1. New cars often come with a feature called cruise control. To activate cruise control, the driver presses a button while traveling at a desired velocity and removes his or her foot from the gas pedal. The control system then automatically maintains whatever speed the car was traveling when the button was pressed in spite of disturbances. For example, when the car starts going up (or down) a hill, the controller automatically increases (or decreases) fuel flow rate to the engine by a proper amount to maintain the set point velocity. a) For cruise control in an automobile, identify the: (21 pts) - control objective - measured process variable - manipulated variable - set point - two different disturbances - measurement sensor - final control element
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For cruise control, the longitudinal motion of a vehicle on a flat road can be modeled by the first-order nonlinear differential equation mv̇ = u - K_fv - K_av^2, where m is the vehicle's mass, v is its speed, u is the tractive force generated by the engine, K_fv is the viscous friction force, and K_av^2 is the aerodynamic drag. Suppose m = 1500kg, K_f = 2.5N / m / s, K_a = 0.8N / m^2 / s. is BIBO stable if and only if it's poles lie in the LHP. Based on that statement, are the linearized vehicles dynamics stable? Now suppose that the system is at equilibrium (at 70mph), and the road grade suddenly increases to 5%. The equations will now change to mv̇ = u - mg sin θ - K_fv - K_av^2, and the speed will drop. Can you use linearization to design a control law of the form u = ū + Δu, Δu = -k(v - v̄) ≜ -kΔv to bring the car speed back (close) to the equilibrium value of 70mph ? If so, show me a simulation for 1 min of the system where the grade abruptly changes from 0 to 10% at 30s.
Adi S.
What two controls on a car cause a change in speed? What control causes only a change in velocity
When I use my electronic cruise control, I set the speed for 70 MPH. The manufacturer says that the electronic cruise control's ability to maintain any speed is better than that of an individual driver. Under electronic cruise control, speeds are normally distributed around the set speed with a standard deviation of only 1.25 MPH. g. Assume that the New York State Police give speeding tickets if they observe someone going faster than 73 MPH. If I am traveling home under cruise control with a set speed of 70 MPH (standard deviation of 1.25 MPH) and go through a speed trap, what is the probability that I will get a ticket? h. When I use my electronic cruise control, what should my maximum speed be if I am willing to risk no more than a 5% chance of getting a ticket? (Assume a 1.25 MPH standard deviation).
Kari H.
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