128 THE DESIGN OF PHOTOGRAMMETRIC PLOTTERS, HELAVA 
speed is the inertia of the physical object to be moved — the smaller the inertia the better 
the speed response of the servo. The speed problem is also connected with the tolerable 
maximum “over-shoot”. If no over-shoot is tolerated, the servo must be designed so that 
it is “critically damped”, that is, approaches the zero error situation steadily in the 
shortest possible time without ever crossing the zero error line. If some over-shoot is 
tolerated, the error may be compensated to the required degree of accuracy in a shorter 
time. In this case the servo approaches the zero situation by oscillation about the zero 
line. The oscillation of course must be strongly damped to prevent harmful effects. Thus 
the requirements set to the accuracy of the positioning also have an effect on the speed 
of response. 
3.4.1.3. Velocity. 
So far we have not assumed any changes of the input during the time the servo is 
compensating for an existing error signal. In the application to a plotter, of course, the 
input is almost always changing at a certain velocity. A simple proportional servo cannot 
cope with this situation. During a constant velocity operation it falls behind by a con- 
stant amount due to increased viscous friction. The magnitude of the residual error is 
proportional to the velocity and friction, and inversely proportional to the gain of the 
system. It follows that a high degree of accuracy is easier to achieve in the case of slow 
motion, particularly if the elements to be moved have low friction. For low speeds these 
measures are sufficient to reduce the magnitude of the velocity lag error. However, the 
electronic image correlation systems may eventually produce very high plotting speeds. 
Fortunately, the velocity lag may be completely compensated by employing more com- 
plieated derivative or integral control servos. 
3.4.1.4. Load torque. 
Another source of error is a change in the load torque. If there is a change in the 
torque needed to move the element controlled by a servo mechanism, an error similar to 
the velocity lag occurs. It is not very likely that noteworthy changes of this kind will 
take place in a photogrammetric plotter. However, if the elements to be moved by the 
servos are open to external forces and disturbances, the chances for an occurrence of this 
error are increased. This aspect should also be considered in the design of the instru- 
ment. At the same time it should be noted that errors due to load torque can be com- 
pletely eliminated in more elaborate servomechanisms. 
3.4.1.5. Stepping motor. 
Before studying the servomechanism as a part of the total system, we will pay at- 
tention to a special solution that is advantageous when an incremental computer is used. 
The heart of this solution is the stepping motor, an electric motor that operates in dis- 
crete steps regulated by input pulses. Since the output of an incremental computer is in 
pulses, a direct connection may be made to a stepping motor to convert the pulses to cor- 
responding physical motion. This solution is basically very simple and leads to light, 
inexpensive mechanisms. Its main limitation is the speed, since only a limited number of 
steps may be executed in a given time interval. The present stepping motors are able to 
handle several hundred steps in a second. This speed is sufficient for the manual opera- 
tion of the plotter. 
8.42. Control system. 
In a photogrammetric plotter the servomechanisms are a part of the larger and more 
involved problem of controlling a plotting process. As in a simple servo system, the input 
and output, the error sensing, controlling and powering elements can be distinguished in 
the controlling system. If the performance of all the individual parts of the system are