From this we see that the terms “plant”, “controlled output” (y) and “manipulated input” (u) takes on different meaning depending on where we are in the hierarchy. To avoid confusion, we reserve special symbols for the variables at the top and bottom of the hierarchy.Thus, as already mentioned, the term process is often used to denote the uncontrolled plant as seen from the bottom of the hierarchy. Here the manipulated inputs are the physical manipulators (e.g. valve positions), and are denoted _ m Correspondingly, at the top of the hierarchy, we use the symbol c to denote the controlled variables for which the setpoint values (cs) are determined by the optimization layer.
Input - Output controllability of a plant is the ability to achieve acceptable control performance,that is, to keep the controlled outputs (y) within specified bounds from their setpoints(r'), in spite of signal uncertainty (disturbances n!, noise n") and model uncertainty, using availableinputs (u) and available measurements. In other words, the plant is controllable if thereis a controller that satisfies the control objectives.
This definition of controllability may be applied to the control system as a whole, or toparts of it (in the case the control layer is structured). The term controllability generally assumes that we use the best possible multivariable controller, but we may impose restrictionson the class of allowed controllers (e.g. consider “controllability with decentralized PI control”).