SETTLING TIME FORMULAE FOR THE DESIGN OF CONTROL SYSTEMS WITH LINEAR CLOSED LOOP DYNAMICS

Two settling time formulae are numerically derived with the 5% and 2% criteria for the step responses of control systems having linear closed loop dynamics that may be designed by the method of pole assignment to have multiple closed loop poles. The formula is shown to be accurate for closed loop systems of up to tenth order. To clarify the use of the formulae, model based and robust control system designs are carried out for a high precision vacuum air bearing application and experimental results presented.