Servo control system

Servo Control System (24) for positioning a load (35). A velocity drive signal (50), derived from a positional error signal, is provided by the outer loop (28) as the input to a velocity servo inner loop (26). The velocity drive signal is non-linear (48) and of the form V=.sqroot.2AD where A is the acceleration of the load and D is positional error (46).

DESCRIPTION 
1. Technical Field 
The present invention relates to servo control systems and more 
particularly relates to position servo control systems for positioning a 
gantry carrying a camera for use in a camera-model visual system of a 
flight simulator. 
2. Background Art 
Servo control systems are in widespread use. A primary purpose of a servo 
control system is to reduce the deviation between the desired position of 
a load and the actual position of the load. A servo control system so 
employed is called a position servo control or position servo. They are 
particularly valuable in the field of flight simulation. 
Flight simulation is a method of training aircraft personnel. In a 
simulator the trainee is placed in a realistically recreated aircraft 
environment designed such that the trainee, without leaving the ground 
feels he is in and operating an actual aircraft. An important element used 
to create this realism is a visual display system which provides the 
trainee with an out-of-the-window scene which varies with his operation of 
the flight control system of the simulator, in a manner which corresponds 
to conditions encountered in actual flight. 
During actual flight operations, for example, a pilot will manipulate the 
aircraft controls and thereby provide control signals to operate the 
control surfaces (rudder, flaps, etc.). As this process occurs, the pilot 
will view a change in the visual scene e.g. an elevational change. 
Accurate simulation requires reproduction of this correspondence between 
manipulations of the controls and changes in visual scene. 
One method devised to effect this desired reproduction employs a camera 
model visual system. In this system, a television camera is positioned on 
a moveable gantry. The moveable gantry is positioned on tracks so that it 
can move across a fixed terrain model that provides the input image to the 
camera. As the pilot moves his controls, the gantry accelerates to a fixed 
velocity. Then, deceleration forces are applied to the gantry so that the 
velocity of the gantry becomes zero precisely at the point where the 
camera will locate a new image on the terrain model in exact 
correspondence with the control commands set by the pilot. 
The goal of realism in flight simulation is in part realized by utilizing a 
position servo control system to control movement of the gantry or load. A 
typical position servo can be logically divided into two blocks: an inner 
loop and an outer loop. The inner loop is a velocity servo composed of a 
motor or actuator, tachometer or other feedback devices, velocity loop 
compensation electronics and drive amplifier. The input to this loop is a 
velocity drive signal provided by the outer loop. The outer loop is 
composed of a position feedback device and position loop compensation 
electronics. 
Position servo control systems for flight simulation are generally designed 
to operate on an error voltage which is representative of the difference 
between the position of the gantry and the position being sought by the 
gantry during a positioning operation. As the gantry approaches the 
selected position, the error voltage is gradually reduced until it reaches 
zero at which point the motor driving the gantry is inactivated. 
During the initial portion of the positioning operation of the gantry, it 
is desirable to have the gantry accelerate to and move with a maximum 
speed with proper care being given to the mechanical aspects involved. At 
a proper distance away from the new selected position, maximum 
deceleration is applied to bring the gantry to a stop. 
In order to achieve high positioning speed at a high positioning accuracy, 
it is necessary to employ a saturated position servo system involving high 
gain during the final (i.e. deceleration) portion of the positioning 
operation. It is also desirable to provide a minimum response time, 
critically damped position servo without overshoot for step positional 
inputs of various magnitudes. 
Previous attempts at satisfying these demands have employed conventional 
linear compensation circuits in the outer loop. However, it has been found 
that, for large positional errors and linear operation in the saturation 
mode, there is tremendous overshoot in such prior art systems and it takes 
a long time for the system to stabilize. This means that the camera on the 
gantry oscillates, defeating the goal of flight simulation realism. 
Some prior art systems use non-linear compensation circuits in the outer 
loop. However, these circuits still require a tradeoff between minimum 
response time and overshoot. 
