Frequency-domain dual-locus method for design of multivariable control systems

A design method is presented for linear multivariable systems with cascade controllers. The method is restricted to general systems with two input and two output variables and is applied in the frequency domain using dual-locus plots. Loci are formed that relate directly to the closed loop characteristic polynomial of the system and conditions are derived from an unambiguous indication of stability. The loci are chosen so that the effects of controller elements can be readily assessed, and this leads to an iterative procedure for controller design. The method has been applied to a position control system for a 2-axis gyroscope and is shown to yield high performance although retaining simplicity in the controller functions.