Real-Time Error-Feedback Output Regulation of Nonhyperbolically Nonminimum Phase System

A real time implementation of an error feedback output regulation problem for the gyroscopical platform is presented here. It is based on a numerical method for the solution of the so-called regulator equation. The regulator equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Error-feedback output regulation problem aims to find a dynamic feedback compensator using only tracking error measurements to ensure tracking given reference and/or rejecting unknown disturbance. Solving the regulator equation is becoming difficult especially for the non-minimum phase systems where reducing variables against algebraic part leads to possible unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize functional expressing the error of its algebraical part. This solution is then used to design real-time controller which is successfully experimentally tested.

[1]  W. Wonham,et al.  Error feedback and internal models on differentiable manifolds , 1982, CDC 1982.

[2]  R. H. Cannon,et al.  Dynamics of Physical Systems , 1967 .

[3]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[4]  W. Rugh,et al.  Stabilization on zero-error manifolds and the nonlinear servomechanism problem , 1992 .

[5]  Christopher I. Byrnes,et al.  Structurally stable output regulation of nonlinear systems , 1997, Autom..

[6]  Lorenzo Marconi,et al.  Implicit fault-tolerant control: application to induction motors , 2004, Autom..

[8]  Jie Huang,et al.  On the solvability of the regulator equations for a class of nonlinear systems , 2003, IEEE Trans. Autom. Control..

[9]  N. Wouw,et al.  Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach , 2005 .

[10]  Jie Huang.  Asymptotic tracking of a nonminimum phase nonlinear system with nonhyperbolic zero dynamics , 2000, IEEE Trans. Autom. Control..

[11]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[12]  Zvi Artstein,et al.  ON SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATIONS WITH MEASURE-VALUED LIMITS , 2002 .

[13]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[14]  A. Isidori.  Nonlinear Control Systems , 1985 .

[15]  Jie Huang,et al.  Output regulation of nonlinear systems with nonhyperbolic zero dynamics , 1995, IEEE Trans. Autom. Control..

[16]  Tingshu Hu,et al.  Magnetically suspended balance beam with disturbances: A test rig for nonlinear output regulation , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[17]  J. R. E. O’Malley.  Singular perturbation methods for ordinary differential equations , 1991 .

[18]  Jie Huang,et al.  On a nonlinear multivariable servomechanism problem , 1990, Autom..

[19]  Polynomial Approach.  REAL-TIME H AND H CONTROL OF A GYROSCOPE USING A , 2005 .

[20]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[21]  H. K. Khalil,et al.  Stability analysis of singularly perturbed systems , 1987 .