Final answer:
To find the maximum overshoot in radians for a step setpoint of 45 degrees with a 5% overshoot specification, the step setpoint is first converted to radians (π/4), and then the formula θ(θdp) = (π/4)(1 + 2) is used yielding a maximum overshoot of 3π/4 radians.
Step-by-step explanation:
To calculate the maximum overshot of the response in radians for a system with a step setpoint of 45 degrees and a 5% overshoot specification, we can use the equation provided in Section 1.1.3 where ymax = θ(tp) and step setpoint R0 = θd(t). The equation transforms into θ(tp) = θd(t)(1+100/PO).
Knowing that PO is the percentage overshoot which is given as 5%, we first need to convert the step setpoint from degrees to radians since the solution requires the answer in radians. 45 degrees is equivalent to π/4 radians.
Therefore, the calculation will be:
- θ(θdp) = (π/4)(1 + 100/5)
- θ(tp) = (π/4)(1 + 2)
- θ(tp) = (π/4)(3)
- θ(tp) = 3π/4 radians
The maximum overshoot is therefore 3π/4 radians, which is the peak value the system reaches before settling down to the desired setpoint.