefano Bonora and Riccardo Muradore (2020), doi:10.1016/j.conengprac.2020.104528 |
| [9] Ezequiel Rodriguez, Ramon Leyva, Christopher D. Townsend, Glen G. Farivar, Josep Pou, Margarita Norambuena and Jose Rodriguez (2020), doi:10.1109/IECON43393.2020.9255123 |
| [10] Anusha Srivastava and Lal Bahadur Prasad (2021), doi:10.1007/s40435-021-00814-3 |
| [11] Anusha Srivastava and L. B. Prasad (2018), doi:10.1109/IAC3T.2018.8674029 |
| [12] Amelia Chindrus, Dana Copot and Constantin F. Caruntu (2022), doi:10.1109/ICSTCC55426.2022.9931791 |
| [13] Nour Bargoth, Christer Dalen and David Di Ruscio (2022), doi:10.4173/mic.2022.3.3 |
| [14] Amelia Chindrus, Dana Copot and Constantin-Florin Caruntu (2023), doi:10.3390/pr11041258 |
[1] Anderson, B.D.O. Moore, J.B. (1989). Optimal Control: Linear Quadratic Methods, Prentice-Hall International Editions.
[2] Åström, K. Hägglund, T. (1995). PID Controllers: Theory, Design, and Tuning, Instrument Society of America.
[3] Bristol, E.H. (1996). On a new measure of interactions for multivariable process control, Transactions on Automatic Control, 1.11:113--114 doi:10.1109/TAC.1966.1098266
[4] Di Ruscio, D. (2009). Closed and Open Loop Subspace System Identification of the Kalman Filter, Modeling, Identification and Control, 3.2:71--86 doi:10.4173/mic.2009.2.3
[5] Di Ruscio, D. (2010). On Tuning PI Controllers for Integrating Plus Time Delay Systems, Modeling, Identification and Control, 3.4:145--164 doi:10.4173/mic.2010.4.3
[6] Di Ruscio, D. Foss, B. (1998). On model based predictive control, In The 5th IFAC Symposium on Dynamics and Control of Process Systems.
[7] Doyle, J.C. (1978). Guaranteed Margins for LQG Regulators, IEEE Transactions on Automatic Control, 2.4:756--757 doi:10.1109/TAC.1978.1101812
[8] Gatzke, E.P., Meadows, E.S., Wang, C., Doyle, F. J.I. (2000). Model based control of a four-tank system, Computers and Chemical Engineering, 24(2):1503--1509 doi:10.1016/S0098-1354(00)00555-X
[9] Jazwinski, A.H. (1989). Stochastic processes and filtering theory, Academic Press.
[10] Johansson, K.H. (2002). Interaction bounds in multivariable control systems, Automatica, 38(2):1045--1051 doi:10.1016/S0005-1098(01)00285-0
[11] Kwakernaak, H. Sivan, R. (1972). Linear Optimal Control Systems, Wiley-Interscience.
[12] Maciejowski, J. (2002). Predictive control: with constraints, Pearson Education.
[13] Skogestad, S. Postlethwaite, I. (1996). Multivariable Feedback Control: Analysis and Design, Wiley.
[14] Söderström, T. (1994). Discrete-time Stochastic Systems: Estimation and Control, Prentice Hall.
BibTeX:
@article{MIC-2012-2-1,
title={{Discrete LQ optimal control with integral action: A simple controller on incremental form for MIMO systems}},
author={Di Ruscio, David},
journal={Modeling, Identification and Control},
volume={33},
number={2},
pages={35--44},
year={2012},
doi={10.4173/mic.2012.2.1},
publisher={Norwegian Society of Automatic Control}
};