Proportional control law issues in control systems
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Regarding the proportional control of the regulator, why is there always a residual error present when the system reaches equilibrium again after a disturbance occurs? The system is in equilibrium at the initial state. According to Δu=K*e(t) and e(t)=y-ys, when a disturbance occurs in the system, e(t) is not zero; as a result, the regulator’s output changes by Δu, which causes the controlled variable y to decrease, thereby reducing e(t) and consequently reducing Δu as well. This process repeats itself, so shouldn’t e(t) eventually approach 0? Why is it said that there must be a residual error?
Since the output signal of a proportional regulator equals the difference between the input signal and the set value multiplied by the proportional gain, if the input signal equals the set value, that is, the deviation is 0, then the regulator’s output is 0. Without a control signal, the control valve ends up in either the fully open or fully closed position, and the system becomes uncontrollable.
Then how to explain the incremental PID controller?
This post was last edited by Ku Liang Zhi Le on 2017-4-12 09:05. Take a look at this schematic diagram. This is a typical proportional control. Assume that the system is stable initially, meaning the total inflow equals the total outflow, and the liquid level is not fixed at its initial position. At a certain moment, the total inflow experiences a step increase. As shown in the diagram, we have: △LV/△LT = L1/L2 = Kp; therefore, △LV = Kp × △LT. △LT represents the difference between the actual liquid level and the desired liquid level. Since the total amount of fluid flowing in changes, the valve position must also change. As Kp is not zero, △LT cannot be zero, meaning that the residual error is not zero.
When the deviation is 0, the output of the regulator is not 0, but rather an initial value; this initial value is usually set at 50% of the output value.