| Popis: |
In the previous chapters, all specifications were restricted to the eigenvalue domain. With respect to the closed-loop transfer functions, their denominator p(s, q k) was considered. Now, the effect of the numerators will also be taken into account. The aim of this chapter is to combine a variety of frequency domain criteria with the parameter space approach. The sequence of the chapters thus follows the historic evolution of the parameter space technique. It was initially developed for mapping of r-stability boundaries into parameter space. However, it is obvious that complete design and analysis of control systems requires consideration of more criteria beyond mere eigen-value specifications. This chapter distinguishes between two types of frequency domain specifications, which will be made accessible for parameter space mapping: Ferquency loci specifications The most common locus used for linear control system analysis in frequency domain is the Nyquist plot. Moreover, there are non-linear stability criteria that refer to frequency loci, like the dual locus method, which uses describing functions as an approximation for non-linear elements, and the Popov criterion which is used for proving absolute stability in the presence of sector non-linearities. Frequency magnitude criteria Frequency domain magnitude specifications put bounds on the magnitude frequency response of specific transfer functions or sensitivity functions. Thus, tracking quality, noise and disturbance rejection, and robustness against unstructured uncertainty (e.g. unmodelled dynamics) can be addressed. Using these criteria with the parameter space technique provides the possibility of combining the advantages of non-conservative mapping of inequalities into parameter space with knowledge and experience in the field of frequency domain control design (e.g. H∞-loop shaping) and analysis (e.g. u-analysis). |
