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  • 1970-1974  (11)
  • 1
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    Pole and zero placement in multivariable control systems (1973)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: A method is proposed for designing multivariable systems based on an alternate derivation of Davison's theorem on pole placement and the solution of the nonlinear equations for the feedback gains by the least square error method. Output feedback is used to control a complex dynamical system. The freedom in design, after allocating poles, is used to place zeros and/or satisfy other design objectives. This method results in algorithms which are computationally attractive. However, this is done at a considerable sacrifice in terms of the design freedom available. For a system with m inputs and p outputs only m + p variables are available instead of mp variables.
    Keywords: MATHEMATICS
    Type: NASA-CR-132962 , TR-73-2
    Format: application/pdf
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  • 2
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    An efficient algorithm for calculation of the Luenberger canonical form (1972)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: An algorithm is suggested to obtain the Luenberger canonical form for multivariable systems. The method computes the canonical form directly without having to compute the transformation matrix. In addition, there is a large reduction in the number of calculations. The reduced computations along with Gaussian techniques lend to greater inherent accuracy and the ability to refine the solution with additional computations.
    Keywords: MATHEMATICS
    Type: NASA-CR-129174 , TR-72-9
    Format: application/pdf
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  • 3
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    A note on pole assignment (1972)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: It is shown that for a controllable, linear time invariant multivariable system at least max (m,p) poles can be assigned arbitrarily. In certain cases more than max (m,p) oikes can be assigned. This result is particularly useful in designing systems for high integrity in the event of transducer failure. In such an event this design takes advantage of the unequal number of inputs and outputs so as to assure no loss in pole assignability.
    Keywords: ELECTRONIC EQUIPMENT
    Type: NASA-CR-127763 , TR-72-2
    Format: application/pdf
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  • 4
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    Pole placement with constant gain output feedback (1972)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Given a linear time invariant multivariable system with m inputs and p outputs, it was shown that p closed loop poles of the system can be preassigned arbitrarily using constant gain output feedback provided (A circumflex, B circumflex) is controllable. These data show that if (A circumflex, B circumflex, C circumflex) is controllable and observable, and Rank B circumflex = m, Rank C circumflex = p, then max (m,p) poles of the system can be assigned arbitarily using constant gain output feedback. Further, it is shown that in some cases more than max (m,p) poles can be arbitrarily assigned. A least square design technique is outlined to approximate the desired pole locations when it is not possible to place all the poles.
    Keywords: ELECTRONICS
    Type: NASA-CR-127446 , TR-72-3
    Format: application/pdf
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  • 5
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    Pole-placement with constant gain output feedback (1973)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: Davison (1970) has demonstrated that it is possible to assign max (m, p) poles of a linear time-invariant controllable and observable multivariable system arbitrarily close to desired locations by using constant gain output feedback. A new proof of Davison's theorem on pole placement is developed, and a system design procedure is described which offers some advantages over Davison's method. It is shown that in some cases more than max (m, p) poles can be assigned arbitrarily, and a least square design procedure is proposed to approximate the desired pole locations when it is not possible to place all the poles.
    Keywords: ELECTRONICS
    Type: International Journal of Control; vol. 18
    Format: text
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  • 6
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    An efficient algorithm for calculation of the Luenberger canonical form. (1973)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Keywords: COMPUTERS
    Type: Joint Automatic Control Conference; Jun 20, 1973 - Jun 22, 1973; Columbus, OH
    Format: text
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  • 7
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    Investigation of rank 2 and higher output feedback for pole placement (1974)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: A common feature of several pole placement techniques is discussed and the use of a dyadic feedback matrix is presented. The limitation of this design is examined and a design involving output feedback matrices of Rank greater than one is developed as a logical extension of the dyadic feedback design. An example is presented to illustrate the design procedure.
    Keywords: THEORETICAL MATHEMATICS
    Type: NASA-TM-X-62385
    Format: application/pdf
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  • 8
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    An efficient algorithm for calculation of the Luenberger canonical form. (1973)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.
    Keywords: MATHEMATICS
    Type: IEEE Transactions on Automatic Control; AC-18; June 197
    Format: text
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  • 9
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    An algorithm for calculation of the Jordan canonical form of a matrix (1973)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.
    Keywords: MATHEMATICS
    Type: NASA-CR-131654 , TR-73-1
    Format: application/pdf
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  • 10
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    On the use and computation of the Jordan canonical form in system theory (1974)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.
    Keywords: MATHEMATICS
    Type: Asilomar Conference on Circuits, Systems, and Computers; Nov 27, 1973 - Nov 29, 1973; Pacific Grove, CA
    Format: text
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