anti-windup PID controller - SIMULINK block

Although many aspects of a control system can be understood based on linear theory, some nonlinear effects must be accounted for in practically all controllers. Windup is such a phenomena, which is caused by the interaction of integral action and saturations. All actuators have limitations: a motor has limited speed, a valve cannot be more than fully opened or fully closed, etc. For a control system with a wide range of operating conditions, it may happen that the control variable reaches the actuator limits. When this happens the feedback loop is broken and the system runs as an open loop because the actuator will remain at its limit independently of the process output. If a controller with integrating action is used, the error will continue to be integrated. This means that the integral term may become very large or, colloquially, it “winds up”. It is then required that the error has opposite sign for a long period before things return to normal. The consequence is that any controller with integral action may give large transients when the actuator saturates.

Ref: http://www.cds.caltech.edu/~murray/courses/cds101/fa02/caltech/astrom-ch6.pdf