Integration time and differentiation time
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This post was last edited by cust008 on 2017-5-9 22:07. I’m not quite understanding integral time and differential time; please help. What does the integration time, for example 5 seconds, mean? Does it mean that once a deviation occurs, the integration process outputs a value based on the integration over the previous 5 seconds every 5 seconds, and keeps that output unchanged during the next 5 seconds? The differential action, for example over 5 seconds – what does that mean? Does it mean that once a deviation occurs, the differential action outputs a value based on the derivative (trend of change) of the current deviation, and then every 5 seconds it outputs another value based on the derivative of the deviation at each fifth second? Moreover, after each output every 5 seconds, the value generated by the differential action remains unchanged for the next 5 seconds.
Great post! I hope professionals in instrumentation can provide a straightforward explanation! Thank you... thank you... thank you
In PID control, the proportional action operates based on the magnitude of the error, and it plays a role in stabilizing the parameter being controlled within the control valve system； The integral action operates based on the presence or absence of deviation, and it serves to eliminate residual errors in the system ； The differential action operates based on the rate of change of deviation, serving as a lead-control mechanism in the system. The adjustment principle for these three control laws is as follows: for each control law, while meeting the production requirements, the proportional action should be stronger, the integral action should be stronger, and the derivative action should also be stronger. When all three control laws are used simultaneously, each of the three control effects should be appropriately reduced, and the differential time is generally set at 1/4 to 1/3 of the integral time.
Integral time and derivative time are parameters in the PID mathematical model, not specific times.
Simply put, the integration time indicates the strength of the integration effect, that is, the strength of the effect in eliminating residual errors； Similarly, the differential time indicates the strength of the differential action, that is, the strength of the lead regulation capability.
I’m confused – why isn’t it called something like the integration coefficient? Why is it called time? This is not that time; it’s all mixed up.
Since it is the integral of an error over time, adding a constant time allows the output to accumulate continuously in order to eliminate the residual error; you can refer to Chapter 8 of \"Dynamic Characteristics and Control of Processes\", which explains this quite clearly
This post was last edited by ylb913 on 2017-5-11 06:35. I’ll share my learning experiences and understanding; I’m not sure if they’re correct or not The formula for proportional control: △MV = KP * DV = (100/P) * DV. P represents the proportionality factor, expressed as a percentage (with the % sign omitted); its reciprocal is multiplied by the difference PV – SV = DV. For example, if P = 100 (where 100% is equivalent to 1), then its reciprocal is also 1. This reciprocal is known as the proportional coefficient KP, and it determines the ratio of the change in MV to the change in DV, relative to the range of that DV value. For example, if P=100, then KP=1, and △MV=DV; that is, if the DV value does not change by 1% of its range, then MV will also change by 1% in terms of its opening degree. I is the integration time (TI); as long as I is set, any deviation will continue to accumulate over time, and the corresponding △MV value will be generated at all times. The integration time is defined as the amount of time it takes for a sudden deviation (DV) to result in a △MV value generated by proportional control. In other words, for a 1% change in DV relative to its range, when KP=1 (or other proportional coefficients), proportional control will cause a 1% (or 2%, etc.) change in valve opening. Assuming that this 1% (or 2%, etc.) deviation remains unchanged even while integration is in effect, then over time integration will ultimately produce the same △MV value as that produced by proportional control (1% or 2%, etc.). In other words, the time I (or TI) refers to is the time you set for completing a change in the △MV value of 1% or 2%, etc. The smaller TI is, the shorter the time required to complete the task, and the faster the valve opening can be adjusted. If I is set to a very high value, then it essentially loses its effectiveness. (The corresponding formula is difficult to enter, so it will be ignored for now.) I don’t fully understand the concept of the differential time (TD); in basic terms, TD is obtained by multiplying the rate of change of DV by itself, which gives the initial value of △MV. Then, with DV remaining constant, the △MV value gradually returns to its original level, and the time it takes for this value to drop to 63.2% of its initial value is considered to be TD (for example, if the valve opening is increased by 10% instantly at the start, then TD is the time it takes for it to be reduced back to 6.32% of that opening). In simple terms, the larger the value given by D, the greater the initial change in △MV will be for the same DV value deviation; moreover, it will take a longer time to reduce this initial △MV by 63.2%, which means that the effect of differentiation is stronger.