The present invention successfully overcomes the shortcomings associated 
with the prior art. According to this new approach a unique non-linear 
compensation method is used with position servo devices. Use of the 
present invention can provide minimum response time without overshoot. In 
addition, very high error sensitivity may be achieved. The present 
invention is therefore particularly suitable in the field of flight 
simulation. 
DISCLOSURE OF THE INVENTION 
Accordingly, a primary object of the present invention is to provide a high 
gain stable position servo system for positioning a load. 
Another object of this invention is to provide a minimum response time, 
critically damped position servo without overshoot for all size step 
positional inputs. 
It is still a further object of this invention to define a non-linear 
compensation method which can provide a minimum response time without 
overshoot. 
In accordance with the present invention, an improved position servo is 
provided for positioning a load. The position servo is of the type having 
a velocity drive signal derived from a positional error signal. The 
improvement comprises means for providing a velocity drive signal 
representative of the square root of the positional error signal, so that 
the position servo response to postional error of the load corresponds to 
a minimum response time, non-overshoot positioning of the load.

BEST MODE FOR CARRYING OUT THE INVENTION 
One utilization for the position servo control system of the present 
invention is shown in FIG. 1. Numeral 10 indicates generally a flight 
simulator employing a camera model visual system and including a simulated 
cockpit 12. Reference character 14 identifies a reduced scale terrain 
model, an image of which is represented to a trainee in the simulator 
cockpit as an out of the window visual scene by cathode ray tubes (CRTs) 
13. A television camera 16 is positioned on a gantry 18 which rides along 
horizontal tracks 20A and 20b in correspondence to commands from the 
trainee. Camera 16 "views" portions of model 14 and provides electrical 
signals to CRTs 13 so that the appropriate visual scene can be observed by 
the trainee. 
According to the present invention, correspondence between gantry movement 
along the tracks and trainee command is effected by position servo control 
system 24, shown in FIG. 2. For purposes of clarity, operation of the 
position servo control system to effect motion in one direction is 
hereinafter described. It will be apparent to those skilled in the art 
that the principles of the present invention may be employed to provide 
position servo control for motion in multiple directions. 
Referring now to FIG. 2, generally the position control system of the 
present invention comprises an inner loop 26 which serves as a velocity 
servo and an outer loop 28 which acts as a position feedback and 
compensation circuit. The outer loop derives a velocity drive signal 50 
from positional information and feeds this drive signal to inner loop 26 
to control gantry driving motor 34. 
Typically, gantry movement is effected in the following manner. First, in 
correspondance to the trainee's commands, a step positioning input signal, 
represented by positioning voltage 42, is applied to summing unit 44. 
Summing unit 44 comprises a conventional operational amplifier which in 
this case performs the function of computing the difference of two 
signals. Positioning voltage 42 is the first of the two input signals to 
the summing unit. The second signal corresponds to the actual position of 
the gantry and is represented by positional voltage signal 40. The value 
of positional voltage signal 40 is derived from a conventional 
potentiometer 38 which in connected to load 35. The output of the summing 
unit, electrical signal 46, represents the positional error D of the load. 
Therefore, D is equal to the difference between the desired position 
commanded by the trainee represented by the input positioning voltage 42, 
and the actual position of the load, represented by the positional voltage 
40. 
As just shown, D represents position error information derived by the outer 
loop 28. However, the position servo requires a velocity drive signal 50, 
derived from the positional error information, in order to control load 
driving motor 34. 
It is at this point that the present invention radically departs from the 
prior art by employing a unique non-linear compensation circuit to derive 
the velocity drive signal from the positional error information D. The 
non-linear compensation circuit includes a square root unit 48 having an 
output equal to .sqroot.D. In order to achieve the proper magnitude of 
velocity drive signal 50, the output .sqroot.D from the square root unit 
is fed to a conventional gain amplifier, 66 of gain magnitude .sqroot.2A. 
In the formula .sqroot.2A, A (acceleration) equals the force of the motor 
divided by the mass of the load. The gain is therefore a function of the 
available motor acceleration. Velocity drive signal 50 is therefore equal 
to .sqroot.D (from square root unit 48) times .sqroot.2A (from gain 
amplifier 66) or .sqroot.2AD. The value .sqroot.2AD derived by the above 
described non-linear compensation electronics is represented by the 
velocity drive signal 50 fed from outer loop 28 to the velocity loop 26. 
