How to design a proportional control law

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Reference no: EM13273562

design an automatic speed control for an automobile. Assume
that (1) the car has a mass m of 1000 kg, (2) the accelerator is the control
U and supplies a force on the automobile of 10 N per degree of accelerator
motion, and (3) air drag provides a friction force proportional to velocity
of 10 N · sec/m.

(b) Assume the velocity changes are given by

V (s) =1/(s+0.002) U(s) + 0.05/(s+0.02) W(s)

where V is given in meters per second, U is in degrees, and W is the percent grade of the road. Design a proportional control law U = -kp V that will maintain a velocity error of less than 1 m/sec in the presence of a constant 2% grade.

(d) Assuming that pure integral control (that is, no proportional term) is advantageous, select the feedback gain so that the roots have critical
damping (d = 1).

(e) For the integral feedback you found in part (c), make a bode plot of the ratio of closed-loop response to road grade divided by the open-loop response to road grade. At what frequency is the ratio greater than 1 (0dB)? If the car is cruising at 25 m/s (about 60mph), what is the minimum distance between peaks of rolling hills for which the integral feedback controller will reduce the speed variations, compared to a simple "constant throttle" controller?

Reference no: EM13273562

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