Page 139 - Modern Control Systems

Section 2.9 The Simulation of Systems Using Control Design Software 113

so
2
V 2(s) = ^ ¼^).
We will use this relationship between V 3(s) and Vz(s) in the subsequent develop-
ment. Continuing with the block diagram reduction, we have
V 3(s) = -ZGV 3(s) + ZGR{h{s) - I 2(s)),

but from the block diagram, we see that
h = GiV.is) - V 2(s)), I 2 = - | A

Therefore,

2
V 3(s) = -ZGV 3(s) + ZG R(V {{s) - V 2{s)) - GRV 3(s).
Substituting for V 2(s) yields

(GR)(GZ)
Vs Vi
^ ~ 1 + 2GR + GZ + (GR)(GZ) ^'
But we know that GR = 1; hence, we obtain

l
Note that the DC gain is / 2, as expected. The pole is desired at p = 27r(106.1) =
666.7 = 2000/3. Therefore, we require RC = 0.001. Select R = 1 k(l and
C = 1 fiF. Hence, we achieve the filter

333.3
T(s) =
(s + 666.7)'

2.9 THE SIMULATION OF SYSTEMS USING CONTROL DESIGN SOFTWARE

Application of the many classical and modern control system design and analysis
tools is based on mathematical models. Most popular control design software pack-
ages can be used with systems given in the form of transfer function descriptions. In
this book, we will focus on m-file scripts containing commands and functions to an-
alyze and design control systems. Various commercial control system packages
are available for student use. The m-files described here are compatible with the
f
MATLAB Control System Toolbox and the LabVIEW MathScript RT Module.*

'See Appendix A for an introduction to MATLAB.
*See Appendix B for an introduction to LabVIEW MathScipt RT Module.