Steady State Error (page 2)
A good example of this is a liquid level system.
At its design steady state operating point, the system runs with a steady level, steady input and output flows, and a steady position on the inlet (control) valve. At this design steady state operating point, all the steady operating values (H, Q, y (inlet valve position)) are taken as reference values. In the control loop, these values are considered 0 and all variables in the loop are calculated as deviations from these values.
If we want to operate at a higher tank level, we will change R so that it is no longer at the steady state operating value. Making this change will cause R to be greater than C, so a positive E will develop. This will cause the controller to command the valve (actuator) to open. The greater flow will cause the height to rise. Eventually the system will come to a new steady state. The tank level will be higher, and the flow through the system will be greater than it was at the design steady state.
If we assume that the inlet pressure to the control valve is constant, the control valve would have to operate with a greater valve opening than it did at the design steady state. The only way for this valve to have this greater opening is for there to be a residual error that commands it to maintain a greater opening. If the tank level were to rise exactly to the new level commanded, E would again be 0 and the control valve would return to its steady state operating point. But at that point, the inlet valve will not pass enough flow to maintain the new, higher demanded level. So some residual error is needed to keep the inlet valve open far enough above its design steady state position to support the flow needed for the new, higher tank level.