Proportional kick

While it will respond to changes in PV, the main purpose of proportional action is to generate a proportional kick whenever the SP is changed. If we assume PV is constant then from Equation (3.1)... 

Many believe therefore that this algorithm should be applied on processes where the MV should be adjusted slowly. However, if this performance were required, it could be achieved by tuning the more conventional proportional-on-error algorithm. Conversely it is important to recognise that the proportional-on-PV algorithm can be retuned to compensate for lack of the proportional kick and so respond well to SP changes. This is illustrated in Figure 3.13. 

Figure 3.14 shows the behaviour of each part of the proportional-on-error control algorithm in response to the SP change above. The proportional kick is clear with the proportional part of the controller returning to zero as the error returns to zero. The derivative action is the greatest as the PV peaks, and so permits more proportional and integral action to be used. It too returns to zero as the rate of change of PV returns to zero. 

Figure 3.15 shows the same disturbance but with the proportional-on-PV algorithm. Note that the vertical scale is much larger than that in Figure 3.14. As expected, there is no proportional kick and, since the action is now based on PV, the proportional part does not return to zero. It can be confusing that the proportional part reduces as the SP is increased but this is because the controller must be configured as reverse acting. The integral action compensates for this so that there is a net increase in controller output. The derivative action...

A more flexible PID control algorithm can be obtained by weighting the set point in both the proportional and the derivative terms. This modification eliminates the proportional kick that also occurs after a step change in set point. For this modified PID algorithm, a different error term is defined for each control mode ... 

F. Kick, The Eaws of Proportional Resistance and Their Applications Arthur Felix, Leipzig, Germany, 1885. 

Figure 1. Spatial distribution of NSs in the Galaxy. The data was calculated by a Monte-Carlo simulation. The kick velocity was assumed following Arzoumanian et al. (2002). NSs were born in a thin disk with a semithickness 75 pc. Those NS that were bom inside R = 2 kpc and outside R = 16 kpc were not taken into account. NS formation rate was assumed to be constant in time and proportional to the square of the ISM density at the birthplace. Results were normalized to have in total 5 x 108 NSs born in the described region. Density contours are shown with a step 0.0001 pc 3. At the solar distance from the center close to the galactic plane the NS density is about 2.8 1CT4 pc 3. From Popov et al. (2003a).

Work Done in Rock Crushing.—It is important, in order to compare the work accomplished by various machines, to have some basis upon which such comparisons may be founded There are two basic laws that have had attention from students of the subject—those of Rittinger and Kick. Rittinger s law states that the power required for reduction is proportional to the increase of surface. Kick s law states, in effect, that the power required varies as the volume or weight. 

Kick s law essentially states that the work required to obtain a given reduction ratio is the same irrespective of starting size. According to Rittinger s law work is proportional to surface created. Rittinger s and Kick s laws are only useful over a limited particle size range and are not utilized today. 

A significant proportion of the applied loads was carried by the concrete and the chains within the concrete, and was not transferred into the steel posts and kick-beams where the strain measurements were taken. 

Kick assumed that the energy required to reduce a material in size was directly proportional to the size-reduction ratio. This implies n = 1 in Eq. (14.5-1), giving... 

Kick (1885) reckoned that the energy required for a given size reduction was proportional to the size reduction ratio and took the value of the power n as 1. In such a way, by integrating Equation 4.1, the following relation, known as Kick s law is obtained ... 

On the basis of stress analysis theory for plastic deformation. Kick (1885) proposed that the energy required in any comminution process was directly proportional to the ratio of the volume of the feed particle to the product particle. Taking this assumption as our starting point, we see that ... 

In other words, there is no derivative action on a set-point change, only proportional action. On a load upset, both proportional and derivative actions are enabled. (Note also that, in some controller implementations, the proportional action is also decoupled from set-point changes, as the kick from a set-point change is also considered to be too aggressive.)... 

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