Design of two-axis multivariable control systems

Abstract

This study is concerned with the engineering design of two-axis multivariable systems. The restriction to two axes is made in order to exploit simplifications which are possible for this class of system. The resulting design method is then more convenient and precise than methods capable of handling arbitrarily large systems. A new design method for linear systems has been developed to cater for general cascade controller design. The method is applied in the frequency domain and uses dual loci. These loci relate directly to the closed loop characteristic polynomial of the system and conditions are derived for an unambiguous indication of stability. The method is applicable to systems having a high degree of interaction and is extended to nonlinear systems by means of describing functions. Design studies have been made with special reference to a system for positioning a free gyroscope. This system presents special problems; in particular a high degree of interaction is involved. The new method of controller design is shown to yield improved performance while retaining simplicity in the controller functions. Analogue simulation has been used to test the design technique.