Gain Equalization and LQG/LTR Controller Design for a 3I3O Multivariable Dynamic System with One Pole at the Origin

This paper addresses the problem of achieving gain equalization on all input-output channels of multivariable square dynamic systems which have a pole at the origin. A mathematical procedure based on linear transformations is proposed to extract the integrator associated with this pole to the outside of the system in a specific output channel. The order of the system model is then reduced, and the removed integrator can be joined with other new integrators that are added to the others output channels of the system in order to accomplish the desired gain equalization. A 5th order, 3I3O system (three inputs and three outputs) is considered as an example, for which a reduced order LQG/LTR controller is also designed.