Solutions for A are below, but would it be possible to get the
working out for it. As im struggling to work out % of setting time.
So any help with that would be good.
Solutions For A Are Below But Would It Be Possible To Get The Working Out For It As Im Struggling To Work Out Of Set 1 (123.39 KiB) Viewed 52 times
(a) A system has the closed loop transfer function: 28.8 G(S) = S2 + 28.8s + 576 For this second order system, evaluate the system time response to a step input of amplitude 5 units. Go on to give approximate values for rise time, peak time, 5% settling time and number of oscillations before settling. [9 marks] (b) You are tasked with designing a cruise control system for a car. The input to the system is the vehicle forward velocity measured in miles per hour (Vin(s)), and the output is the actual vehicle speed in metres per second (Vout(s)). The system will use a Pl controller, and needs to take into account engine dynamics, defined by the second order system where wn = 4 rad/s and ( = 0.7 and a gain of 1000. The system also has a disturbance input, D(s) to account for elevation changes. The mass of the car is 1000 kg. Note that 1 mph = 0.447 m/s. i. Based on this information, design a block diagram to represent this system ii. Evaluate the system closed loop transfer function describing the relationship be- tween the output velocity and the desired input velocity. iii. Evaluate the system closed loop transfer function describing the relationship be- tween the output velocity and the disturbance input. (16 marks] Total for Question 2: 25 marks Solution: (a) Second order time response (from equation sheet): c(t) = 0.25 (1 1-e14.4t [cos(19.2t) +0.75 sin(19.2t)]) Rise time: t, = 0.082 sec Peak time: tp = 0.164 sec 5% settling time: ts = 0.208 sec Number of oscillations: Number of oscillations = 1 oscillation
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