94733f57-5797-4bf2-975a-90660b86d9a720210318034418622wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL1991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073220202022020201510.37394/23203.2020.15http://wseas.org/wseas/cms.action?id=23195The H∞ Model Following Control: An LMI ApproachMuratAkinGalatasaray University, Computer Engineering Department, Ortakoy/Istanbul, TURKEYTankutAcarmanGalatasaray University, Computer Engineering Department, Ortakoy/Istanbul, TURKEYThe aim of this paper is to develop a new approach for a solution of the model following control (MFC) problem with a dynamic compensator by using linear matrix inequalities (LMIs). TheH1 model following control problem is derived following LMI formulation. First, the H1 optimal control problem is revisited by referring to Lemmas assuring all admissible controllers minimizing the H1 norm of the transfer function between the exogenous inputs and the outputs. Then, the solvability condition and a design procedure for a two degrees of freedom (2 DOF) dynamic feedback control law is introduced. The existence of a 2 DOF dynamic output feedback controller for the model following control is proven and the stability of the closed-loop system is satisfied by assuring the Hurwitz condition. The benchmark thermal process (PT-326) as the first order process with timedelay is regulated by the presented 2 DOF dynamic output feedback controller. The simulation results illustrate that the presented controller regulates a system with dead-time as a large set of generic industrial systems and the H1 norm of the closed-loop system is assured less than the H1 norm of the desired model system.222202022220201118https://www.wseas.org/multimedia/journals/control/2020/a045103-924.pdf10.37394/23203.2020.15.2http://www.wseas.org/multimedia/journals/control/2020/a045103-924.pdfM. Akin and A. Bir, The H∞ Model Matching Problem with One Degree of Freedom Static State Feedback,Turkish Journal of Electrical Engineering and Computer Sciences, 2003, Vol.11, No.1.M. Akin and T. Acarman, The Continuous-Time H∞ Model Matching Problem: 1 DOF StaticState Feedback with Integral Control Approach,International Journal of Control Systems and Robotics, 2016, Vol.1, pp. 113-122.10.1109/cdc.1998.758548P. Apkarian and H. D. Tuan, Parameterized LMIs in Control Theory,Proceedings on the 37th IEEE Conference on Decision and Control,1998, pp. 152-157.10.1137/1.9781611970777S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan,Linear Matrix Inequalities in Systems and Control Theory, 1994, Vol.15, SIAM.10.1109/9.486637M. Chilali and P. Gahinet, H∞ Design with Pole Placement Constraints: An LMI Approach, IEEE Transactions on Automatic Control, 1996, Vol. 41, No.3, pp. 358-367.10.1109/9.811208M. Chilali, P. Gahinet and P. Apkarian, Robust Pole Placement in LMI Regions, IEEE Trans-actions on Automatic Control, 1999, Vol.44,No.12, pp. 2257-2270.M. Chilali, P. Gahinet and C. Scherer, Multiob-jective Output-Feedback Control via LMI Opti-mization,Proceedings on IFAC13thTriennialWorld Congress, 1996.U. Christen, M. F. Weilenmann and H. P. Geering, Design of H2 and H∞ Controllers with Two Degrees of Freedom,Proceedings of the American Control Conference, 1994, pp. 2391-2395.10.1007/bfb0113855H. Duda, G. Bouwer, J. M. Bauschat and K.U. Hahn, RCAM Design Challenge Prensentation Document: A Model Following Control Approach, GARTEUR Group For Aeronautical Re-search and Technology in Europe, 1997.G. Dullerud and F. Paganini, A Course in Robust Control Theory, a Convex Approach,Springer-Verlag, 2000.FEEDBACK, Process Trainer PT-326/PCS-327, Feedback Instruments Limited, 1985.10.1002/rnc.4590040403P. Gahinet and P. Apkarian, A Linear Matrix In-equality Approach to H∞ Control, International Journal of Robust and Nonlinear Control, 1994,Vol.4, pp. 421-448.P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, The LMI Control Toolbox for Use with MATLAB, The Math Works Inc., 1995.10.1016/s0959-1524(00)00057-3M. Ge, M. Chiu and Q. Wang, Robust PID Controller Design via LMI Approach, Journal of Process Control, 2002, 12, 3-13.O. R. Gonzales, H∞ Design with Two-Degrees-of-Freedom Controllers, Proceedings of the American Control Conference, 1994, pp. 2421-2423.M. J. Grimble, Robust Industrial Control, Optimal Design Approach for Polynomial Systems, Prentice-Hall International, 1994.V. Kucera, Analysis and Design of Discrete Linear Control Systems,Prentice-Hall International, 1991.W. A. Wolovich, Linear Multivariable Systems,Springer-Verlag, 1974.