INTEGRITY OF INVERSE-BASED MULTIVARIABLE CONTROLLERS - CONVENTIONAL FEEDBACK STRUCTURE

Increased availability of inexpensive and powerful process control computers does not lead to widespread acceptance of multivariable controllers. One of the reasons is that the failure conditions of multivariable controllers are not well understood. This paper analyzes the failure tolerance and integral controllability of inverse-based controllers under the conventional feedback structure. Failure tolerance is addressed on the basis of the stability of the subsystems, e.g., to avoid instability as the result of positive feedback. Complete integral controllability (CIC) is defined according to the operability of the subsystems, i.e., without causing instability as the controller gains in the tuning matrix are reduced arbitrarily. Necessary and/or sufficient conditions for CIC are derived. The results show that, similar to multiloop single input-single output systems, some sort of pairing, e.g., taking the corresponding sensor off under actuator failure, is required for the inverse-based multivariable controllers. Furthermore, the well-known interaction measures, e.g., Niederlinski index, relative gain array, and block relative gain are useful in determining the appropriate pairings. Rules for the pairing are summarized that ensure complete integral controllability for the inverse-based controller of the size 2 x 2, 3 x 3, and 4 x 4.