Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure CP8.8 (a).The transfer function of the system is

The design objective is to balance the pendulum (i.e., 0(f) ‰ˆ 0) in the presence of disturbance inputs. A block diagram representation of the system is depicted in Figure CP8.8(b). Let Ms = 10 kg, Mb =100 kg, L = 1 m, g = 9.81 m/s2, a = 5, and b = 10. The design specifications, based on a unit step disturbance, are as follows:
1. Settling time (with a 2% criterion) less than 10 seconds,
2. Percent overshoot less than 40%, and
3. Steady-state tracking error less than 0.1° in the presence of the disturbance.
Develop a set of interactive m-file scripts to aid in the control system design. The first script should accomplish at least the following:
1. Compute the closed-loop transfer function from the disturbance to the output with K as an adjustable parameter.
2. Draw the Bode plot of the closed-loop system.

1. Plot the response, 9{t), to a unit step disturbance with K as an adjustable parameter, and
2. Label the plot appropriately. Utilizing the interactive scripts, design
Utilizing the interactive scripts, design the controller to meet the specifications using frequency response Bode methods. To start the design process, use analytic methods to compute the minimum value of K to meet the steady-state tracking error specification. Use the minimum K as the first guess in the design iteration.

G(s) = (M,M/M L)