Stable compensation of right half plane zeros in multivariable processes with time delays

It is known that the right half s-plane zeros (RHPZ) have negative effects on the control of a process. Those processes having time delays may have infinite number of RHPZ. This problem can be overcome by factorizing the system into two parts: one having RHP zeros and the other not. Inserting some poles at the location of the minor images of the RHPZ minimizes the integral squared error. However, when the process has both right and left half plane zeros, adding some RHP poles to cancel the zeros in RHP may be required. This cancellation can not be implemented exactly by the finite digit arithmetic since the location of the zeros are expressed by irrational numbers. Hence, the overall system will be unstable unless some extra precautions are taken. In this study, a new RHPZ compensation scheme which yields a stable controller has been established. The new method uses the shifted mirror images of the zeros of the process transfer matrix.