New PDF release: A Practical Approach to Robustness Analysis with
By Gilles Ferreres
1. MOTIVATION in lots of actual events, a plant version is frequently supplied with a qualitative or quantitative degree of linked version uncertainties. at the one hand, the validity of the version is assured in basic terms within a frequency band, in order that approximately not anything should be stated concerning the habit of the genuine plant at excessive frequencies. nonetheless, if the version is derived at the foundation of actual equations, it may be parameterized as a functionality of some actual parameters, that are frequently now not completely identified in perform. this is often e.g. the case in aeronautical platforms: for example, the ae- dynamic version of an aircraft is derived from the flight mechanics eq- tions. whilst synthesizing the plane keep watch over legislations, it really is then essential to take note of uncertainties within the values of the steadiness derivatives, which correspond to the actual coefficients of the aerodynamic version. additionally, this plane version doesn't completely signify the be- vior of the true plane. As an easy instance, the flight keep watch over process or the autopilot tend to be synthesized simply utilizing the aerodynamic version, hence with no accounting for the versatile mechanicalstructure: the c- responding dynamics are certainly regarded as excessive frequency ignored 1 dynamics, with admire to the dynamics of the inflexible version .
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Extra resources for A Practical Approach to Robustness Analysis with Aeronautical Applications
In an obvious way, the zero point (which corresponds to and belongs to this domain of nonsingularity. represents the size of the largest square in the space of the which is centered on the zero point and inside which the matrix is guaranteed to be nonsingular. 16, the sensitivity with 26 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS respect to is strictly positive, whereas the sensitivity with respect to is zero. , 1991). v. , 1994), so that the computational burden of the algorithms, which compute the exact value of is necessarily an exponential function of the size of the problem.
On the other hand, some of the flexible modes are moved into the left half plane in order to increase their damping ratio. Following the previous subsection, the design model is built by adding the rigid and flexible models at the outputs. 2). Second order transfer functions are finally added at the inputs, with and These filters increase the roll-off properties of the controller, and thus its robustness with respect to unmodeled flexible modes. Notice that the maximal frequency of the bending modes in the previous subsection is about 15 rad/s.
At each point of a frequency gridding The robustness margin is deduced as: When choosing a sufficiently fine frequency gridding, good results are obtained in many practical examples. 17). v. over the frequency range). In the context of this new and difficult problem, chapter 10 proposes a method for computing a reliable estimate of as a function of 28 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS Chapter 2 APPLICATIVE EXAMPLES The first section describes the rigid and flexible models of the transport aircraft, while the second section describes the nonlinear and linearized missile models.
A Practical Approach to Robustness Analysis with Aeronautical Applications by Gilles Ferreres