SYNOPTIC: Automatic Frequency-Domain Synthesis of Multiloop Control Systems

A computerized algorithm to facilitate the automatic synthesis of time-invarian t linear compensation for highly complex multiloop control systems is discussed. Performed in the frequency domain to attain desired open-loop frequency response characteristics, the algorithm is applicable equally to continuous-ti me systems in the S domain and sampled data systems in the W or Z domains. It is executed by a digital computer program, AUTO, which uses a gradient-search algorithm to select the coefficients of multiloop feedback compensation transfer functions. These coefficients provide an open-loop frequency response, optimum in the sense that its deviation from the one desired is minimal in the weighted leastsquares sense. The selection of a method for incrementing compensation parameters that alleviates ridge following convergence problems is discussed, as are the geometric properties of the least-squares cost function itself. Examples of cost function geometries are presented to provide insight into their nature.