Constrained spectrum control using MPC

Well-known model predictive control (MPC) theory for constrained linear time-invariant (LTI) systems is extended to accommodate hard constraints and cost penalizations on the spectra of the system's output trajectories. Thus the proposed method facilitates enforcing constraints, and placing weights, on the harmonic content of input-, state- and output-trajectories, in addition to the usual constrained control objectives. The proposed methods are demonstrated by the example problem of reducing torsional vibrations in a drive-shaft.

[1]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[2]  K. F. Riley,et al.  Mathematical methods for the physical sciences , 1975 .

[3]  N. Gupta.  Frequency-shaped cost functionals - Extension of linear-quadratic-Gaussian design methods , 1980 .

[4]  B. Anderson,et al.  Adaptive frequency sampling filters , 1981 .

[5]  Romeo Ortega,et al.  Adaptive Tuning to Frequency Response Specifications , 1990 .

[6]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[7]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[8]  Romeo Ortega,et al.  Adaptive tuning to frequency response specifications , 1993, Autom..

[9]  J. H. Wright,et al.  Advanced Modern Engineering Mathematics , 1993 .

[10]  Stephen A. Martucci,et al.  Symmetric convolution and the discrete sine and cosine transforms , 1993, IEEE Trans. Signal Process..

[11]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[12]  J. Hennet,et al.  (A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems , 1999 .

[13]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[14]  David Q. Mayne,et al.  Correction to "Constrained model predictive control: stability and optimality" , 2001, Autom..

[15]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[16]  Boualem Boashash,et al.  Time-Frequency Signal Analysis and Processing , 2002 .

[17]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[18]  R. Bitmead,et al.  Robust constrained model predictive control using closed-loop prediction , 2003, Proceedings of the 2003 American Control Conference, 2003..

[19]  J. Löfberg,et al.  Approximations of closed-loop minimax MPC , 2003, CDC.

[20]  D. N. Walker.  Torsional vibration of turbomachinery , 2004 .

[21]  D.E. Quevedo,et al.  Control of EMI from switch-mode power supplies via multi-step optimization , 2004, Proceedings of the 2004 American Control Conference.

[22]  Graham C. Goodwin,et al.  Constrained Control and Estimation , 2005 .

[23]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

[24]  D. Limón,et al.  MPC FOR TRACKING OF PIECE-WISE CONSTANT REFERENCES FOR CONSTRAINED LINEAR SYSTEMS , 2005 .

[25]  Graham C. Goodwin,et al.  Constrained Control and Estimation: an Optimization Approach , 2004, IEEE Transactions on Automatic Control.

[26]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[27]  Eric C. Kerrigan,et al.  Optimization over state feedback policies for robust control with constraints , 2006, Autom..

[28]  B. Allard,et al.  A predictive control for a matrix converter-fed permanent magnet synchronous machine , 2008, 2008 IEEE Power Electronics Specialists Conference.

[29]  Eduardo F. Camacho,et al.  MPC for tracking piecewise constant references for constrained linear systems , 2008, Autom..

[30]  D.E. Quevedo,et al.  Predictive Current Control Strategy With Imposed Load Current Spectrum , 2008, IEEE Transactions on Power Electronics.

[31]  Antonio Ferramosca,et al.  MPC for tracking with optimal closed-loop performance , 2009, Autom..

[32]  Leopoldo García Franquelo,et al.  Model Predictive Control of an Inverter With Output $LC$ Filter for UPS Applications , 2009, IEEE Transactions on Industrial Electronics.

[33]  T. Singh.  Optimal Reference Shaping for Dynamical Systems: Theory and Applications , 2009 .

[34]  Tristan Perez,et al.  Motion Control of Marine Craft , 2010 .

[35]  Henri P. Gavin,et al.  Earthquake Response Control for Civil Structures , 2010 .

[36]  Michael Athans,et al.  Linear Quadratic Regulator Control , 2010, The Control Systems Handbook.

[37]  A. P. Bovsunovskii,et al.  Fatigue damage and failure of steam turbine rotors by torsional vibrations , 2010 .

[38]  H. Hindi,et al.  Coordinating regulation and demand response in electric power grids using multirate model predictive control , 2011, ISGT 2011.

[39]  Marc Moonen,et al.  A fast projected gradient optimization method for real-time perception-based clipping of audio signals , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).