Control system for a vehicle to follow a path (loop failure when reference signal passes below zero)

Hi,

I got a simple 3DOF model of a car(Yaw, lateral and longitudinal displacement). I'm trying to control this with constant velocity and a simple control system to follow a path. (next step is to introduce a torque and brake control system).

I'm using the simple control system as displayed below. The output S is the distance travelled by the car. (integral of the constant velocity). That is fed into a lookup table where the distance corresponds to a track radius value. As I'm using constant velocity at the moment and therefore the lateral velocity of the car is limited. the rate of change of track radius have to be limited so the car can follow the path.

the radius signal is then passed through a gain an into the steering angle demand. (gain of 3 seem to be working)

When the reference signal (the Radius) passes below zero which in this case indicates that the car need to change direction from a right-hand corner to a left-hand corner. the simulation fails.

In the car model, as the steer angle goes towards zero the radius goes towards infinity. The data in the lookup table (which is collected from a car) behaves in a similar way when changing direction. Two large radius peaks occur around zero.

Is the problem that it's trying to find a steering angle for zero radius and the calculated radius shoots off to infinity in a way the the controller can't control? the steer angle should just go towards zero.

the second picture below shows a trace of the simulation with radius on the y-axis and time on the x-axis.

the purple signal is the look/up table out put

the turquoise line is the signal after the rate limiter

The yellow signal is the Radius output from the car model.

as can be seen the simulation traces the reference signal quite well until it reaches zero where it fails.

I'm grateful for any help that might help me solve this problem.

Thanks,

Marcus