5 - Stability and control modes of closed loops

Abstract

This chapter focuses on the function and use of proportional, integral, and derivative control in the context of stability and control of loops. Proportional control is the principal means of control. The automatic controller needs to correct the controller output OP, with an action proportional to the error term ERR. The correction starts from an OP value at the beginning of automatic control action. Integral action is used to control towards no offset in the output signal. This means that it controls towards no error (ERR = 0). Integral control is normally used to assist proportional control. The combination of the two is called PI-control. As integral control (I-control) integrates the error over time, the control action grows larger the longer the error persists. This integration of the error takes place until no error exists. Every integral action has a phase lag of 90°. The only purpose of derivative control is to add stability to a closed loop control system. The magnitude of derivative control is proportional to the rate of change of the process variable (PV). Derivative action is in essence the inverse of the example for integral action. Taking a fully charged capacitor and discharging it through a resistor results in an exponential decay, as the difference in capacitor voltage reduces from its maximum value to zero.