Difference between deviation and residual
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In PID control, what is error, what is offset, and what is the difference between them?
The residual error should be said to be better eliminated when using PI control, that is, proportional plus integral control; it is difficult to eliminate the residual error with pure P control, proportional control alone.
The deviation is the difference between the measured value PV and SP, while the residual error should be the deviation when the PID reaches steady state
Deviation: The difference between the measured value PV and the set value SP. Residual error: The difference between the steady-state value reached by the control loop and the set value SP.
Deviation is an instantaneous error that exists throughout the entire adjustment process. The residual error is the difference between the measured value and the set value once the system reaches steady state; it is a performance indicator for control systems.
In my understanding, residual error refers to the situation in simple proportional control, where after the change is adjusted proportionally, equilibrium is achieved; however, there is still a certain deviation from the set value, and this remaining difference is what is called residual error. This residual error can be eliminated through PI control. Deviation, on the other hand, is the difference between the measured value and the set value. These two concepts are related to each other – deviation includes residual error~~
Definition of deviation: Deviation = Given – Measured. Deviation is a function of time, that is, the difference between the measurement at a certain moment and the given value. If e(t) represents the deviation, r(t) represents the given value, and z(t) represents the measurement, then e(t) = r(t) – z(t). In a system with a constant value, r(t) remains unchanged, so the deviation e(t) varies depending on the measurement z(t). When enough time has passed, that is, as time approaches infinity, the deviation at this point is known as the residual, sometimes also called the remainder, denoted as c=e(∞). Under pure proportional control, the error cannot be zero; to eliminate the error, integral action must be added. Both P and PD control methods result in an error, whereas PI and PID control methods can eliminate it.