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This post was last edited by Green Lotus on 2018-3-4 15:28. The effect of changes in the scale factor δ on the adjustment process. The greater the proportionality, the weaker the regulatory effect, which inevitably results in a slow change in the process curve. The oscillation period is long, and the attenuation is relatively large. If it is a pure proportional action, the residual error remains large after stabilization. Conversely, reducing the proportional value is equivalent to strengthening the regulatory effect; the curve fluctuates more rapidly, the oscillation period becomes shorter, and the attenuation ratio decreases. As the proportionality degree δ decreases, the oscillations of the curve intensify gradually, the periods become shorter, and the attenuation ratio also gets smaller. (2) Effect of integral time TI variation on the regulation process: The strength of the integral action depends on the value of the integral time TI. A large TI results in a weak integrating effect, while a small TI leads to a strong integrating effect. The oscillations of the curve gradually intensify, the period gradually shortens, and the residual error also becomes smaller and smaller. However, when TI is too small, the strong integrating effect causes severe oscillations in the curve, resulting in unstable operation ； When TI is infinite, the regulator becomes a pure proportional regulator. (3) Effect of the change in differential time TD on the regulation process: The strength of the differential action depends primarily on the value of TD; the larger TD is, the stronger the differential action, which is exactly the opposite of what happens with the integral time TI. The stronger the differential effect, the stronger the regulatory effect as well; as a result, the oscillations become more intense and their period becomes shorter. The residual error also decreases after applying differentiation. However, when the differential action is inappropriate, if TD is too large it will cause significant oscillations; if it is too small, the effect will not be noticeable enough and there will be little improvement in the quality of regulation. When TD is zero, there is no differential action. When the parameter being regulated deviates from its set value, the degree to which the valve is opened or closed is first determined based on the size of the deviation, thereby applying a regulatory force to bring the parameter back to its set value. Since this regulatory force is proportional to the size of the deviation, it is called proportional control. Proportional action responds quickly, with no lag; it has the ability to overcome disturbances that cause fluctuations in the controlled parameter fairly swiftly, and this ability can be enhanced depending on the magnitude of the deviation. These are the advantages of proportional control. Its drawback is that a residual error remains after the adjustment process is complete, affecting the final quality of the parameter being adjusted. Therefore, for control systems with stringent requirements, corresponding measures must be taken to eliminate the residual error, thereby improving the quality of control. 2. The effect of integral control: The control mechanism in which the change in the regulator’s output is proportional to the integral of the error value over time is known as integral control. This is denoted by I. Therefore, as long as there is an input error, even if it is small, the rate of change of the regulator’s output will not be zero; the output will continue to change. The longer the error persists, the greater the change in the output, until the input error becomes zero at which point the rate of change of the regulator’s output becomes zero as well, and the output stabilizes. This shows that for integral control to reach stability in the end, the error must be zero. Therefore, the integral action automatically eliminates residual errors. The control principle of the differential regulator (denoted by D) is to act based on the trend of change in the deviation, that is, the \"rate of change of the deviation\"; mathematically, this is known as differential action. Differential control has a leading effect, and thus it can be used for control systems with large delays. In oil refineries, it is generally employed in temperature control systems. Put simply, the smaller the value of P, the faster the valve will act; the smaller the value of I, the shorter the delay in valve operation. The value of D is generally not adjusted. In production automation systems, the proportional, integral, and derivative control mechanisms are often combined to form proportional-integral-derivative control, also known as PID control. In its input-output mathematical expressions, there are three characteristic constants: the proportional band δ(P), the integration time TI, and the differentiation time TD, which are used to represent the tuning characteristics of proportional-integral-differential control. The proportional band is the reciprocal of the proportion, expressed as a percentage; therefore, the larger the proportional band, the smaller the proportion. When a step disturbance is applied to a proportional-integral-derivative controller, the control signal output by the controller equals the sum of the outputs from the proportional, integral, and derivative actions. The output of proportional action is proportional to the magnitude of the error ； The output of the integral action is proportional to the rate of change of the deviation. The magnitude of the output change depends not only on the size of the deviation but also on how long the deviation persists. As long as there is an input deviation, the output continues to change; it is only when the input deviation is zero that the output stops changing. Thus, the integral action can eliminate deviations ； The output of differential action is proportional to the rate of change of the deviation; it performs regulation based on the speed at which the deviation changes. This is known as lead action – regulation takes effect as soon as any change in the deviation occurs, while when there is no change in the deviation, differential regulation has no effect. The order of action of the three characteristic parameters is as follows: when a deviation is present, the differential action takes effect immediately, causing a sudden and significant change in the regulator’s output, after which this output gradually decreases. The proportional action also activates at the same time, reducing the deviation. Subsequently, the integral action comes into play; over time, it becomes increasingly dominant until the deviation is finally eliminated. Let’s use an example of filling a water tank to illustrate the above relationship. When it is detected that the water level in the tank is below the desired level, our brain immediately thinks of opening the valve wider to add more water to the tank. The amount of water added will be large; if it is anticipated that opening the valve too wide will make it difficult to control the water level and cause it to exceed the desired level soon, then the valve is gradually closed to regulate the amount of water added. This is the principle of differential action ； At the same time, opening or closing the valve to different degrees determines different water supply amounts, and the water level rises in proportion to these amounts; this is the principle of proportional action ； Whether the valve is fully open or partially closed affects the time it takes to reach the desired water level; the greater the degree of opening of the valve, the shorter the time required, while the smaller the degree of opening, the longer the time needed. Normally, over time the water level gradually reaches the desired value, after which we close the valves; however, even while closing the valves, water continues to flow in, causing the water level to exceed the desired value. To better control the water level, we gradually close the valve to reduce the water supply volume, until the water level reaches the desired value and the valve is fully closed. This process takes some time; the smaller the degree to which the valve is closed, the longer it will take, and vice versa. This is the principle of integral control.