EEEN3015J Control Theory - Lab 1 - Task A: Cruise Control
Lab Course 1: System Modelling and Analysis
Task A Cruise Control
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 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.
For this example, let's assume that the parameters of the system are:
(m) vehicle mass 1000 kg
(b) damping coefficient 50 N.s/m
Task 1: Identify the reference, input and output signals and write down the system equation
Task 2: Take the Laplace transform of the system equation and enter the transfer function model
The next step is to come up with some design criteria that the compensated system should achieve. When the engine gives a 500 Newton force, the car will reach a maximum velocity of 10 m/s (22 mph). An automobile should be able to accelerate up to that speed in less than 5 seconds. In this application, a 10% overshoot and 2% steady- state error on the velocity are sufficient.
Keeping the above in mind, we have proposed the following design criteria for this problem:
▪ Rise time < 5 s
▪ Overshoot < 10%
▪ Steady-state error < 2%
Task 3: Find the poles of the open-loop system and analyze its stability
Task 4: Plot the open-loop response of the system to a step input force of 500
Newtons and compute the rise time, overshoot and steady-state error
Task 5: Draw the Bode plot of the open-loop system
Task 6: Draw the Root Locus of the closed-loop system with C(s) = K
Task 7: Find a gain K to place the closed-loop poles in the desired region
Task 8: Plot the time response of the closed-loop system to a step input force of 500
Newtons and compute the rise time, overshoot and steady-state error
