Feedback control system synthesis for plants with large parameter variations

A synthesis procedure is developed for a dominant third-order system (as opposed to the usual dominant second-order system) where the size of the complex closed-loop pole region is not specifically restricted but is contained within a circular boundary. The plant considered is of third order, with a real pole at the origin and a pair of complex poles with negative real parts. The added real pole affords an additional degree of freedom with which to meet the system-time domain specifications. The compensation prescribed is a biquadratic network with complex zeros, and compensation poles are constrained to exhibit only second-order effects. The procedure is based on the association of the desired closed-loop pole parameter values with open-loop parameter values in the (Omega^{2},Sigma) plane, which is in actuality the natural-frequency-squared damping-constant plane. A constant gain factor is assumed, but this constraint may be removed if a tandem gain control system is employed. This assures that the gain variations are much slower than the system response. Relations between the desired nominal closed-loop poles and the plant region and compensation locations are derived for a prescribed circular closed-loop pole region. The nominal plant pole location is a design specification, while the allowable plant region depends on the closed-loop pole location and region, i.e., a change in size of one region is reflected as a proportional change in size of the plant closed-loop pole region. The remote compensation pole location is primarily determined by minimizing transient distortion while ensuring a specified degree of stability.