- You Are Designing An Rc Car To Traverse The Terrain Of North Campus You Want To Implement A Variety Of Controllers On T 1 (372.39 KiB) Viewed 20 times
(a) [7 pts] As part of your design process, you need to add a transmission between the motor and the rear wheels. You want the RC to be able to travel up a 45° incline at a constant speed of 0.5 m/s for short periods of time. Calculate the minimum transmission ratio needed to achieve this, given the motor and car specifications in the table. Round your final calculated minimum transmission ratio to the nearest whole number. (Note: Assume the one motor is driving both of the rear wheels and there is no slipping between the wheels and the ground.) 0.5 m/s M 450 (b) [7 pts] As part of your control scheme, you are implementing a PD position controller such that, when not moving, the RC car will try to maintain its position in response to any disturbance. Assume the car is on a flat horizontal surface and the total load inertia (including the mass of the car) at the wheels is 0.06 kg-m². Determine the values of K, and K, so that the system has a damping ratio of 1 and a circular frequency (natural frequency) of 5 rad/s. (Note: If you did not find a transmission ratio above, use a transmission ratio of 3.) Hint: Calculate the equivalent inertia at the output of the motor using your transmission ratio calculated above and derive the second-order differential equation at the output of the motor.
(c) [4 pts] Suppose the RC car is now placed on a 45° incline. Using the PD controller and equation of motion developed in part b, calculate the equilibrium linear position of the car, Xeq. Assuming both the acceleration and velocity of the car are equal to 0, and x = 0 corresponds to the position where the car is first placed on the incline, which is not on the bottom of the incline. X M CHCEAN 450