definition for gain margin and phase margin of control system
Phase margin Phase margin and its important companion concept, gain margin, are measures of stability in closed-loop, dynamic-control systems. Phase margin indicates relative stability, the tendency to oscillate during its damped response to an input change such as a step function. Gain margin indicates absolute stability and the degree to which the system will oscillate, without limit, given any disturbance.
Span of control The sum of these three types of interactions is the number of potential relationships of a supervisor. Graicunas showed with these formulas, that each additional subordinate increases the number of potential interactions significantly. It appears natural, that no organization can afford to maintain a control structure of a dimension being required for implementing a scalar chain under the unity of command condition. Therefore, other mechanisms had to be found for dealing with the dilemma of maintaining managerial control, while keeping cost and time at a reasonable level, thus making the span of control a critical figure for the organization. Consequently, for a long time, finding the optimum span of control has been a major challenge to organization design. As Mackenzie (1978, p 121) describes it: