Recall the concept of degrees of freedom (DoF) discussed in Module II. It is clear that in order to determine a system completely, its DoF should be equal to zero. There are two sources of additional specifications/equations that would reduce the DoF to zero, viz . control system and its surroundings. The surrounding refers to everything outside the domain of closed loop system which has the capability of influencing the operating conditions. The process disturbances and few externally specified inputs fall under this category. Remaining equations are provided by the control system that imposes certain relationships between outputs to be controlled and the inputs to be manipulated. These relationships are nothing but the controller equations. It is evident that number of controlled outputs should be equal to number of controller equations. Let us assume that there are N number of controlled outputs and M number of inputs are available for their manipulation . To have a unique solution to the number of controller equations one has to have exactly number of freely adjustable manipulations. In other words, for a perfect design of control system one needs to identify the best number of manipulated variables among the available number of inputs for possible manipulation. This is termed as square system where number of manipulated inputs and number of controlled outputs are same. It is however possible to design a non-square control system where more number of inputs are manipulated to control less number of outputs. This concept is however out of the scope of this course.