Optimization-based decoupling controller design for discrete systems

Decoupling has been studied as a means of improving control loop behavior in the presence of strong interactions, particularly in high-purity distillation. The design of optimal multivariable decoupling controllers is the main topic of this work. The stabilizing and decoupling controllers are described through the Youla parametrization and linear equalities. Then, for given time-domain performance envelopes, a numerical optimization method based on exact penalty functions and linear programming is presented that identifies the multivariable controller that decouples the closed loop and optimizes its performance. It is also shown that this approach can be extended to encompass traditional decoupling techniques based on (possibly low order) decouplers. Finally, the problem of decoupling is discussed in relation to simultaneous and decentralized multivariable control where it is demonstrated that approximate decoupling may be a necessary compromise when there are not enough degrees of freedom.