Optimal tracking performance for non-square plant models with input disturbance and feedback channel noise

In this paper, the optimal tracking performance for linear time invariant (LTI) and non-square plants was investigated. An H2 norm of error signal between the reference input and the output of system is used as the tracking performance index. Due to the limitations of non-square plants in tracking reference input signals, two-degrees-of-freedom controller was adopted to control the system. The reference input under consideration is a step signal and there exists input stochastic disturbance and feedback channel noise. Explicit expression is given to show that the tracking performance in these kinds of systems is critically dependent on the intrinsic characteristics of the given plant, including the locations not the directions of the nonminimum phase zeros and unstable poles, which is different from the plants that have the same input and output dimensions. It is also shown that the input disturbance and feedback channel noise may degenerate the tracking performance. Finally, computer simulation is provided to illustrate the analytical results.