Analytical design procedures for a class of linear time-invariant multivariable regulators

Three analytical design procedures are developed which make consistent the primary regulator requirements of static accuracy and stability and speed of transient response for plants which have, or may be given, the same number of independent inputs and outputs as state variables. Some discussion is given concerning limits imposed by gain or control signal constraints, dynamic interaction properties, transient oscillation and overshoot, and sensitivity to changes in plant parameters for each of the three designs. A simple illustrative example is given. Two of the procedures may be applied to plants which are open-loop stable or unstable, and, because of the provision for step reference inputs and the nature of their transient response, they should prove useful for the design of servos to track relatively low-frequency reference inputs.