Properties of single input, two output feedback systems

We describe properties of linear multivariable feedback systems for which the plant has a single control input and two measured outputs. Particular attention is paid to 'algebraic' design tradeoffs that occur between different feedback properties at the same frequency. To describe these tradeoffs, we use concepts of plant and controller direction and alignment. We show that if plant/controller alignment is poor, then closed loop response to noise and disturbances will be large unless the loop gain is sufficiently small. Moreover, the closed loop system will exhibit large interactions. We also describe a dual set of results that are applicable to feedback systems for which the plant has two control inputs and a single measured output.