How to control two values from a matrix with one PID-controller?

Hi, is it possible to control two values (velocities) at once from one matrix with a PID-controller? In this task, there is a car accelerated with the force F. A trailer is coupled with the car by a spring (k). The car has a velocity v1 (shown in matrix C = [0 1 0 0]) and the trailer has a velocity v2 (shown in matrix C = [0 0 0 1]).

      g = 9.81;                 
        M1=1000;                  % mass car in kg
        M2=1000;                   % mass trailer in kg
        k=10;                   % spring constant in N/m
        F=2600;                   % accelerating force in N
        u=0.015;                 % friction constant in s/m

    A=[    0    1     0      0;   % matrix with dynamic equations
     -k/M1  -u*g  k/M1    0;
        0    0     0      1;
      k/M2   0   -k/M2  -u*g];
    B=[  0;
    1/M1;   
      0;
      0];
    C=[0 1 0 0
       0 0 0 1];    %Graphs velocities
    D=[0];

    v=ss(A,B,C,D);
    stepplot (v, 100)
    title(' v1 und v2')
    hold on
    [Eigenwerte, Eigenvektoren] = eig (A) 

    %-----> the following does NOT work to control both velocities (car and trailer)
    Kp=350;
    Ki=300;
    Kd=5000;
    contr= Kp;  
    sys_cl= feedback (contr*v, 1);
    t = 0: 0.0001: 100;
    step(sys_cl,100)

Answer 1

[Arkadiy Turevskiy]

what do you mean when you say "control two velocities". You can have a PID controller on car speed or trailer speed that would bring both speeds to the same desired level in steady state.

D=zeros(2,1);
v=ss(A,B,C,D);
contr=pidtune(v(1,1),'pid');
feedin=[1];
feedout=[1];
ol=contr*v;
cloop=feedback(ol,1,feedin,feedout);
step(cloop(1,:));
hold on;
step(cloop(2,:),'r');
legend('car speed','trailer speed');