# Eigenstructure assignment in robot tracking applications

01 Jun 1993-International Journal of Systems Science (Taylor & Francis Group)-Vol. 24, Iss: 6, pp 1017-1026

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.

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09 Dec 2003

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.

9 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.

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01 Jan 1986

TL;DR: This chapter discusses Jacobians: Velocities and Static Forces, Robot Programming Languages and Systems, and Manipulator Dynamics, which focuses on the role of Jacobians in the control of Manipulators.

Abstract: 1. Introduction. 2. Spatial Descriptions and Transformations. 3. Manipulator Kinematics. 4. Inverse Manipulator Kinematics. 5. Jacobians: Velocities and Static Forces. 6. Manipulator Dynamics. 7. Trajectory Generation. 8. Manipulator Mechanism Design. 9. Linear Control of Manipulators. 10. Nonlinear Control of Manipulators. 11. Force Control of Manipulators. 12. Robot Programming Languages and Systems. 13. Off-Line Programming Systems.

5,891 citations

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TL;DR: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized.

Abstract: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

1,010 citations

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TL;DR: Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.

Abstract: A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by "aggregating" the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.

490 citations

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Abstract: The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is named D -pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified disk D are determined for the proposed control.

271 citations

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01 Dec 1969Abstract: The paper presents a scheme for obtaining a linear-feedback law for a linear system as a result of, minimising a quadratic-performance index; the resulting closed-loop system has the property that all its poles lie in a halfplane Re (s) 0 may be chosen by the designer. The advantages of this arrangement over conventional optimal design are considered. In particular, it is shown that the reduction of trajectory sensitivity to plant-parameter variations as a result of any closed-loop control is greater for α > 0 than for α = 0, that there is inherently a greater margin for tolerance of time delay in the closed loop when α > 0, that there is greater tolerance of nonlinearity when α > 0, and that asymptotically stable bang-bang control may be achieved simply by inserting a relay in the closed loop when α > 0. The disadvantage of the scheme appears to be that, with α > 0, more severe requirements are put on the power level at which input transducers should operate than for α = 0.

127 citations

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