Kernels of Anti-Causal Operators and the Multivariable Generalized PredictiveControl Problem

摘要

Eigenvector or principal direction projections provide a convenient means ofdecomposing the multivariable problem into a set of scalar control problem. They can be solved using single input single output generalized predictive control. The bicausal nature of eigenvector or principal direction representations leads to anticausality difficulties. The use 'kernels' of bicausal operators is proposed as an effective remedy for the scalar case. The relationship between these kernels and scaling of the bicausal representations is studied. Algorithms which overcome the pseudodelay problems in the multivariable case are proposed. An algorithm for the characterization of all the available degrees of freedom is given. They are introduced into the scalar predictive control cost and the control law is computed by a process of back projection. The algorithms proposed match the set point following behavior and remove the problem of pseudo delays.