A calculation method of root loci band and its applications to robust control system design

This paper presents a method to calculate the characteristic root areas and loci band of control systems with uncertainties. First, equations of boundary curves of root areas in the case of additive and multiplicative perturbation are derived. Then, an algorithm for the calculation of the array of closed curves is presented. When the upper bound of the absolute values of frequency responses for the uncertain part, is also frequency-dependent, the frequency-dependent, terms are included in the characteristic equation of the nominal system. This lead to the boundary equations of the root, areas for control systems with frequency-dependent uncertainty. Numerical examples of the control systems with multiplicative perturbations including frequency-dependent terms are presented to verify this calculation method. Finally, its applications to the design of robust control systems, e.g., passive adaptive control systems are also discussed.