"Not Enough Input Arguments" Error Calling ODE45

Hello:

I am running into "not enough input arguments" when calling ODE45 for a system of differential equations defined in the function below. Can you help me determine what I need to fix? The line throwing the error is line 12 where I define rdot.

function  dz = sys(t,z)
    b = 1000;
    bT = 250;
    k=17000;
    kT=136000;
    m1=300;
    m2=30;

   A = [0 0 1 -1;0 0 0 1; -k/m1 0 -b/m1 b/m1;k/m2 -kT/m2 b/m2 -(b+bT)/m2];
   B = [0;-1;0;bT/m2];

   rdot = -9.42*0.05*sin(9.42*t);
   dz = A*z + B*rdot;
end

I tried to put this into the form of dx = A*x + B*u, where u is the input function into the system (represented in my function as rdot), but whenever I try to call ODE45 it gives me a "not enough input arguments" error.

This is how I am calling ODE45 in Matlab:

[t,z] = ode45(@sys,[0:0.1:100],0)

For a little more background - I am trying to solve a state-space representation of differential equations representing a quarter car model, with the sprung mass being represented as m1, k, b and the unsprung mass by m2, kT, bT.

I attached a screenshot of the written out form of the DE system. P1, P2 are the suspension stroke and tire deflection respectively. V1, V2 are the velocities of the sprung and unsprung masses respectively.

Answer 1

[Walter Roberson]

[t,z] = ode45(@sys,[0:0.1:100],0)

You are passing a single initial state, the 1x1 value 0, into sys. The result of calling sys needs to be a single output state, 1 x 1. But instead dz is 4 x 4.

dz comes out 4 x 4 because your z value is scalar instead of 4 x 1. If you were passing a 4 x 1 initial state instead of a 1 x 1 initial state then your dz would come out as 4 x 1.

[Walter Roberson]

By the way, there is no error about missing inputs.

[t,z] = ode45(@sys,[0:0.1:100],0)

  Name      Size            Bytes  Class     Attributes

  A         4x4               128  double              
  B         4x1                32  double              
  dz        4x4               128  double              
  rdot      1x1                 8  double              
  z         1x1                 8  double              

Error using odearguments (line 95)
SYS must return a column vector.

Error in ode45 (line 104)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

function  dz = sys(t,z)
    b = 1000;
    bT = 250;
    k=17000;
    kT=136000;
    m1=300;
    m2=30;

   A = [0 0 1 -1;0 0 0 1; -k/m1 0 -b/m1 b/m1;k/m2 -kT/m2 b/m2 -(b+bT)/m2];
   B = [0;-1;0;bT/m2];

   rdot = -9.42*0.05*sin(9.42*t);
   dz = A*z + B*rdot;
   whos A z B rdot dz
end

Answer 2

[Sam Chak]

Hi @Henry

The quarter car system has four states: {P1, P2, V1, V2}. When using the ode45 solver, it is necessary to supply four known initial values for these states. In the demo below, the initial state values at time are assumed to be zeros, indicating zero deflections and zero velocities.

% simulation time interval
tspan   = [0, 4];

% initial state values at time t = 0
z0      = [0;   % P1(0) = 0
           0;   % P2(0) = 0
           0;   % V1(0) = 0
           0];  % V2(0) = 0

% call ode45 to solve the dynamic state-space equations
[t, z]  = ode45(@sys, tspan, z0);

% plot results
plot(t, z), grid on
xlabel('time, t')
ylabel('amplitude')
legend('P_1', 'P_2', 'V_1', 'V_2')

% quarter car system
function  dz = sys(t, z)
    % parameters
    b   = 1000;
    bT  = 250;
    k   = 17000;
    kT  = 136000;
    m1  = 300;
    m2  = 30;
    
    % matrices
    A   = [0      0      1     -1;
           0      0      0      1; 
          -k/m1   0     -b/m1   b/m1;
           k/m2  -kT/m2  b/m2 -(b+bT)/m2];
    
    B   = [0;
          -1;
           0;
           bT/m2];
    
    % input
    rdot= -9.42*0.05*sin(9.42*t);
    
    % state space
    dz  = A*z + B*rdot;
end