University Curtin of Technology Department of Electrical and Computer Engineering Control Systems 301
Laboratory Session 5
Computer Simulation II
1
Example
Example 1.1 Plot the root locus for the open-loop transfer function s+2 G(s) = 2 s + 2s + 3 Solution. The root locus plot as shown below can be generated by executing a Matlab program containing the following statements: num=[0 1 2]; den=[1 2 3]; sys=tf(num, den); rlocus(sys); v=[-5 1 -2.5 2.5]; axis(v)
Root Locus 2.5 2 1.5 1 0.5
Imag Axis
0 -0.5 -1 -1.5 -2 -2.5 -5
-4
-3
-2 Real Axis
-1
0
1
2
Exercises
+
Kr s+1 s+a
Exercise 1 Consider the feedback system shown as follows. R -
K s(T s+1)
Y
(a) Determine the transfer function from r to y. (b) Determine the stead-state error due to a step input. (c) Discuss the effect of different values of (Kr , a) on the system's response. (d) For the following case, K = 1, T =1 find values for Kr and a so that (if possible) the rise time is less than 1.5 sec; the settling time is less 10 than sec, the overshoot is less than 20%, and the steady-state error is less than 5%. If the specifications are easily met, ty to make the rise time as small as possible. If the specifications cannot be met, find the best design possible. Exercise 2 Plot the root roci for the unity-feedback system whose open-loop transfer function is given by K G(s) = 2 s (s + 2)(s + 3) Exercise 3 Plot the root roci for the unity-feedback system whose open-loop transfer function is given by K(s + 9) G(s) = s(s2 + 4s + 11) Locate the dominant closed-loop poles on the root locus such that the poles have a damp...