Filter
Top Products
Chapter 1 Introduction
Xmath Control Design Module 1-10 ni.com
Figure 1-4. Block Diagram of the Closed-Loop Controller
This is a block diagram of the closed-loop controller with compensator
K
c1
K
1
(s) in the feedforward path and K
c2
K
2
(s) in the feedback path.
This time, instead of having all your gain K
c
in the forward path of the
closed-loop system, the system gain is split between the two compensators.
The gains K
c1
and K
c2
are defined such that K
c
=2=K
c1
K
c2
and the
closed-loop transfer function T
c1
(s) is unity at s =0(DC).
The closed-loop transfer function is represented by:
You can find the values of the individual transfer functions at s =0 using
freq( ), and then substitute to solve the previous equation:
a = makematrix(freq(K1s*Gs,0));
b = makematrix(freq(K1s*K2s*Gs,0));
Solving:
Kc1 = (1+2*b)/a
Kc1 (a scalar) = 0.0241778
Kc2 = 2/Kc1
Kc2 (a scalar) = 82.7206
You now call feedback( ) again, this time using its second input
argument to indicate that the outputs of the first input system (forward path)
are fed back as the inputs to the second system (feedback path) in a
negative-feedback loop.
cl_syscomp2 = feedback(Kc1*K1s*Gs, Kc2*K2s);
U(s) Y(s)
G(s)
K
c2
K
2
(s)
K
c1
K
1
(s)
+
–
T
cl
s()
K
c1
K
1
s()Gs()
1 K
c1
K
c2
K
1
s()K
2
s()Gs()+
-------------------------------------------------------------------=