Properties and control of the quadruple-tank process with multivariable dead-times

The well known laboratory quadruple-tank process (QTP) has been introduced in the laboratories of many schools around the world as it is ideally suited to illustrate concepts in multivariable control. In this paper the QTP is extended to include independent multivariable dead times (DTs) and their effects on the properties and control of the QTP are studied. DTs are very common in many various processes and make the control of the QTP more interesting and challenging. The addition of DTs may introduce infinite, finite or not any number of non-minimum-phase (NMP) zeros. As shown in the paper it depends on a particular combination of the multivariable DTs. The conditions for each case are stated and the location and behavior of the zeros closest to the imaginary axis due to the DTs are specified. Other properties of the QTP with DTs as the output real NMP zero directions, the decentralized integral controllability of the process and time-domain bounds on closed loop performance are derived and discussed. Also, a novel laboratory QTP with DTs is described and used to demonstrate the main results.