A PID control system and method which maintains continuity of the control output in spite of changes in controller parameters. The controller parameters include a proportional gain, an integral gain, a derivative gain, and a manual/automatic mode parameter. The control output at the time of a parameter change is set equal to the previous controller output, and the integrated error is set to a value consistent with the previous controller output according to a PID controller equation. This value for the integrated error serves to ensure the sustained continuity of the control output after the controller parameter change. Alternatively, the control output at the time of a parameter change is set equal to a first value continuous with respect to one or more previous control output values, and the integrated error is set to a value consistent with the first value according to the PID controller equation. Furthermore, the system and method employs integrator anti-windup. If the control output saturates, i.e. falls outside a control region defined by a lower control bound and an upper control bound, the system and method of the present invention prescribe (a) setting the control output to the value of the control bound which is exceeded, and (b) setting the integrated error equal to a value consistent with the exceeded control bound according to the PD controller equation.