Appliance with modified proportional-integral control

An electrical appliance includes a controller operatively connected to a power circuit, a control circuit, a power source, a sensor for sensing a parameter level, and an active element. The controller is configured to receive an input of the parameter level from the sensor and to output a duty cycle for controlling a power level of the active element via the control circuit at various times to achieve a target set point of the parameter, the duty cycle based on proportional and integral control. The controller uses the proportional control and the integral control when the control circuit is energized, and accumulates integral error only when a parameter process variable sensed by the sensor is determined to be within an interval of the target set point.