| Time delays and right half plane transmission zeros are commonly occurring, but troublesome, elements in the control of chemical processes. This work details important similarities and differences between the two. The Freudenberg phase angle is used to define non-minimum phase behavior in MIMO systems. In addition, this work establishes a foundation for using Pade approximations of time delays by detailing the derivation of the approximation and the features of both SISO and MIMO delay systems that the approximation matches. Factoring the minimum delay in each output is shown to be crucial in order to yield good approximation of MIMO delay properties with low order approximations. With this foundation, the use of Pade approximations in system analysis and control is presented. The analysis of Pade approximations is demonstrated to approach the results of the delay system analysis, in terms of integral square error, for low order approximations if the minimum delay is factored. Also, if the minimum delay is factored before approximating, low order Pade approximations are shown to yield rational controller designs with relatively good performance and robustness. This is demonstrated for both IMC and discrete LQG design techniques. |
