Car with and without Feedback Control. Consider the car shown below, which can be modeled as...

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Car with and without Feedback Control. Consider the car shown below, which can be modeled as a mass-damper. (Linear damping is an approximation for the effects of drag and tire rolling resistance.) The transfer function for this plant is shown in the block diagram for part (a). x (position) f (force) m (mass) b (damping) (a) As shown in the simple block diagram below, the input to the system is force, F(s), and the output is position, X(s) (5 pts). F(s) force 1 ms+bs car Test the following inputs, where A is any constant, to see if any of them will be able to make the car move to and stay at a desired position: i. Impulse: F(s) = A ii. Step: F(S) = 4 X(s) position Will either of these inputs make the car move to and stay at a desired position? If so, which one(s)? Show why or why not by finding x(t) analytically for each of these inputs. Assume zero initial conditions. Car with and without Feedback Control. Consider the car shown below, which can be modeled as a mass-damper. (Linear damping is an approximation for the effects of drag and tire rolling resistance.) The transfer function for this plant is shown in the block diagram for part (a). x (position) f (force) m (mass) b (damping) (a) As shown in the simple block diagram below, the input to the system is force, F(s), and the output is position, X(s) (5 pts). F(s) force 1 ms+bs car Test the following inputs, where A is any constant, to see if any of them will be able to make the car move to and stay at a desired position: i. Impulse: F(s) = A ii. Step: F(S) = 4 X(s) position Will either of these inputs make the car move to and stay at a desired position? If so, which one(s)? Show why or why not by finding x(t) analytically for each of these inputs. Assume zero initial conditions.