Compatibility of a two-degree-of-freedom system with a set of independent specifications

In feedback control systems in which more than one transfer function must be specified, a multi-degree-of-freedom configuration is required. In many practical situations a two-degree-of-freedom configuration is of interest. This paper deals with the conditions that must be fulfilled in the choice of transfer functions so that two sets of specifications can be fulfilled by a given configuration. The possibility of implementing two sets of specifications independently is determined by the degree of complexity allowed in the individual transfer functions of the system. A method is described by which the compatibility of a given structure with a set of specifications can be insured. With the aid of a procedure which is illustrated in two examples, the minimum degree of complexity in the individual blocks is determined in relation with the high-frequency behavior of the system.