Input–output operability of control systems: The steady-state case

For high-dimensional systems with more outputs than inputs, some outputs must be controlled within ranges, instead of at set-points. This may also be true if the outputs are equal in number to the inputs and disturbances of high magnitude exist. A linear programming framework is postulated to calculate the tightest achievable operating ranges of the outputs, given the ranges of the inputs and the expected disturbances, for any linear input–output control system at the steady-state. This approach removes the computational constraints on the size of the problem that a previous communication of the authors [1] could address. The hyper-volume obtained for the tightest achievable outputs’ region of a high-dimensional industrial process is calculated to be four orders of magnitude smaller than the one initially assumed, enabling much tighter control.