Robust Pole Placement With Moore's Algorithm

Abstract

We consider the classic problem of pole placement by state feedback. We adapt the Moore eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix, and introduce an unconstrained nonlinear optimization algorithm to obtain a gain matrix that will deliver robust pole placement. Numerical experiments indicate the algorithm's performance compares favorably against several other notable robust pole placement methods from the literature.

A unified method for optimal arbitrary pole placement

“…However, when we compare the matrix gain used to achieve this eigenstructure we observe that our method was able to use less gain in 5 of the sample systems, and in two cases (System 2 and 5) the reduction in gain was very considerable. The results are in agreement with the findings of the survey in (Schmid et al, 2014), which considered sample systems with non-defective eigenstructure and found that our method could achieve comparable robust conditioning with that of Ait Rami et al (2009), but with reduced gain.…”

“…Maximum generality in these parametric formulae has however been achieved at the expense of efficiency, as the square matrix X has n 2 free parameters. By contrast, methods (Kautsky et al, 1985, Fahmy and O'Reilly, 1983, Bhattacharyya and de Souza, 1982, Schmid et al, 2014 all employ parameter matrices with mn free parameters.…”

“…Numerous results (Chatelin, 1993) have appeared linking the sensitivity of the eigenvalues to various measures of the condition number of X. Another commonly used robustness measure is the departure from normality of the closed loop matrix A + B F. For the case of diagonal Λ, there has been considerable literature on the REPP, including (Kautsky et al, 1985, Byers and Nash, 1989, Tits and Yang, 1996, Varga, 2000, Ait Rami et al, 2009, Chu, 2007, Li et al, 2011, Schmid et al, 2014. Papers considering the REPP for the general case where (L , M , P) defines an admissible Jordan structure include and (Ait Rami et al, 2009).…”

“…In each case we assigned Jordan blocks of sizes equal to the controllability indices. Using the toolbox rfbt to implement the method of (Ait Rami et al, 2009) that we created for our earlier computational survey in (Schmid et al, 2014), we obtained the matrices F and X delivered by this method, for each of the 11 sample systems. We also implemented our own method on these systems.…”

Mechanical Admittance Realization Control Based on Feedforward Compensation for Fine Realization of Impedance

“…In this paper, these control parameters are theoretically determined by the poles placement method (26) (27) . In (6), the denominator polynomial of the poles that are independent of the environmental parameters is given by…”