The outer loop 28 thus derives a velocity drive signal 50 equal to 
.sqroot.2AD from positional error signal 46 and feeds it to inner loop 26 
to control gantry driving motor 34. The inner loop functions to ensure 
that the position servo, in fact, accelerates the motor to the velocity 
input 50 indicated by the outer loop. 
Generally, the inner loop comprises a velocity loop compensator 30, a drive 
amplifier 32, a motor 34 and a tachometer 36. These components are all 
standard items, well known in the art and commercially available. 
The inner loop elements are connected so that a first signal input to the 
velocity loop compensator 30 is velocity drive signal 50. The output 
signal of velocity loop compensator 30 is fed to drive amplifier 32. The 
output signal of drive amplifier 32 is fed to motor 34. Finally, 
tachometer 36 forms part of a feedback loop in the inner loop. The 
tachometer is connected to the motor and provides a feedback signal which 
is the second signal input to the velocity loop compensator 30. 
The inner loop, as described, functions to insure that the position servo 
in fact, accelerates the motor to the velocity indicated by drive signal 
50. This is accomplished by the tachometer feedback loop. Tachometer 30 
functions to measure the actual velocity of the motor 34. Velocity loop 
compensator 30 functions to first compare the actual velocity of the motor 
(which information is supplied by the tachometer) to the velocity that 
corresponds to velocity drive signal 50. Then, velocity loop compensator 
provides an output signal to drive amplifier 32 which causes speed up or 
slow down of the motor so that the motor moves at the same velocity as the 
velocity drive signal 50. 
In the embodiment just described, a rotary motor is used to drive the load. 
Auxiliary means (not shown) but conventional in the art are used to 
convert the rotational output of the motor to linear motion of the load. 
As will be obvious to those skilled in this art, other load driving means 
such as a linear actuator with corresponding velocity measuring means can 
also be employed in the present invention. 
The FIG. 2 embodiment of the present invention provides a high gain stable 
position servo system for positioning a load. It also provides a minimum 
response time, critically damped position servo without overshoot for all 
size step positional inputs. These advantages are achieved in the present 
invention by uniquely utilizing a non-linear compensation function 
(V=.sqroot.2AD) during a positioning operation. 
During a positioning operation of the load, in response to a position step 
input 42 that corresponds to the trainee's commands, the load accelerates 
to and moves with a maximum speed. A maximum speed is achieved by 
operating the motor in a saturation mode. As the load moves toward the 
desired position, represented by signal 42, the summing unit calculates 
the difference between the desired position 42 and actual position of the 
load, represented by signal 40. The difference signal 46 represents a 
positional error D. 
As shown above, the inner loop of the position servo requires a velocity 
drive signal 50 which is derived from positional error signal 46. What is 
required therefor, is a transformation operation which uniquely transforms 
positional error information to velocity drive information. The 
transformation operator must ensure that the outer loop will drive the 
load to a desired position with the maximum acceleration/deceleration, 
thus insuring minimum response time without overshoot. 
The unique transformation operator is given by the equation V=.sqroot.2AD. 
This equation transforms positional error information D into velocity 
information V. For each value of D, which represents the differences 
between desired position and actual position, a unique value of V is 
computed and implemented by the inner loop. As D becomes smaller and 
smaller, approaching zero, the velocity of the motor and thus of the load 
becomes less and less. When the positional error is zero, the velocity of 
the motor is zero. There is therefore no overshoot--the load reaches the 
desired position with zero velocity and in the minimum time. 
FIG. 3 is a twofold modification of the position servo control system of 
FIG. 2, and represents the preferred embodiment. 
The first modification concerns eliminating any possible limit cycle 
condition, since a limit cycle condition will result in the continuous 
oscillation of the load. The continuous oscillations occur in a non-linear 
system (e.g. .sqroot.D) because the gain increases to a very high value as 
the positional error D approaches zero. The gain must therefore be limited 
at small positional errors so that oscillations are not produced. 
