ESDU Dynamics Series

This Series treats the stability, response and controllability of any system that can be modelled, for some part of its motion, by linear constant coefficient differential equations.

Part of the Series is devoted solely to aircraft topics which includes the equations of motion, conversion formulae for rotation and translation of body axes, geometric and kinematic relationships for various axis systems, direction and incidence angles and measures of damping. Lateral aircraft motion covers inertia cross coupling during rapid rolling manoeuvres, including the theoretical background, a discussion of simplified stability boundaries and an estimation of the critical roll rate. Approximation to the roots of the lateral equations of motion with and without a simple yaw damper is also covered. Other topics include handling qualities, loading and aeroelasticity. The design of linear systems includes a number of Items dealing with stability, response, control and assessment. The methods start with the mathematical description of a system, including feedback, in transfer function form and system stability is assessed using Routh-Hurwitz. The methods cover the graphical approaches of the one-parameter (root locus) and two-parameter stability diagrams, and those based on frequency response, such as Bode and Nyquist, and the unity feedback methods of Nicholls, inverse Nyquist and Hall. Other areas covered deal with the specification and measures of system performance, the control of dynamic systems and the selection of appropriate assessment methods.

Methods for the treatment of first- and second-order systems are provided, together with a variety of methods dealing with mathematical techniques, including the Laplace transform, an introduction to random processes, quadrature and the numerical solution of differential equations. A number of other topics include the design of nonlinear systems using Describing functions, the transfer functions of a wide range of servomechanisms and the analysis of sampled-data systems which includes the Z-transform.

The parameter estimation of linear systems is treated by a number of Data Items, featuring methods based on the least-squares principle, the Maximum Likelihood method, the Kalman filter, the Maximum Likelihood method in the presence of process noise and the parameter estimation method applied to frequency response methods.