CONTROL SYSTEM DESIGN FOR MULTIVARIABLE SYSTEMS WITH TIME DELAYS AND RIGHT HALF PLANE ZEROS

Design of controllers for multivariable systems that can be modeled as Laplace transfer function matrices whose elements contain delays (which may differ in different elements) or as sets of linear differential difference equations is considered. These systems may also have right half plane (RHP) transmission zeros, possibly infinite numbers of them.;The methods presented build upon the Ogunnaike-Ray compensator, which is itself a multivariable extension of the SISO Smith Predictor. The approach deals first with the delays. Three important properties of the Smith Predictor are described (two previously unknown) and methods of compensator design extending any or all of the MIMO case are given. The RHP zeros are dealt with through augmenting the resulting compensator. This involves factoring the original transfer function model into invertible and noninvertible parts, and new techniques for doing this in the presence of both multiple delays and infinite numbers of RHP zeros are presented. Some new results for nonsquare systems with more inputs than outputs are also given.;A detailed design procedure is presented explicitly describing exactly how to design the controller for each of the following design objectives: dynamic decoupling of all outputs with minimum ISE servo responses, dynamic decoupling of all outputs with minimum settling time servo responses, and confinement of dynamic interactions to one of a few outputs in exchange for improved performance in all remaining outputs. As the procedure is carried out, the available performance trade offs are made clear, and the designer is able to favor the most important outputs if desired.;The resulting controller structure is capable of effective control even in the case of constrained manipulated variables. This is illustrated with numerous examples, many of which are taken from the literature.