An apparatus for dealing with the limit cycle condition is shown in FIG. 3, 
indicated generally by numeral 52. The modification comprises inserting 
position error voltage 46 into a linear compensation system 54 in parallel 
with a non-linear compensation system 56, and providing an apparatus for 
switching (described hereinafter) to the linear system at near zero 
positional error, thus eliminating the limit cycle condition. 
The linear system 54 comprises a first conventional amplifier 60 with gain 
k, in series with a conventional rectifier 62. The linear system functions 
to produce a voltage signal 76 that corresponds to linear velocity drive 
function V=kD. 
The non-linear system 56 comprises a conventional rectifier 64 in series 
with a conventional square root device 49 in series with a second 
conventional amplifier 66 with gain .sqroot.2A. The non-linear system 
functions to produce a voltage 78 that corresponds to non-linear velocity 
drive function V=.sqroot.2AD. 
The outputs of the two parallel blocks are fed into a conventional voltage 
comparator 58. In turn, the output of the voltage comparator is fed to a 
conventional mode switch 68. Mode switch 68 switches from the linear 
system 54 to the non-linear system 56 in correspondence with voltage 
magnitudes determined by the voltage comparator. This switching procedure 
is best understood by referring to FIG. 4. 
FIG. 4 is a plot of motor velocity versus position error. The abscissa 
represents position error (D) and the ordinate velocity (V). Both position 
error and velocity are shown by their voltage equivalents. Also shown is 
linear velocity signal 76 representing the curve V=kD, and a non-linear 
velocity signal 78 representing the curve V=.sqroot.2AD. 
For each point of position error, voltage comparer 58 measures the voltage 
representative of the velocity of the inputs, here linear signal 76 and 
non-linear signal 78. Whichever voltage has an absolute value which is 
lower becomes the operating signal. Mode switch 68 than switches to the 
operating signal. For example, in FIG. 4, at a position error of the point 
identified by A (reference numeral 80), mode switch 68 will switch from 
the non-linear signal 78 to the linear signal 76 as the position error 
becomes smaller, because the absolute value of the voltage of the linear 
curve is less than the absolute value of the voltage of the non-linear 
curve. A similar situation also occurs at point 82. The solid line 84 
indicates the resulting drive velocity as a function of the position 
error. 
The first modification eliminates the potential problem of the limit cycle. 
The position servo operates in a non-linear, saturated mode for large 
values of positional error. The non-linear expression .sqroot.2AD ensures 
that the velocity of the load changes within the maximum deceleration 
limits of the system. There is therefore, complete control of the gantry 
movement. As the positional error becomes small, the potential for 
infinite gain, attendant upon use of the non-linear square root function 
(V=.sqroot.2AD), is eliminated by switching to a linear mode of operation 
(V=kD). The linear mode is only active for small position errors. It is 
therefore possible to achieve a much higher overall gain than with linear 
compensation circuits alone. This provides very high static accuracy. 
Moreover, position loop compensation is reduced to two simple gain 
adjustments. First, the gain of amplifier 66 is derived from the available 
motor acceleration and the scaling of the velocity servo. Then the gain of 
amplifier 60 is adjusted to provide optimum stability under states of 
small step input positional voltages 42. 
The first modification thus eliminates the potential limit cycle problem. 
The second modification of the position servo control system of FIG. 2, 
shown in detail in FIG. 3, concerns eliminating a problem associated with 
the square root circuit 49. The square root circuit works only for 
positive input voltages and not for negative input voltages. This problem 
is solved by rectifying the position error by rectifier 64, taking the 
square root 49 of the absolute value of the error signal and then 
assigning the appropriate sign to the result based on the sign of the 
position error. A conventional inverting amplifier 86 connected to the 
output of amplifier 66, is switched in or out of the circuit depending on 
the polarity of the error voltage 46 by a conventional polarity switch 88 
connected to a conventional polarity comparator 90. This will ensure the 
correct polarity of the velocity drive voltage. 
FIG. 5, indicated generally by numeral 90, shows a generalized embodiment 
of the present invention. The generalization concerns extending the 
principles of the mathematical model of the position servo. 
