PID for fixed distance

Hello everyone, I attach here my model of a car moving towards that must maintain a fixed distance of 100m from the car in front of it. I have drawn all the schemes which seem to be correct. I have a signal reference that must be followed with a constant error, but I'm not able to understand why I have divergence between the reference signal and the actual position of my vehicle, whichever value of the gains I use, from the smallest to the largest.

I really hope someone could help me. Thank you very much!

Answer 1

[Sam Chak]

Hi @Andrea Tonelli

I think your control design part is okay. But the divergence issue is probably related to the way you setup the simulation (Error – 100). Thus, I have made a super simple model (ignoring the aerodynamics and frictions) in this example.

The Auto-Cruise Control Car should follow the Reference, which is the trajectory of the "Car-in-front – 100".

% Super Simple Car motion model
J  = 1000;
s  = tf('s');
Gp = minreal(1/(J*s^2))

Gp =
 
  0.001
  -----
   s^2
 
Continuous-time transfer function.

% Super Simple PID Controller
Gc  = pid(0, 0, 500, 0.5)

Gc =
 
               s    
  Kp + Kd * --------
             Tf*s+1 

  with Kp = 0, Kd = 500, Tf = 0.5
 
Continuous-time PDF controller in parallel form.

Gcl = minreal(feedback(Gc*Gp, 1))

Gcl =
 
        1
  -------------
  s^2 + 2 s + 1
 
Continuous-time transfer function.

Amp    = 50;
Tp     = 300;                           % 1 cycle period
Tf     = 300;                           % final time simulation (5 minutes)
Ts     = 0.1;                           % sampling time interval
[u, t] = gensig('sine', Tp, Tf, Ts);	% standard sine wave generation
Car    = Amp*u + 150;                   % Car in front of your vehicle
Ref    = Car - 100;                     % Reference for Auto-Cruise Control Car
y      = lsim(Gcl, Ref, t);
plot(t, Car, t, y, 'linewidth', 1.5), grid on, xlabel('t'), ylabel('Position of Vehicles')
legend('Car-in-front', 'Auto-Cruiser', 'location', 'best', 'FontSize', 14)

error = Car - y;        % relative distance of Car-in-front ahead of your vehicle
plot(t, error, 'linewidth', 1.5), grid on, xlabel('t, sec'), ylabel('Relative Distance, m')
title('ACC Car attempts to maintain a relative distance of 100 m')

By the way, in your 1st question, have you identified the cause of the problem (fuzzy controller) based on the given advice?

https://www.mathworks.com/matlabcentral/answers/1761210-fuzzy-controller-warning-solving

You can update the progress, or close it if your problem solved. Thanks.

[Andrea Tonelli]

Thank you very much for your answer! But I still don't get how to fix the problem on simulink unfortunatly.

About the question on the fuzzy controller, it was a previous project, not related with this one, but thank you for the answer to that too :)

[Sam Chak]

I'm unsure, but it seems that inside the feedback loop, you keep on injecting "–100" into error (relative distance between Car-in-front and your ACC car).

Try modifying your Simulink model such that the blocks work like these functions:

Car = trajectory;       % Car in front of your vehicle
Ref = Car - 100;        % Reference for Auto-Cruise Control Car

[Andrea Tonelli]

Still nothing changes. I will try to work on the gains.