Abstract
This paper proposes a new controllability index based on the Hankel singular values (HSV) which is applicable for both single-input single-output (SISO) and multivariable processes. The new index quantifies the inherent performance limitation in terms of closed-loop response speed by associating it with the control effort, which is directly related to the inverse of the HSVs. It is also shown that for specific system there is a direct linear relationship between the inverse of the minimum Hankel singular value and desired closed loop pole locations. The controllability index is thereafter exemplified on several SISO examples systems to show some of its properties. Thereafter two well-known multivariable benchmark processes, quadruple tank and two-continuous-stirring-tank-reactor are used to show the effectiveness of the index. It is concluded that the index provides valuable insights to practitioners on the achievable performance of processes with actuator constraints, while being easy to use and requiring little computational effort.
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