If the water temperature is at the value of C in Illustration 2-3, the flame is sputtering O half value on O off Desired output value Controller Actuator input Plant Output Actual output value Desired Actual Water water Flame water tank temperature temperature Actuator = Kp*Error + Ki*Integ - Kd*Deriv Illustration 2 Water Heater Control System Illustration 2 shows a water heater control system. Consider that the water heater control is limited to an On/Off system. Illustration 2 also contains the equation for a PID control system. Water С temperature A F D E B Time Illustration 3 Illustration 3 plots the On/Off system response with time.