Page 500 - Mechanical Engineers' Handbook (Volume 2)

8 Simulation for Control System Analysis 491

Figure 34 Error performance curves.

essary to try out the controller on the actual system. This involves experimentation. Computer
simulation may also be viewed as experimentation where the synthesized controller is in-
serted into a very sophisticated model of the actual physical system and the system response
computed. Extensive simulation studies can reduce the cost of experimentation and may even
at times serve as the final controller to be implemented on the actual physical plant. So in
simulation the burden of experiment is transformed into generating accurate models for all
the components in a system without oversimplifying assumptions. Simulations can be per-
formed on analog, digital, or hybrid computers. 7

Table 5 Optimal Form of the Closed-Loop Transfer Function Based on the ITAE Criterion for
Step Inputs
C(s) a 0
, a n n
n
R(s) s a n 1 s n 1 as a 0 0
1
s n
2 2
s 1.4 s n
n
3 2 2 3
n
n
s 1.75 s 2.15 s n
4 3 2 2 3 4
s 2.1 s 3.4 s 2.7 s n
n
n
n
5 4 2 3 3 2 4 5
n
n
s 2.8 s 5.0 s 5.5 s 3.4 s n
n
n
6 5 24 33 42 5 6
n
n
n
n
n
s 3.25 s 6.60 s 8.60 s 7.45 s 3.95 s n