Consider the stable system represented by the differential equation
where u(t) - sin 3t. Determine the phase lag for this system.
In Problems 7 and 8, consider the feedback system in Figure 8.55 with the loop transfer function
Problems 7
Driverless vehicles can be used in warehouses, airports, and many other applications. These vehicles follow a wire embedded in the floor and adjust the steerable front wheels in order to maintain proper direction, as shown in Figure P8.7 (a) [10]. The sensing coils, mounted on the front wheel assembly, detect an error in the direction of travel and adjust the steering. The overall control system is shown in Figure P8.7 (b). The loop transfer function is
We want the bandwidth of the closed-loop system to exceed 2π rad/s. (a) Set Kv = 2π and sketch the Bode diagram, (b) Using the Bode diagram, obtain the logarithmic-magnitude versus phase angle curve.
Problems 8
A feedback control system is shown in Figure P8.8.The specification for the closed-loop system requires that the overshoot to a step input be less than 15%. (a) Determine the corresponding specification Mpω) in the frequency domain for the closed-loop transfer function
(b) Determine the resonant frequency ωr. (c) Determine the bandwidth of the closed-loop system.
