bu CRUISE CONTROL M Figure 1. Cruise Control System Automatic cruise control is an excellent example of a feedback control system found in many modern vehicles. The purpose of the cruise control system is to maintain a constant vehicle speed despite external disturbances, such as changes in wind or road grade. This is accomplished by measuring the vehicle speed, comparing it to the desired or reference speed, and automatically adjusting the throttle according to a control law. We consider here a simple model of the vehicle dynamics, shown in the free-body diagram (FBD) above. The vehicle, of mass m, is acted on by a control force, u. The force u represents the Task 1 - Control System Analysis/Design v=i a = v= force generated at the road/tire interface. For this simplified model we will assume that we can control this force directly and will neglect the dynamics of the powertrain, tires, etc., that go into generating the force. The resistive forces, bv, due to rolling resistance and wind drag, are assumed to vary linearly with the vehicle velocity, v, and act in the direction opposite the vehicle's motion. R() For the cruise control system given in Fig 1. 1. Obtain nonlinear mathematical model that describes input-output relationship. 2. Identify each block e.g., plant, actuator, etc., give individual transfer function and describe their role in the system. (Notice that the angle of the beam is changed with the rotational actuator connected to the beam not a linear actuator like servo motor!) 3. Obtain the transfer function for this model (Linearize if needed, choose the most appropriate values for the variables and indicate them in a table in your report.). Controller 20 Ge(s) Process G(s) Figure 2. Negative feedback Control System F(x)