Page 135 - Modern Control Systems

Section 2.8 Design Examples 109
-P P -P - 2
Y(s) = -^- + 7 + ^7 zr. (2.137)
w v
2s s + 1 2(5 + 2) '
Therefore, the output measurement is

2
At) = \l-P + -Pe"* - (P + 2)e~ % t > 0.
A plot of y{t) is shown in Figure 2.46 for P — 3. We can see that y(t) is propor-
tional to the magnitude of the force after 5 seconds. Thus in steady state, after 5 sec-
onds, the response y{i) is proportional to the acceleration, as desired. If this period is
excessively long, we must increase the spring constant, k, and the friction, b, while
reducing the mass, M. If we are able to select the components so that b/M = 12 and
k/M = 32, the accelerometer will attain the proportional response in 1 second. (It is
left to the reader to show this.) •

EXAMPLE 2.16 Design of a laboratory robot

In this example, we endeavor to show the physical design of a laboratory device and
demonstrate its complex design. We will also exhibit the many components com-
monly used in a control system.
A robot for laboratory use is shown in Figure 2.47. A laboratory robot's work
volume must allow the robot to reach the entire bench area and access existing ana-
lytical instruments. There must also be sufficient area for a stockroom of supplies for
unattended operation.
The laboratory robot can be involved in three types of tasks during an ana-
lytical experiment. The first is sample introduction, wherein the robot is trained
to accept a number of different sample trays, racks, and containers and to intro-
duce them into the system. The second set of tasks involves the robot transport-
ing the samples between individual dedicated automated stations for chemical
preparation and instrumental analysis. Samples must be scheduled and moved
between these stations as necessary to complete the analysis. In the third set of
tasks for the robot, flexible automation provides new capability to the analytical
laboratory. The robot must be programmed to emulate the human operator or
work with various devices. All of these types of operations are required for an
effective laboratory robot.
The ORCA laboratory robot is an anthropomorphic arm, mounted on a rail, de-
signed as the optimum configuration for the analytical laboratory [14]. The rail can
be located at the front or back of a workbench, or placed in the middle of a table
when access to both sides of the rail is required. Simple software commands permit
moving the arm from one side of the rail to the other while maintaining the wrist po-
sition (to transfer open containers) or locking the wrist angle (to transfer objects in
virtually any orientation). The rectilinear geometry, in contrast to the cylindrical
geometry used by many robots, permits more accessories to be placed within the
robot workspace and provides an excellent match to the laboratory bench. Move-
ment of all joints is coordinated through software, which simplifies the use of the
robot by representing the robot positions and movements in the more familiar
Cartesian coordinate space.