The non-linear compensation function described above is based on a simple 
mathematical model F=MA where F is the motor force and M the mass of the 
load. This mathematical model will become more developed if additional 
factors are included in the mathematical model. 
A first additional factor to incorporate in the model is non-linearities 
that exist throughout the position servo. For example, proper modeling of 
the velocity loop compensator 30, potentiometer 38, tachometer 36 and 
motor 34 requires mathematical expression for the non-linearities that 
exist in these components over specified ranges of positional error D. A 
second additional factor recognizes the fact that the motor itself has 
mass, which must be added to the load mass. A third factor accounts for 
the fact that frictional forces exist throughout the system. Therefore, 
there are lags or phase delays in the feedback loops. 
These additional factors and others can be routinely implemented into the 
mathematical model of the position servo system. When these factors are 
included, the velocity drive signal as a function of positional error 
could be of the form, e.g., V=.sup.3 .sqroot.D, V=.sup.n .sqroot.D as well 
as the form V=kD, V.alpha..sqroot.D. 
FIG. 6 is a graph 100 that incorporates the principles that are included in 
the developed mathematical model. Graph 100 shows the piecewise 
approximation of a velocity drive signal 74 as a function of position 
error. As positional error D increases, the velocity drive signal curve is 
approximated by contributing functions F(D.sub.1), F(D.sub.2), F(D.sub.3), 
F(D.sub.4). For example, for small values of positional error D that 
approach zero error in the limit, (when actual position equals desired 
position), the optimal velocity drive signal is V=kD. This expression is 
optimal because it avoids the limit cycle condition discussed above. For 
larger values of positional error D, the required velocity drive signal is 
V=.sqroot.2AD in conformity with the mathematical model of the position 
servo. For even larger values of positional error D, the required velocity 
drive signal, in conformity with the more developed mathematical model, is 
expressed by e.g. V=.sup.3 .sqroot.D, V=.sup.N .sqroot.D. 
FIG. 5 comprises a switching circuit that may be employed to operate the 
position servo in conformity with graph 100. The input to the circuit, 
positional error voltage 46, is fed into one of a plurality of parallel 
branches. Each branch provides a different transformation operation to D. 
For example, a first branch implements the function V=kD; a second branch 
implements the function V=.sqroot.2AD; a third branch implements the 
function V=.sup.3 .sqroot.D etc. The criteria for switching to a 
particular branch is provided by conventional multiplexer controller 98. 
The multiplexer controller functions to determine which transformation 
function, evaluated at a given positional error, corresponds to the lowest 
magnitude of voltage. When this has been determined, a conventional (N to 
1) multiplexer 96 switches to that branch. The output of the switching 
circuit corresponds to the transformed function of D and is the velocity 
drive signal 50 which is fed to the inner loop. 
The switching circuit therefore provides the advantages of implementing 
disparate mathematical models of the position servo. Each model 
corresponds to the optimal acceleration/deceleration characteristics of 
the position servo for a given range of positional error D. The position 
servo thus positions a load with a minimum response time and with no 
overshoot for all values of positional error. 
The criteria for the selection of a particular model includes the greater 
expense incurred in using the more developed models, and the particular 
utilization of the position servo. For example, it has been determined 
that the FIG. 3 embodiment of the present invention is particularly 
suitable for employment in positioning the gantry. 
Although specific embodiments of the invention have been described herein, 
it will be obvious to those skilled in the art that various modification 
may be made without departing from the spirit of the invention. For 
example, the principles of the present invention may be employed to 
position a projector and lens system. In this system, there are five 
coordinates of position: azimuth, elevation, roll, zoom, and focus. The 
first three coordinates position the projector. The zoom and focus 
coordinates position the lens. Positioning of the projector and lens 
systems may be accomplished by employing a five position loop servo. A 
five position loop servo is a system of five independent position servos 
that employ the principles of the present invention to selectively 
position the five coordinate positions of the projector and lens system. 
With the foregoing in mind, it is understood that the invention is 
intended to be limited solely by the appended claims.