Eigenstructure assignment in robot tracking applications
01 Jun 1993-International Journal of Systems Science (Taylor & Francis Group)-Vol. 24, Iss: 6, pp 1017-1026
TL;DR: In this paper, a computation-effective control design procedure for eigenstructure assignment using aggregation is presented, where Dominant eigenvalues are placed at specified locations in the complex plane and the non-dominant eigen values are placed in a specified disk.
Abstract: Design procedures based on exact eigenstructure assignment are not suitable because of very high computational requirements. A computation-effective control design procedure for eigenstructure assignment using aggregation is presented. Dominant eigenvalues are placed at specified locations in the complex plane and the non-dominant eigenvalues are placed in a specified disk. The proposed design procedure is applied to the trajectory tracking problem of a robot manipulator. An error-pattern based payload estimation and compensation scheme is also proposed to improve performance robustness.
Citations
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09 Dec 2003
TL;DR: In this paper, the problem of partial eigenstructure assignment (PESA) by state feedback in R-controllable, time-invariant descriptor linear systems is investigated.
Abstract: This paper investigates the problem of partial eigenstructure assignment (PESA) by state feedback in R-controllable, time-invariant descriptor linear systems. Simple, complete, parametric solutions to PESA are obtained. Two special cases are especially examined, one is replacing a single real eigenvalue and its corresponding eigenvector, the other is replacing a pair of conjugate eigenvalues together with their eigenvectors. Based one these results, a circulation method for PESA is developed, which does not involve inverses of matrices. The parameter vectors in the proposed solutions give all the degrees of design freedom which can be further utilized to achieve additional system specifications. A numerical example shows the effect of the proposed approach.
11 citations
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30 Aug 2006TL;DR: The sufficient and necessary conditions for the poles of the closed-loop descriptor systems to locate in an LMI region are given in this paper in terms of only one positive definite matrices P, Hence the controller gain matrix K can be obtained explicitly.
Abstract: The sufficient and necessary conditions for the poles of the closed-loop descriptor systems to locate in an LMI region are given in this paper in terms of only one positive definite matrices P. Hence the controller gain matrix K can be obtained explicitly. Compared to the literature, the exact eigenstructure assignment problem for descriptor systems is usually solved via extremely constrained procedures. On the other hand, for the LMI region pole clustering problem, the solvable conditions are expressed in terms of two positive definite matrices P and Q. Consequently, The controller gain matrix K can not be obtained explicitly. An example has been solved in the literature using a complicated procedure of eigenstructure assignment is solved significantly easier as a demonstration.
References
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TL;DR: A new procedure of selecting weighting matrices in linear quadratic optimal control problems (LQ-problems) is proposed, which has merits of an LQ-problem as well as a pole-assignment problem and will be useful for designing a linear feedback system.
106 citations
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TL;DR: In this paper, a method for finding the linear quadratic regulator such that the optimal closed-loop system has eigenvalues lying within a vertical strip in the complex plane is presented.
Abstract: A computational method is presented for finding the linear quadratic regulator such that the optimal closed-loop system has eigenvalues lying within a vertical strip in the complex plane. The proposed method is suitable for the two-stage optimal design of two-time scale systems.
86 citations
01 Mar 1990
TL;DR: In this paper, two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane.
Abstract: Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.
55 citations
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TL;DR: Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, and the general expression for finding the lower bound of a constant gain gamma is developed.
51 citations
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TL;DR: A new procedure for constrained pole-placement is presented via linear quadratic design for a transformed system and the circle can be chosen in order to obtain good transient properties of the closed loop system.
42 citations