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Problem: Model a basic cruise control system

Let us model a basic cruise control system. We first assume that the Inertia of the vehicle wheels are negligible, and it is understood that the viscous friction created from the car's speed is completely in the direction of the opposing motion of the automobile. Therefore, our cruise control problem is now reduced to a single mass and a constant damper system as shown in Figure 1.

Figure 1: Simple Cruise Control System.

Given: b = 55 N*sec/m (damper constant), m = 1220 kg (vehicle mass), u = 1000 N (engine force),
x (position of the vehicle in m), v (velocity of the vehicle in m/s)

Objective: Once you determine the modeling equations of this control system, find the response of the car velocity when the input (u) is 1000 N. Use MATLAB to determine the following control characteristics of this cruise control system:

1. Transfer Function
2. Determine Poles: Are the poles stable?
3. Step Response: At what amplitude does it settle to?
4. Root-Locus: Explain the behavior.

Calculated: State-Space variable form

Extra Credit: If you were to vary the mass of the automobile from 1220 kg to either 500 kg or 2000 kg, what effect does this do to the response of the cruise control system?

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