08. Proportional Control 3
SOLUTION:
Magnitude of overshoot increases and oscillations occur faster
Many real-world systems are governed by second-order differential equations and exhibit a transient, oscillatory response to a step input before setting to some steady-state value. The main features of this oscillatory response are shown here,
where,
- Rise time, T_r, is the time required for the response to move from a specified low value to a specified high value, often expressed as percentages of the final value. For example, 0% to 100% of its final (steady-state) value.
- Peak time, T_p, is the time required to reach the first overshoot peak
- Maximum percent overshoot =
- Settling time, T_s, is the time required for the response to reach and stay within a range about the final, steady-state value (often defined as 2 to 5 percent of y_{ss})
Oscillations are strongly related to the amount of damping within a system. Damping is fancy term for any mechanism to dissipate energy, e.g., shock absorbers on a car or bicycle, or friction. Lightly damped systems oscillate with greater magnitude and frequency than more heavily damped systems. A critically damped system has no oscillations. Over damped systems (i.e., even more damped than critically damped) also do not oscillate and their time to reach a steady-state value increases.
