Interaction in multivariable systems

Abstract

Interaction in multivariable systems is precisely defined using the P-canonical form. A frequency response of interaction strength that is derived using numerical methods is given to define consistently interaction strength in a usable form. The frequency response is based on the non-diagonal terms of the inverse plant matrix (P�¹). A direct relationship between this frequency response of interaction strength and the design of controllers is discussed. A method is given by which a totally-interacting plant can be reduced to a plant that is not totally-interacting. The dependency between the outputs that caused the plant to be totally-interacting can be observed and the desired output or outputs can be removed. A strongly-interacting multivariable plant may be reduced to a less strongly-interacting system. The order of the magnitudes of the frequency response of interaction strength between outputs can be found for the entire system. With this information it is known which outputs can be altered most easily without affecting any other outputs. An analytical method of designing controllers is indicated. The design procedure can be programmed on the digital computer. By using the frequency response of interaction strength, one can minimize the number of controllers needed. The design method given is based on well-known filter theory. A systematic method is illustrated for obtaining the frequency response of the desired controller matrix. Using approximations, one then can synthesize the needed controllers.