Two degree of freedom robust optimal control design using a linear matrix inequality optimization

This paper proposes a new method for the control design for reference tracking in a two degree-of-freedom (2DOF) robust optimal control framework. The main contribution of this paper is formulation of 2DOF multi-objective optimal control problem in terms of linear matrix inequalities. The proposed method enables formulating and solving for a larger set of performance specifications than existing conventional 2DOF designs. This method also provides a platform for implementing mixed-norm optimization problems that model many tracking applications. The theoretical results are corroborated by experiments that apply the proposed control design for a tracking problem on a positioning system.

[1]  C. Scherer.  Lower Bounds in Multi-Objective Hz / H , Problems , 2004 .

[2]  Uri Shaked,et al.  Two-degree-of-freedom H/sub infinity /-optimization of multivariable feedback systems , 1991 .

[3]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  G. Dullerud,et al.  A Course in Robust Control Theory: A Convex Approach , 2005 .

[6]  D. Limebeer,et al.  An H/sub infinity / approach to two degree of freedom design , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[7]  K. Glover,et al.  Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty , 1989 .

[8]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[9]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[10]  D. Youla,et al.  A feedback theory of two-degree-of-freedom optimal Wiener-Hopf design , 1985 .

[11]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[12]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[13]  C. D. Souza,et al.  Continuous-time tracking problems in an H∞ setting: a game theory approach , 1995, IEEE Trans. Autom. Control..

[14]  Mathukumalli Vidyasagar,et al.  Control System Synthesis: A Factorization Approach, Part I , 2011, Control System Synthesis Part I.

[15]  Chibum Lee,et al.  Robust broadband nanopositioning: fundamental trade-offs, analysis, and design in a two-degree-of-freedom control framework , 2009, Nanotechnology.

[16]  J. Freudenberg,et al.  Right half plane poles and zeros and design tradeoffs in feedback systems , 1985 .

[17]  J. Geromel,et al.  An LMI optimization approach to multiobjective controller design for discrete-time systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[18]  Chibum Lee,et al.  Optimal Model Matching Design for High Bandwidth, High Resolution Positioning in AFM , 2008 .

[19]  C. W. Schere.  Lower bounds in multi-objective H/sub 2//H/sub /spl infin// problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[21]  Michael J. Grimble.  Two-degrees of freedom feedback and feedforward optimal control of multivariable stochastic systems , 1988, Autom..