page_title: Control system
section_title: Integral action
hierarchical_section_title: Control system / Linear control / PID control / Integral action
caption_attribution_description: Change of response of second order system to a step input for varying Ki values. Prepared for use in PID controller article.
context_page_description: A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large Industrial control systems which are used for controlling processes or machines.
  For continuously modulated control, a feedback controller is used to automatically control a process or operation. The control system compares the value or status of the process variable being controlled with the desired value or setpoint, and applies the difference as a control signal to bring the process variable output of the plant to the same value as the setpoint.
  For sequential and combinational logic, software logic, such as in a programmable logic controller, is used.
context_section_description: The integral term magnifies the effect of long-term steady-state errors, applying an ever-increasing effort until error is removed.  In the example of the furnace above working at various temperatures, if the heat being applied does not bring the furnace up to setpoint, for whatever reason, integral action increasingly moves the proportional band relative to the setpoint until the PV error is reduced to zero and the setpoint is achieved.
caption: Change of response of second-order system to a step input for varying Ki values.
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