A PRACTICAL METHOD FOR OPTIMUM TRANSIENT RIDDANCE IN DAMPED LINEAR SYSTEMS.
Abstract
The damping rate of a stable damped linear system can be defined as the negative of the real part of the eigenvalues which is closest to the imaginary axis. Consequently, the most rapid decay of transients can be achieved by selecting the design parameters in such a way that the damping rate is as large as possible. However, the discontinuity in the derivatives of the damping rate with respect to the design parameters, especially in the neighbourhood of its maximum, causes difficulty or even failure with the classical theory of maxima and minima, and other direct or indirect optimization methods. This problem is reformulated as an optimization problem wherein a function of several design parameters is maximized using a linear transformation of the eigenvalues in the complex plane and two Hurwitz criteria as constraints. The optimum damping rate and its associated design parameters are then the solution to a set of nonlinear, simultaneous, algebraic equations. A modified Newton-Raphson version in which a relaxation parameter is introduced and the inverse Jacobian matrix is approximated, is used for numerical solution. Two examples of second and fourth order systems are discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1970
- Accession Number
- AD0708826
Entities
People
- Phung Khac Nguyen
Organizations
- University of Toronto