14.9 Summary

Transmission zeros are the multivariable equivalent of SISO transfer function zeros. RHP (positive) transmission zeros indicate that the process inverse will be unstable. A transfer function matrix may have no individual transfer functions with RHP zeros, and yet have a RHP matrix transmission zero. Similarly, a transfer function matrix may have an element with a RHP zero, and yet have no RHP matrix transmission zeros. Processes with RHP transmission zeros have inherent closed-loop performance limitations; often there is not a significant advantage to full multivariable control (using decoupling or MV IMC) of these processes.

Multivariable processes exhibit a directional sensitivity, where two different input vector directions could result in outputs with a significantly different output magnitude. Processes that are ill-conditioned (high condition number, or ratio of maximum to minimum singular values) will often be too sensitive for full multivariable control.

Processes with RHP transmission zeros have internal closed-loop performance limitations; often there is not a significant advantage to full multivariable control (using decoupling or MV IMC) of these processes.