Problems
Problem 7.1
If a closed-loop system has a set of complex conjugate poles at \(p=-2.5\pm j 4.33\) and no zeros, what is the system's natural frequency, damping ratio, overshoot, and settling time?
Problem 7.2
Given the block diagram in figure 7.4a, with \(K=1\), \[G(s)=\frac{0.5}{s+0.5}\ ,\] and \(H=1\),
- Find the closed-loop transfer function.
- Find the location of the closed-loop poles.
- Determine if the closed-loop system is stable.
Problem 7.3
Let a system have the plant transfer function \[G_P(s) = \frac{10}{(s+2)(s+5)}.\] Design a PI controller such that the closed-loop system has an overshoot of \(20\) percent and zero steady-state error.
Problem 7.4
Given the unity feedback system shown in the block diagram of figure 7.23, do the following:
- Design a PI controller \(G_C\) to yield a closed-loop system with about a 15 percent overshoot and minimal settling time.
- Plot the system response.
- Determine \(K_I\) and \(K_P\).
