Stabilizability and Disturbance Rejection with State-Derivative Feedback

In some practical problems, for instance in the control of mechanical systems using accelerometers as sensors, it is easier to obtain the state-derivative signals than the state signals. This paper shows that (i) linear time-invariant plants given by the state-space model matrices with output equal to the state-derivative vector are not observable and can not be stabilizable by using an output feedback if and (ii) the rejection of a constant disturbance added to the input of the aforementioned plants, considering , and a static output feedback controller is not possible. The proposed results can be useful in the analysis and design of control systems with state-derivative feedback.

[1]  Gregory N. Washington,et al.  Acceleration-based vibration control of distributed parameter systems using the reciprocal state-space framework , 2002 .

[2]  Michael Valásek,et al.  Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case , 2005, Kybernetika.

[3]  Gregory N. Washington,et al.  Acceleration Feedback-Based Active and Passive Vibration Control of Landing Gear Components , 2002 .

[4]  Frank L. Lewis,et al.  A geometric theory for derivative feedback , 1991 .

[5]  M. Valasek,et al.  Pole-placement for SISO linear systems by state-derivative feedback , 2004 .

[6]  Marcelo C. M. Teixeira,et al.  LMI-based digital redesign of linear time-invariant systems with state-derivative feedback , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[7]  T. H. S. Abdelaziz.  Pole assignment by state-derivative feedback for single-input linear systems , 2007 .

[8]  Michael Valásek,et al.  Eigenstructure assignment by proportional-plus-derivative feedback for second-order linear control systems , 2005, Kybernetika.

[9]  Marcelo C. M. Teixeira,et al.  DESIGN OF STATE-DERIVATIVE FEEDBACK CONTROLLERS USING A STATE FEEDBACK CONTROL DESIGN , 2007 .

[10]  Eduardo T. F. Santos,et al.  COMPARATIVE STUDY ON STATE FEEDBACK AND STATE-DERIVATIVE FEEDBACK IN LINEAR TIME INVARIANT SYSTEMS , 2007 .

[11]  Marcelo C. M. Teixeira,et al.  Robust state-derivative pole placement LMI-based designs for linear systems , 2009, Int. J. Control.

[12]  Edvaldo Assunção,et al.  Control Designs for Linear Systems Using State-Derivative Feedback , 2008 .

[13]  T H S Abdelaziz.  Robust pole assignment for linear time-invariant systems using state-derivative feedback , 2009 .

[14]  Yi-Qing Ni,et al.  State‐Derivative Feedback Control of Cable Vibration Using Semiactive Magnetorheological Dampers , 2005 .

[15]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[16]  Katsuhiko Ogata,et al.  Modern Control Engineering , 1970 .

[17]  R. Cardim,et al.  Robust state-derivative feedback LMI-based designs for multivariable linear systems , 2007, Int. J. Control.

[18]  José Mário Araújo,et al.  Alocação de pólos em sistemas lineares invariantes no tempo utilizando realimentação da derivada de estados e a equação de Lyapunov , 2009 .

[19]  Marcelo C. M. Teixeira,et al.  Realimentação da derivada dos estados em sistemas multivariáveis lineares usando LMIs , 2009 .

[20]  Eduard Reithmeier,et al.  Robust vibration control of dynamical systems based on the derivative of the state , 2003 .

[21]  Marcelo C. M. Teixeira,et al.  Robust State-Derivative Feedback LMI-Based Designs for Linear Descriptor Systems , 2010 .

[22]  Taha H. S. Abdelaziz,et al.  Optimal control using derivative feedback for linear systems , 2010 .

[23]  Henk Nijmeijer,et al.  Stabilizability and Stability Robustness of State Derivative Feedback Controllers , 2008, SIAM J. Control. Optim..