Setpoint force

It is important to realize that such a significant difference in f-d curves may also occur in aqueous medium in areas with different surface charge density [88]. In this situation, a preset deflection (setpoint) value below the hard wall contact (force larger than the force required to overcome the electrostatic repulsion) may lead to artifacts in the constant force (i.e. height) image (Fig. 3.40). This kind of artifact is based on the fact that under these conditions the constant setpoint force corresponds to a different tip-sample distance (similar to the difference between the lines labeled with 1 and 2 in Fig. 3.39). 

If the process is second- or higher-order, we will not be able to make a discontinuous change in the slope of the response curve. Consequently we would expect a second-order process to overshoot the setpoint if we forced it to reach the setpoint in one sampling period. The output would oscillate between sampling periods and the manipulated variable would change at each sampling period. This is called rippling and is illustrated in Fig. 20.2c. 

In contrast, the Morse force is not monotonic. For a force setpoint of e.g. —InN, two solutions are possible z 2 A and z 4 A. The slope of the force curve is different for the two solutions. Assume that we wish to operate the AFM at a distance of 4 A and a corresponding force of —InN. We would have to wire up the feedback such that it approaches if the actual force is greater than —1 nN, and withdraws if the actual force is smaller than — 1 nN. However, if the tip would encounter an upward atomic step of Az = 2 A, the actual force would be +10nN. Because this value is greater than the setpoint, the feedback would inevitably drive the tip into the sample, leading to a premature and unintended end of the experiment. 

Elimination of parallel ramping is accomplished by introducing an integral function (Figure 2.16 middle) which continuously sums the difference between furnace and setpoint temperatures as swept through time. This area, multiplied by a weighting factor, is added to the proportional portion of the control instruction. If the furnace temperature is persistently below the setpoint, this area continues to accumulate until the furnace temperature is forced up to the setpoint, at which time no additional area is accumulated. 

Increase or decrease the force control setpoint to increase or decrease the tablet weight, respectively. The new force control set point is calculated by means of the machine manufacturer s control algorithm. Typically after adjustment to the new force control set point, the weight control system should resample and verify that the average tablet weight is now within the average control limits. 

The weight control systems that change the force control setpoint result in a change of the compression force throughout the run with a relatively constant tablet thickness. On the other hand, by changing the machine tablet edge thickness, the compression force remains relatively constant throughout the run while the tablet thickness varies. Since these adjustments are usually relatively small, both methods of machine adjustment typically produce similar results. 

Fig. 1.16 Average tip—sample force and oscillation frequency as a function of reduced amplitude (setpoint). The dashed resonance corresponds to a damped driven oscillator without sample—tip interactions. Reprinted from [16], copyright American Physical Society...

The gains do require adjustment if we alter the scan rate, the scan size, and the setpoint, i.e., the imaging force. It is particularly important to remember that both scan size and rate influence the tip velocity, i.e., if the scan size is increased, the rates should be decreased correspondingly if the feedback loop should operate with a similarly negligible error. Thus, the force and parameter settings that were optimized for a scan size of 1 x 1 pm2, cannot be the same for a scan size of 10 x 10 pm2 at constant scan rate, as the tip velocity is increased by a factor of 10. 

Fig. 2.13 Schematic of force displacement curve and relation of load, adhesion (pull-off force), and imaging force on the one hand and setpoint on the other hand...

For many fragile materials and research/practical questions, intermittent CM is preferred as the lateral forces are practically avoided. Thus, sample damage or deformation is circumvented. However, despite the absence of shear forces, too high amplitudes or too low setpoint ratios may lead to damage of the sample or the tip as well. 

Thus, in practice we record friction data (images or loops) for both trace and retrace for different setpoints. We also acquire and capture for each setpoint the entire f-d curve to calculate the mean pull-off force (= adhesion A) and the load L. The analysis of the friction data provides the half width of friction loop W = (Mu-Md)/2) and the friction loop offsets (A (Mu + Md)/2) for sloped and flat surfaces for each load, i.e., we measured and calculate the following ... 

Vanishing contrast may be caused by selecting a setpoint that is almost equal to the differential signal for the undeflected cantilever and equal to the rms amplitude of the freely oscillating forced oscillator for CM and TM, respectively. 

For the operation of contact mode AFM under liquid there are only few details that differ from operation in air. The imaging forces can often be controlled much more precisely if the adhesion is lower due to the absence of capillary forces. Hence the adjustment of the setpoint requires more attention and can be done with much more precision. The adjustment can be based on acquired force-displacement curves (see below, Fig. 3.39). Setpoint deflection values close to the out of contact deflection yield minimized normal forces [82-84],... 

The forces operating between tip and sample in the liquid may be distinctly different from the situation in ambient conditions. As mentioned capillary forces are absent and hence weaker interactions may become significant in liquids. Electrostatic repulsion may also occur between tip and sample, which has an impact on the selection of proper imaging conditions. The situation is exemplified in Fig. 3.39, where force-displacement curves obtained in different media are compared. For the same preset deflection (i.e. setpoint) the z-position corresponds to a different value. At the point where the repulsion is overcome, the tip penetrates through the bilayer. 

Sometimes clearly audible feedback may occur during the engagement process or when the deflection of the cantilever is nearly equal to the setpoint. The former problem can lead to a false engagement in the worst case and may be avoided by reducing the gains and increasing the differential offset. In the latter case it is recommended to adjust the setpoint to slightly increased forces. 

The valve positioner, which is usually contained in its own box and mounted on the side of the valve actuator, is designed to control the valve stem position at a prescribed position in spite of packing friction and other forces on the stem. The valve positioner itself is a feedback controller that compares the measured with the specified stem position and makes adjustments to the instrument air pressure to provide the proper stem position. In this case, the setpoint for the valve positioner can be a pneumatic signal coming from an l/P converter or the 4-20 mA analog signal coming directly from the controller. A valve with a deadband of 25% can provide flow rate precision... 

Equation (2.21) also shows how state behaviour depends on the forcing variables, in this case the externally determined setpoint for liquid level, / and the demanded valve travels for inlet valve 1, x i, and inlet valve 2, x i-... 

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